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AFRL-RV-PS- 

TR-2015-0107 


AFRL-RV-PS- 

TR-2015-0107 


NASCAP-2K VERSION 4.2 USER’S MANUAL 


V.A. Davis, et al. 


Leidos, Inc. 

10260 Campus Point Drive, Mailstop C4 
San Diego, CA 92121 


31 October 2014 


Technical Report 


APPROVED FOR PUBLIC RELEASE; DISTRIBUTION IS UNLIMITED. 



AIR FORCE RESEARCH LABORATORY 

Space Vehicles Directorate 

3550 Aberdeen Ave SE 

AIR FORCE MATERIEL COMMAND 

KIRTLAND AIR FORCE BASE, NM 87117-5776 






DTIC COPY 


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1. REPORT DATE (DD-MM-YYYY) 
31-10-2014 


4. TITLE AND SUBTITLE 

Nascap-2k Version 4.2 User’s Manual 


2. REPORT TYPE 

Technical Report 


3. DATES COVERED (From - To) 
19 Sep 2011-31 Oct 2014 


5a. CONTRACT NUMBER 

FA9453-1 l-C-0262 


6. AUTHOR(S) 

V. A. Davis, B. M. Gardner, and J. J. Mandell 


5b. GRANT NUMBER 


5c. PROGRAM ELEMENT NUMBER 

62601F 


5d. PROJECT NUMBER 

1010 


7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 

Leidos, Inc. 

10260 Campus Point Drive, Mailstop C4 
San Diego, CA 92121 


5e. TASK NUMBER 

PPM00012836 


5f. WORK UNIT NUMBER 

EF003277 


8. PERFORMING ORGANIZATION REPORT 
NUMBER 


9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 

Air Force Research Laboratory 
Space Vehicles Directorate 
3550 Aberdeen Avenue SE 
Kirtland AFB, NM 87117-5776 


12. DISTRIBUTION / AVAILABILITY STATEMENT 

Approved for public release; distribution is unlimited. (377ABW-2015-0419 dtd 28 May 15) 


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AFRL/RVBXR 


11. SPONSOR/MONITOR’S REPORT 
NUMBER(S) 

AF RL -RV-PS-TR-2015-0107 



14. ABSTRACT 

Nascap-2k is a spacecraft charging and plasma interactions code designed to be used by spacecraft designers, aerospace and materials 
engineers, and space plasma environments experts to study the effects of both the natural and spacecraft-generated plasma environments on 
spacecraft systems. 

This document describes the user interface, how to use the code, and some of the physical assumptions of the computation models included 
in the code. 


15. SUBJECT TERMS 

Nascap-2k, Spacecraft Charging, Space Environment 


16. SECURITY CLASSIFICATION OF: 

17. LIMITATION 

OF ABSTRACT 

18. NUMBER 
OF PAGES 

19a. NAME OF RESPONSIBLE PERSON 

Adrian Wheelock 

a. REPORT 

Unclassified 

b. ABSTRACT 

Unclassified 

c. THIS PAGE 

Unclassified 

Unlimited 

252 

19b. TELEPHONE NUMBER (include area 
code) 


Standard Form 298 (Rev. 8-98) 

Prescribed by ANSI Std. 239.18 

































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TABLE OF CONTENTS 


List of Figures.ix 

List of Tables.xvii 

Summary.1 

I Overview.3 

1 Need for Nascap-2k .3 

2 What is Nascap-2kl .3 

2.1 Units.7 

2.2 Limits.7 

3 Formatting Conventions.8 

4 Installation.8 

4.1 Requirements.8 

4.2 Nascap-2k Installation.9 

4.3 Java Installation.9 

II Using Nascap-2k .11 

5 Basic Approach.11 

6 Creating or Opening a Project.12 

7 Main Menus.13 

8 Defining the Problem (Problem Tab).15 

9 Creating a Spacecraft Model.17 

9.1 Obj ect Requirements.17 

9.1.1 General.18 

9.1.2 Material Name Attributes.18 

9.1.3 Conductor Number Attributes.18 

9.1.4 Closed Surfaces.18 

9.1.5 Surface Elements.18 

9.1.6 Resolution.18 

9.1.7 Compatibility (Edge).19 

9.1.8 Special Objects (Ion Thrusters, Neutralizers, Magnetic 

Dipoles).20 

9.1.9 Emitters, Detectors, and Injection Points.20 

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10 Creating a Grid System Around the Spacecraft.21 

10.1 GridTool .21 

10.2 GridTool Menu Options.23 

10.3 Grid Requirements.23 

10.3.1 Parameters Defining a Grid.23 

10.3.2 Grid Size.23 

10.3.3 Object Placement.23 

10.3.4 Subdivision Recommendations.23 

10.3.5 Child Grid.25 

10.3.6 Grid Overlap.25 

10.3.7 Boundary Plane Resolution.25 

10.3.8 Grid Resolution.25 

11 Specifying the environment (Environment Tab).26 

11.1 Geosynchronous Earth-Orbit Environment.26 

11.2 Low-Earth-Orbit or Plume Environment.29 

11.3 Auroral Environment.31 

11.4 Interplanetary Environment.33 

11.5 Using Photoemission Spectra.34 

12 Specifying Potentials on Surfaces (Applied Potentials Tab).35 

13 Surface Charging (Charging Tab).37 

13.1 Background.37 

13.2 Numerical Approach and Implementation in Nascap-2k .39 

13.3 Monitoring the Calculation.40 

13.4 Materials.41 

13.5 Surface Conductivity.44 

14 Calculating Electric Potentials in Space (Space Potentials Tab).45 

14.1 Available Space Charge-Density Models.47 

14.2 Grid Boundary Conditions.48 

14.3 Advanced Potential Solver Parameters.48 

14.4 Monitoring the Calculation.50 

15 Calculations Using Particles (Particles Tab).50 

15.1 Generating Particles.53 

15.2 Tracking Particles.57 

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15.3 Particle Advanced Parameters.59 

16 Generating and Executing a Script (Script Tab).62 

16.1 Run Script Subtab.62 

16.2 Script Commands.63 

16.3 Edit Script Subtab.71 

17 Viewing Results.72 

17.1 Time-Dependent and Numerical Results (Results Tab).72 

17.2 Three-Dimensional Results (Results 3D Tab).75 

17.3 Output Files.81 

17.3.1 Embed Object in Grid.81 

17.3.2 Potentials in Space.82 

17.3.3 Create Particles.82 

17.3.4 Track Particles.83 

III Examples.85 

18 Spacecraft Charging in a Tenuous Plasma (example name: “GeoCharging”).85 

18.1 Background.85 

18.2 Object Definition.85 

18.3 Surface Charging Calculation.87 

18.3.1 Case 1: Charging in Sunlight.87 

18.3.2 Case 2: Eclipse Exit.97 

19 Current Collection in a Low-Earth-Orbit Plasma (example name: “Bipolar”).99 

19.1 Background.99 

19.2 Object and Grid Definition.99 

19.3 Case 1: Electron Collection.106 

19.3.1 Potentials in Space Calculation.106 

19.3.2 Surface Currents Calculation.112 

19.4 Case 2: Ion Collection.117 

19.5 Case 3: Current Balance.119 

20 Wake Effects and Current Collection in Low Earth Orbit (example name: 

“CHAWS”).124 

20.1 Background.124 

20.2 Object and Grid Definition.125 

20.3 Calculating Space Potentials and Current Collection in the Wake.128 

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20.3.1 Case 1: Current Collection by a Stationary Spacecraft.128 

20.3.2 Case 2: Current Collection in the Wake using Analytic Space 

Charge Formulation.133 

20.3.3 Case 3: Current Collection in the Wake using “Self- 

Consistent with Ion Trajectories.”.138 

20.3.4 Case 4: Current Collection in the Wake using “Self- 

Consistent with Ion Trajectories” and 10% H + .142 

21 Time Dependent Plasma (example name: “Dynamic”).146 

21.1 Background.146 

21.2 Object and Grid Definition.146 

21.3 Dynamic Calculations.149 

21.3.1 Case 1: Short Time-scales for Both Species.150 

21.3.2 Case 2: Short Time-scale for Ions, Equilibrium (Barometric) 

Electrons.152 

21.3.3 Case 3: Time-dependent Ions, Equilibrium (Barometric) 

Electrons.153 

22 Additional Examples.160 

22.1 Detector.160 

22.1.1 Object and Grid.160 

22.1.2 Problem Specification.161 

22.1.3 Results.163 

22.2 Current Balance in a System with an Electron Gun (Emitter).165 

22.2.1 Object and Grid.165 

22.2.2 Problem Specification.166 

22.2.3 Building and Modifying the Script.168 

22.2.4 Results.171 

Common Gotchas and Frequently Asked Questions.174 

Caveats.174 

Frequently Asked Questions.174 

References.178 

Appendices.181 

A. Files.181 

A. 1 Files Associated with a Project.181 

A.2 Contents of Input Files.182 

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A.3 Contents of Output Files.187 

A.3.1 Embed Object in Grid.187 

A.3.2 Potentials in Space.189 

A.3.3 Create Particles.193 

A.3.4 Track Particles.195 

A.4 Installed Files.198 

A.5 File Formats.199 

A.5.1 XML.199 

A.5.2 Object Definition File Format.199 

A.5.3 SEE Interactive Spacecraft Charging Handbook Material 

Definition File.203 

A.5.4 Grid File Format.205 

A.5.5 Plume Map File Format.205 

B. Using the Nascap-2k Script Runner.209 

C. Template for Nascap-2k Custom Current DLL.211 

C.l Purpose.211 

C.2 Mechanics of Use.211 

C.3 Template.211 

C.4 Entry Points.211 

C.5 The Vector3 Class.212 

C.6 Other Files.212 

C. l Surface Element Properties.212 

D. Disjoint Grids in Nascap-2k .213 

D. l Overview.213 

D.2 Defining the Objects and Grids.214 

D.3 Combining the Grids.215 

D.4 Creating the Combined Project and Database.216 

D.5 Calculating Potentials.218 

D. 6 Displaying Trajectories.221 

E. Using Plume Densities in Nascap-2k .223 

E. 1 Problem Tab.224 

E.2 Space Potentials Tab.224 

E.3 Particles Tab.224 


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E.4 Results 3D Tab.224 

E.5 Files.224 

Glossary.225 


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LIST OF FIGURES 


Figure 1. Selected Views of the Nascap-2k User Interface.4 

Figure 2. Nascap-2k Structure.5 

Figure 3. Opening Screen of the Nascap-2k User Interface.12 

Figure 4. Opening a New (left) or Existing (right) Project in Nascap-2k .12 

Figure 5. Problem Tab in Nascap-2k .15 

Figure 6. Object Toolkit Screen Showing Standard Components.17 

Figure 7. Example Showing Incompatible Edges and their Repair.20 

Figure 8. Grid in Space Generated Using GridTool .22 

Figure 9. Child Grid Dialog Box for Defining or Modifying a Child Grid in GridTool .22 

Figure 10. Examples of Correct (Left and Center) and Incorrect (Right) Subdivision.25 

Figure 11. The Environment Tab for Studies in a Geosynchronous Plasma.27 

Figure 12. Measured Spectrum Editor Dialog Box.29 

Figure 13. The Environment Tab for Studies in a Low-Earth-Orbit or Plume Plasma.30 

Figure 14. The Environment Tab for Studies in an Auroral Environment.31 

Figure 15. The Environment Tab for Studies in Interplanetary Space.33 

Figure 16. Photoemission Spectrum Dialog Box.35 

Figure 17. Potential Initialization for Objects in a Two-Conductor Problem.36 

Figure 18. High Negative Potentials Can Result from the Accumulation of Charge on 
Spacecraft Surfaces.38 

Figure 19. Circuit Model of a Spacecraft with One Insulating Surface Element.38 

Figure 20. Charging Tab: Specifying Parameters for Spacecraft Charging Calculations.40 

Figure 21. Script Running Monitor Showing Charging Calculation.41 

Figure 22. Nascap-2k Materials Menu Showing Material Property Editing Dialog Box.41 

Figure 23. Electron Secondary Yield as a Function of Incident Energy.43 

Figure 24. Illustration of Surface Resistivity.44 

Figure 25. Space Potentials Tab, Used to Specify Options and Parameters for Calculation of 
Potentials in Space.45 

Figure 26. Advanced Potential Solver Parameters Dialog Box.48 

Figure 27. Script Running Monitor Showing “Potentials in Space” Calculation Progress.50 

Figure 28. Surface Currents Subtab for Generation and Tracking of Surface Currents.51 

Figure 29. Ion Densities Subtab for Generation and Tracking of Particles for Potentials that 
are “Self-Consistent with Ion Trajectories”.52 


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Figure 30. Time-Dependent Subtab for Generation and Tracking of Time-Dependent 

Plasma.52 

Figure 31. Sample External File for Specifying Initial Particle Distribution.56 

Figure 32. Script Running Monitor Showing Progress in Particle Generation.57 

Figure 33. Script Running Monitor Showing Progress in Particle Tracking Calculation.57 

Figure 34. Advanced Particle Parameters Dialog Box.60 

Figure 35. Run Script Subtab for a Typical Geosynchronous Charging Problem with 
Computation of Potentials about Spacecraft.62 

Figure 36. Edit Script Subtab: Making Problem Changes by Directly Modifying the Script.71 

Figure 37. Results Tab: Plotting Minimum, Maximum, and Average Values of Elements 

with Specified Conductors and/or Materials.73 

Figure 38. Results tab: Plotting Values at Surface Elements.74 

Figure 39. Text Output in the Results Tab.74 

Figure 40. Results 3D tab: Displaying Potentials on a Plane through the Center of the Box, 
Together with Results for a Selected Surface Element.75 

Figure 41. Results 3D: Displaying Potential on the Surface Elements.78 

Figure 42. Particle Visualization Dialog Box.78 

Figure 43. Selected Particle Trajectories (0+) in “CHAWS” Example.79 

Figure 44. Particle Distribution During Time-dependent Ion Collection by a Negatively 
Biased Cube.79 

Figure 45. Illustrative Spacecraft for Sample Charging Calculation Using Nascap-2k .85 

Figure 46. Spacecraft Model Used in the “GeoCharging” Example Showing Material (Top) 
and Conductor (Bottom) Definition.86 

Figure 47. Problem Tab for the “GeoCharging” Example.87 

Figure 48. Geosynchronous Environment Tab for Case 1 of the “GeoCharging” Example.88 

Figure 49. Applied Potentials Tab for the “GeoCharging” Example.88 

Figure 50. Charging Tab for the “GeoCharging” Example.89 

Figure 51. Script for Case 1 of the “GeoCharging” Example.90 

Figure 52. Script Running Monitor During Calculation for Case 1 of the “GeoCharging” 

Example.90 

Figure 53. Results Tab for Case 1 of the “GeoCharging” Example Comparing Evolution of 
Potential Between Sunlit and Dark Surface Elements on the Cylindrical Antenna.91 

Figure 54. Results Tab for Case 1 of the “GeoCharging” Example Comparing Evolution of 
Potential for Different Surface Elements.92 

Figure 55. Results Tab Showing mean Current density to the Conductor as a Function of 
time for Case 1 of the “GeoCharging” Example.93 

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Figure 56. Results Tab Showing Text Subtab with Tabulated Results.94 

Figure 57. Sensitivity of Results on Choice of Number of Timesteps in the Charging 
Calculation of Case 1 of the “GeoCharging” Example.94 

Figure 58. Results 3D Tab for Case 1 of “GeoCharging” Showing Spacecraft Potentials of 
Sunlit (Top) and Dark (Bottom) Surface Elements.96 

Figure 59. Edit Script Subtab for Case 2 of the “GeoCharging” Example.97 

Figure 60. Expanded Script for Case 2 of the “GeoCharging” Example.98 

Figure 61. Results Tab for Case 2 of the “GeoCharging” Example.99 

Figure 62. Object Constructed for the Study of Current Collection from a Bipolar Sheath in 
a Low-Earth-Orbit Environment. Top: Object Materials. Bottom: Object Conductors.101 

Figure 63. Specifications of Gold-plated Cube in Figure 62.102 

Figure 64. Specifications of Graded Boom in Figure 62.102 

Figure 65. Specifications of Kapton Support Boom in Figure 62.103 

Figure 66. Specifications of Main Rocket Body in Figure 62.103 

Figure 67. Grid Specifications for the Parent and Child Grids Used in the “Bipolar” 

Example.104 

Figure 68. Grid Arrangement Showing All Six Grid Levels and Embedded Object for the 
“Bipolar” Example.105 

Figure 69. Problem Tab for the “Bipolar” Example.106 

Figure 70. Environment Tab for the “Bipolar” Example, for Case 1 and Zero Ambient 
Magnetic Field.107 

Figure 71. Applied Potentials Tab for Case 1 of the “Bipolar” Example.108 

Figure 72. Space Potentials Tab for the “Bipolar” Example.109 

Figure 73. Run Script Subtab Showing the List of Commands and Arguments for Case 1 of 
the “Bipolar” Example.109 

Figure 74. Script Running Monitor Showing Computational Diagnostics at the 10th Space 
Charge Calculation.110 

Figure 75. Distribution of the Electric Potential on a Y=0 Cut Plane for Case 1 of the 
“Bipolar” Example.Ill 

Figure 76. Particle Visualization Dialog Box for Case 1 of the “Bipolar” Example.Ill 

Figure 77. Electron Trajectories for Case 1 of the “Bipolar” Example.112 

Figure 78. Parameters on the Surface Currents Subtab Used to Compute the Electron 

Current Collection for the “Bipolar” Example.113 

Figure 79. Potential Distribution Showing Sheath Edge on Mesh for Case 1 of the 

“Bipolar” Example.113 


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Figure 80. Partial Contents of the bipolar_potent_0_out.txt File Showing Highlighted 


Sheath Potential for Grid #2 for Case 1 of the “Bipolar” Example.114 

Figure 81. Partial Contents of the bipolar_tracker_traj_0_out.txt File Showing 
Current Collection Results for Case 1 of the “Bipolar” Example.114 

Figure 82. Electron Trajectories Around the Positively Biased Cube when Bx=0, By=0.4 G, 

Bz=0 for Case 1 of the “Bipolar” Example (Bottom is rotated view of top).116 

Figure 83. Applied Potentials on Conductors and Insulators for Ion-current Collection 
Calculation for Case 2 of the “Bipolar” Example.117 

Figure 84. Potential Distribution Showing Ion and Electron Sheath Edges on the Mesh for 
Case 2 of the “Bipolar” Example.118 

Figure 85. Oxygen Ion Trajectories for Case 2 of the “Bipolar” Example.118 

Figure 86. Problem Tab for Case 3 of the “Bipolar” Example.119 

Figure 87. Applied Potentials Tab for Case 3 of the “Bipolar” Example.120 

Figure 88. Charging Tab for Case 3 of the “Bipolar” Example.120 

Figure 89. Space Potentials Tab Showing Number of Iterations for Case 3 of the “Bipolar” 
Example.121 

Figure 90. Surface Current Subtab for Case 3 of the “Bipolar” Example.121 

Figure 91. Results Tab Showing Evolution of Conductor Potentials Toward Current 

Balance for Case 3 of the “Bipolar” Example.122 

Figure 92. Current Collection by Conductors as a Function of Time for Case 3 of the 
“Bipolar” Example.123 

Figure 93. Potential Distribution at Equilibrium (-Zero Net Current) in the “Bipolar” 

Example.123 

Figure 94. Selected Ion and Electron Trajectories at Equilibrium in the “Bipolar” Example.124 

Figure 95. WSF Object. Top: Materials; Bottom: Conductors.126 

Figure 96. Grid Used to Calculate Electric Potentials around WSF. Top: All Nested 15 

Grids Highlighting Grid #1. Bottom: Grid #8 (Surrounding the Cylindrical Probe).127 

Figure 97. Problem Tab for Case 1 of the “CHAWS” Example.128 

Figure 98. Environment Tab for Case 1 of the “CHAWS” Example.129 

Figure 99. Applied Potentials Tab for the “CHAWS” Example.129 

Figure 100. Space Potentials Tab for Case 1 of the “CHAWS” Example.130 

Figure 101. Location of Sheath Edge Potential for Case 1 of the “CHAWS” Example.131 

Figure 102. Surface Currents Subtab for Case 1 of the “CHAWS” Example.131 

Figure 103. Script for Case 1 of the “CHAWS” Example.132 

Figure 104. Potential Profile for Case 1 of the “CHAWS” Example.132 

Figure 105. Space Potentials Tab for Case 2 of the “CHAWS” Example.134 

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Figure 106. Advanced Potential Solver Parameters Dialog Box for Case 2 of the “CHAWS” 
Example.134 

Figure 107. Surface Currents Subtab for Case 2 of the “CHAWS” Example.135 

Figure 108. Advanced Particle Parameters Dialog Box for Case 2 of the “CHAWS” 

Example.135 

Figure 109. Potential Distribution for Case 2 of the “CHAWS” Example.136 

Figure 110. Ion Trajectories for Case 2 of the “CHAWS” Example.137 

Figure 111. Particle Parameters Dialog Box for Graphical Display of Trajectories for 
“CHAWS” Example.137 

Figure 112. Advanced Particle Parameters Dialog Box for Graphical Display of 

Trajectories for “CHAWS” Example.138 

Figure 113. Problem Tab for Case 3 of the “CHAWS” Example.139 

Figure 114. Space Potentials Tab for Case 3 of the “CHAWS” Example.140 

Figure 115. Ion Densities Subtab for Case 3 of the “CHAWS” Example.140 

Figure 116. Advanced Particle Parameters Dialog Box for Particle Generation and Tracking 
for Case 3 of the “CHAWS” Example.141 

Figure 117. Potential in the Wake of WSF for Case 3 of the “CHAWS” Example.141 

Figure 118. Trajectories for Case 3 of the “CHAWS” Example.142 

Figure 119. Environment Tab for Case 4 of the “CHAWS” Example Showing Addition of 
10% H + Species.143 

Figure 120. Space Potentials Tab for Case 4 of the “CHAWS” Example.143 

Figure 121. Ion Densities Subtab for Case 4 of the “CHAWS” Example.144 

Figure 122. Script Used in Case 4 of the “CHAWS” Example.144 

Figure 123. Potential Distribution in the WSF Wake for Case 4 of the “CHAWS” Example.145 

Figure 124. Problem Tab Showing “Time Dependent Plasma” Checked for the “Dynamic” 
Example.146 

Figure 125. Gold-plated Cube Used in the “Dynamic” Example.147 

Figure 126. Grid Definition for the “Dynamic” Example. Top: Primary Grid Definition. 

Bottom: Child Grid Definition.148 

Figure 127. Environment Tab for the “Dynamic” Example.149 

Figure 128. Applied Potentials Tab for the “Dynamic” Example.150 

Figure 129. Space Potentials Tab for Case 1 of the “Dynamic” Problem.151 

Figure 130. Results 3D Tab Showing Laplacian Space Potential Distribution.151 

Figure 131. Space Potentials Tab for Case 2 of the “Dynamic” Example.152 

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Figure 132. Results from Case 2 of the “Dynamic” Example Compared with Laplacian 
Solution (Upper Left).153 

Figure 133. Space Potentials Tab Depicting “Hybrid PIC” Choice for Case 3 of the 
“Dynamic” Example.154 

Figure 134. Time-Dependent Subtab for Case 3 of the “Dynamic” Example.154 

Figure 135. Script for the “Dynamic” Example Showing Four Iterations.155 

Figure 136. Problem Tab for Case 3 of the “Dynamic” Example.156 

Figure 137. Particle Distribution for Case 3 of the “Dynamic” Example at t=4 ps.157 

Figure 138. Particle Visualization Dialog Box Selections to Display Particle Locations.157 

Figure 139. Partial contents of the HybridPIC_tracker_4_out.txt file showing total 
current collected for first five timesteps.158 

Figure 140. Particle Distribution for Case 3 of the “Dynamic” Example at t=10 ps.158 

Figure 141. Ion Collection (Current) by Gold-plated Cube as a Function of Time for Case 3 
of the “Dynamic” Example.159 

Figure 142. Steady-state Potential Profile for Comparison with Transient Results for the 
“Dynamic” Example.159 

Figure 143. Object for “Detector” Example.160 

Figure 144. Definition of the Detector “PartDetect” of the “Detector” Example.161 

Figure 145. Particles Tab for the “Detector” Example.162 

Figure 146. Advanced Particle Parameters Dialog Box for “Detector” Example.162 

Figure 147. Results Tab for “Detector” Example Following Execution.163 

Figure 148. Results3D tab Showing Bowing Out of Potentials Through the Collimator.164 

Figure 149. Tracker Output from Detector Run.165 

Figure 150. Aluminum Cylinder Showing Emitter Surface Element.166 

Figure 151. Definition of the Emitter “EGun” of the “Emitter” Example.166 

Figure 152. Environment Tab for “Emitter” Example.167 

Figure 153. Particles Tab Specification for Emitter Electrons.168 

Figure 154. Edited Script Used to Write Input Files for Creating Macroparticles to 

Represent those Originating at the Emitter.169 

Figure 155. Particles Tab Specification for Sheath Electrons.170 

Figure 156. Final Script for Current Balance Calculation.171 

Figure 157. Potential versus Time for the Emitter Example.172 

Figure 158. Net Current versus Potential for the Emitter Problem.172 

Figure 159. Charging Dynamics with the Stabilizing Current Derivatives Set to Zero.173 


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Figure 160. Example of an Object Toolkit XML Output File.200 

Figure 161. Series of Node Tags.201 

Figure 162. Series of Element Tags.201 

Figure 163. Attribute Properties for a Specified Value of “Subsystem”.201 

Figure 164. Special Component Properties for an Instance of “Thruster”.202 

Figure 165. Material Properties Specification in Object Definition File.203 

Figure 166. SEE Handbook Material Definition File for Material Kapton with Default 
Properties.203 

Figure 167. Contents of Plume Map File Shown Nearly Fully Contracted.205 

Figure 168. Problem Specification Portion of Plume Map XML File, Part 1 (Tags Shown in 
Blue are Understood by Nascap-2k ).206 

Figure 169. Problem Specification Portion of Plume Map XML File, Part 2 (Tags Shown in 
Blue are Understood by Nascap-2k) .207 

Figure 170. Contents of Plume Map File with the First Level Under “PlumeData” Node 
Expanded.209 

Figure 171. Edit Script Subtab of Script Tab Showing “Save Files” Button at the Bottom of 
the Screen.210 

Figure 172. Output File Showing Beginning of Execution of N2kScriptRunner .211 

Figure 173. The “Lower” Object and Grid.214 

Figure 174. The “Upper” Object and Grid.215 

Figure 175. The CombineGrids User Interface.215 

Figure 176. Script Used to Append “Upper” Object.217 

Figure 177. XML Version of Script Used to Append “Upper” Object 

(CombinedDriver.xml).217 

Figure 178. View of Combined Object.218 

Figure 179. Script for Calculating Potentials.218 

Figure 180. Potential Solver Input File (Combined_potent_0_in.txt).219 

Figure 181. Results 3D Picture after Running Potential Script. Note Magnetically Induced 
Potential Variations on Object.220 

Figure 182. Expanded View of “Lower” part of Figure 181, Showing that the Potentials 
Have Been Correctly Calculated and Plotted.221 

Figure 183. Trajectories of Particles Generated at the Intersection of the 0.5 V Contour and 
the Y = 0 Plane, which ExB Drift Along the Potential Contour.222 

Figure 184. Trajectories of Electrons Generated at the intersection of the 0.5 V Contour and 

the Plane X = 0, Superimposed on Potential Contours on Y = 0 Plane Showing that 

Electrons Follow Magnetic Field Lines (Parallel to Y) to Hit or Miss the Object.222 


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Figure 185. Trajectories of Electrons Generated at the Intersection of the 0.5 V Contour and 
the Plane X = 0, Superimposed on Potential Contours on Y = 0 Plane (Magnetic Field 
Direction Normal to Paper) Showing that Electrons that Miss the Object ExB Drift Along 
the Potential Contour in a Clockwise Direction until the Calculation Runs Out of Time. 


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223 


xvi 




LIST OF TABLES 


Table 1. Nascap-2k Limits.7 

Table 2. Formatting Conventions.8 

Table 3. Nascap-2k Menu Options.14 

Table 4. Input Parameters for the Problem Tab.16 

Table 5. GridTool Menu Options.24 

Table 6. Predefined Geosynchronous Charging Environments.28 

Table 7. Input Parameters for the Geosynchronous Environment Tab.28 

Table 8. Input Parameters for the LEO or Plume Environment Tab.30 

Table 9. Input Parameters for the Auroral Environment Tab.32 

Table 10. Input Parameters for the Interplanetary Environment Tab.34 

Table 11. Input Parameters for the Applied Potentials Tab.37 

Table 12. Input Parameters for the Charging Tab.40 

Table 13. Input Parameters for the Space Potentials Tab.46 

Table 14. Input Parameters for the Advanced Potential Solver Parameters Dialog Box.49 

Table 15. Input Parameters for Generating and Tracking Particles.58 

Table 16. Input Parameters for the Advanced Particle Parameters Dialog Box.61 

Table 17. Attributes of Loop Command.63 

Table 18. Attribute of Read Object Command.63 

Table 19. Attributes of Append Object Command.63 

Table 20. Second-Level Commands of the Charge Surfaces Command and their Attributes.65 

Table 21. Attributes Contained in “Environment” Folder.67 

Table 22. Attributes Contained in “TimeParams” Folder.68 

Table 23. Attributes Contained in “FourierComponent” Folder.68 

Table 24. Attributes of Embed Object in Grid Command.68 

Table 25. Attributes of Potentials in Space Command.69 

Table 26. Attributes of Static A Field Command.69 

Table 27. Attributes Contained in “Components” Folder.69 

Table 28. Attributes of Create Particles Command.70 

Table 29. Attributes of Track Particles Command.70 

Table 30. Attributes of Save Files Command.71 

Table 31. Elements on the Script Tab.72 

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Table 32. Quantities in Contour Plots.76 

Table 33. Input Parameters for Displaying Results on the Results 3D Tab.80 

Table 34. Additional Input Parameters for Displaying Particles. Also See Table 15.81 

Table 35. Absolute and Differential Spacecraft Potentials after 300 seconds for the 
“GeoCharging” Example.93 

Table 36. Files Created and Used by Nascap-2k .181 

Table 37. Contents of Input File for Embed Object in Grid Module.182 

Table 38. Contents of Input File for Potentials in Space Module.183 

Table 39. Contents of Input File for Create Particles Module.185 

Table 40. Contents of Input File for Track Particles Module.186 

Table 41. Installed Files of Nascap-2k .198 

Table 42. Correspondence Between Material Property Numbers and Names.204 

Table 43. Format of Grid Definition File.205 

Table 44. Problem Specification Tags in Plume Map File Understood by Nascap-2k .208 

Table 45. Surface Element Properties.213 


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xviii 

















SUMMARY 


Nascap-2k is a spacecraft charging and plasma interactions code designed to be used by 
spacecraft designers, aerospace and materials engineers, and space plasma environments experts 
to study the effects of both the natural and spacecraft-generated plasma environment on 
spacecraft systems. Survival in the plasma environment is a concern for virtually all Earth 
orbiting satellites, be they in low Earth orbit (LEO), geostationary orbit (GEO), polar orbit, or 
others, and for interplanetary and planetary missions as well. Increased power requirements have 
pushed spacecraft subsystem design parameters, such as solar array voltage and power, to higher 
values than ever before, while demand for resources, especially in the commercial 
telecommunications industry, has resulted in the need for longer mission lifetimes. Additionally, 
electric propulsion critical to the success of many exploration as well as commercial missions, 
produces a high-energy, high-density plasma, the effects of which can result in serious erosion 
and contamination problems for spacecraft surface coatings and for sensitive instruments. As a 
result, design strategies for mitigation of deleterious plasma effects require rethinking to meet 
these changing requirements and more severe environments. 

Nascap-2k was developed as part of a program sponsored jointly by the Air Force Research 
Laboratory and by the NASA Space Environments and Effects (SEE) Program at Marshall Space 
Flight Center. 

This manual is designed to be used in several different ways: as a help reference to interface 
menus, field variables, and actions; as a guide to perfonning specific tasks such as defining the 
type of problem to be solved or the particular environment to use; as a guide to start-to-finish 
performance of typical problems such as charging in a tenuous plasma; and as general 
documentation of the physics and engineering models implemented in Nascap-2k. Nascap-2k 
Scientific Documentation describes the physical and numerical models used in the surface 
charging, potential solution and particle tracking portions of the code. 

This document is comprised of the following general parts: 

Part I, Overview, is a general overview of Nascap-2k containing infonnation on its capabilities 
and approach, the various modules that comprise the tool and the high-level architecture that 
joins them, the units used, computational and file size limitations, and installation requirements 
and procedure. 

Part II, Using Nascap-2k, provides the details of how to use the code. This part is further divided 
into several sections that address opening a project, the menus, the tabs, and the output files. 

■ Section 5 describes the basic approach to using Nascap-2k. 

■ Section 6 describes how to get started by creating a new project or opening an existing 
project. 

■ Section 7 describes the various menu items available, including view and material 
definition. 

■ Section 8 describes the options for specifying the type of problem. 


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1 




■ Sections 9 and 10 describe the requirements to be aware of when creating an object 
(detail on object creation is in the Object Toolkit User s Manual) and how to grid the 
space surrounding an object. 

■ Sections 11 through 15 describe the various physical and computational parameters used 
by Nascap-2k. These sections also discuss the physics models used in the computations. 

■ Section 16 describes the process of generating and executing the script that directs the 
desired calculations. 

■ Section 17 describes how to view results either numerically, as a time-dependent plot, or 
as a three-dimensional graphical representation of surface and volume values. 

Part III contains four start-to-finish examples that illustrate the use of Nascap-2k’s computational 
capabilities: charging in a geostationary orbit, current collection in low-Earth orbit, calculation of 
wake effects, and calculation involving a time-dependent plasma environment. 

These three primary parts are followed by a glossary of terms, some common “gotchas” and 
Frequently Asked Questions (FAQs), and a set of appendices containing information for the 
advanced user and the just plain curious. 


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2 



I OVERVIEW 


1 Need for Nascap-2k 

Designers of spacecraft for government, commercial, and research purposes require advanced 
modeling capabilities to guide the design of satellites that can survive and operate properly in the 
natural environment. In the past, computer modeling of flight experiments (such as SCATHA 
(Spacecraft Charging at High Altitude), 1 the SPEAR (Space Power Experiment Aboard 
Rockets) ’ series, and CHAWS (Charging Hazards and Wake Studies) ) demonstrated excellent 
ability to predict both steady-state and dynamic interactions between high-voltage spacecraft and 
the ambient plasma. This ability was also extended to inherently dynamic problems involving 
three-dimensional space charge sheath formation, current flow in the quasi-neutral presheath, 
breakdown phenomena, plasma kinetics, ionization processes, and the effect of unsteady 
processes on spacecraft charging. 

Nascap-2k builds on these capabilities, giving the spacecraft designer much-improved modeling 
capabilities by taking advantage of a greater understanding of the pertinent phenomena, 
employing more advanced algorithms, and implementing a state-of-the-art user interface, 
including three-dimensional post-processing graphics. 

Nascap-2k was developed a as part of a program sponsored jointly by the Air Force Research 
Laboratory (now at Kirtland Air Force Base) and by NASA’s Space Environments and Effects 
(SEE) Program (at Marshall Space Flight Center). 

2 What is Nascap-2k ? 

Nascap-2k is an interactive toolkit for studying plasma interactions with realistic spacecraft 
models in three dimensions. Nascap-2k is designed for use by spacecraft design engineers, 
spacecraft charging researchers, and aerospace engineering students. Nascap-2k also enables 
plasma-interactions specialists to perform realistic analyses with direct application to engineering 
problems. 

The Nascap-2k interface employs an index-tab metaphor; several of these tabs are shown 
in Figure 1. The graphical user interface is designed to help less experienced users easily solve 
moderately complex plasma-interactions problems. 

The core capabilities of Nascap-2k are as follows: 

■ Define spacecraft surfaces and geometry and the structure of the computational space 
surrounding the spacecraft. 

■ Solve for time-dependent potentials on spacecraft surfaces. 

■ Solve the electrostatic potential around the object, with flexible boundary conditions on the 
object and with space-charge computed either fully by particles, fully analytically, or in a 
hybrid manner. 

■ Generate, track, and otherwise process particles of various species, represented as 
macroparticles in the computational space. 


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3 




View surface potentials, space potentials, particle trajectories, and time-dependent potentials 
and currents. 


H Nascap2k - C:\MyCalculations\Manuals\bipolar\bipolar2\bipolarProject.xml 


File Edit View Materials Help 


U1JPI 


Problem^ Environment Applied Potentials j Charging | Space Potentials ["Particles | Script Results Results 3D 


0 Nascap2k - C:\MyCalculations\Manuals\bipolar\flipolarProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging | Space Potentials Particles Script 


O Geosynchronous 
(D LEO or Plume 
O Auroral 
O Interplanetary 

O Radiation Belt 


Object Status: Loaded 


Grid Status: Loaded 




□ Surface Charging 

O Analytic Currents 
® Tracked Particle Currents 
O Tracked Ion & Analytic Electron Cum 
O Custom Current Module 

V- Potentials in Space or Detector Analysis 
® Analytic Space Charge 
O Self-consistent with Ion Trajectories 
O Consistent with Plume Ion Densities 
[^Surface Currents 

□ Time Dependent Plasma 

® Fixed Surface Potentials 
O Self-consistent Surface Potentials 
® Tracked Particle Currents Only 
O Tracked Ion & Analytic Electron Currents 

□ Deep Dielectric 


L3(T - » « ~ » « fctgdOEQEEEEE) 

Cl I lm*i 1 Duett Miiwmxtil K lti<«lnn 


tea 5) 

Dj 

HMtOtfKt 

[ ShuvSatMriMdGild 



Figure 1. Selected Views of the Nascap-2k User Interface 


Nascap-2k Scientific Documentation describes the physics and numeric models used in the 
surface charging, potential solution and particle tracking portions of the code. 

Figure 2 shows an overview of the Nascap-2k structure. There are three main programs: 
Nascap-2k, Object Toolkit, and GridTool. Object Toolkit and GridTool can be invoked either as 
separate programs or from the main Nascap-2k user interface. 


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Figure 2. Nascap-2k Structure 


Object Toolkit is a three-dimensional object generator tailor-made for spacecraft modeling. It is 
used to create finite-element representations of spacecraft surfaces for Nascap-2k (and other 
environmental interactions computer codes, such as EPIC {Electric Propulsion Interactions 
Code)). 5 It also has materials editing capability and can import objects from standard finite- 
element preprocessors such as PATRAN. In this way, the spacecraft geometry can be realistically 
represented, and existing finite-element models of spacecraft constructed for other purposes can 
be adapted for use in Nascap-2k. Object Toolkit output (in extensible Markup Language (XML)) 
contains the recipe for re-creating/reassembling the object, object definition by nodes and 
elements, and material definitions. Object Toolkit is described in Section 9, and more fully in the 
Object Toolkit User s Manual 6 . 

The computational space around the spacecraft is constructed interactively using the GridTool 
module. Arbitrarily nested subdivision allows resolution of important object features while 
including a large amount of space around the spacecraft. GridTool is described in Section 10. 

The main Nascap-2k user interface uses an index-tab metaphor, and contains tabs for problem 
selection, initial conditions, parameter specification, script writing, time-dependent results 
analysis, and two- and three-dimensional displays of surface potentials and fields. 

The kind of problem is specified on the Problem tab. The choices made on this tab tailor the rest 
of the interface’s appearance. The various choices regarding initial conditions, environment, and 
computational parameters are available on subsequent tabs. Advanced parameters that are useful 
only to a limited number of users are found on dialog boxes that are accessed by clicking 
“Advanced” buttons on the various tabs. 


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The Nascap-2k computational engines are accessed through the Script tab. The five 
computational modules are Charge Surfaces, Embed Object in Grid, Potentials in Space, 
Create Particles, and Track Particles. The script can be run either within the GUI or from the 
standalone executable N2kScriptRunner. 

Nascap-2k calculates surface charging in tenuous plasma environments, such as geosynchronous 
Earth orbit (GEO) and interplanetary (Solar Wind) environments, using the Boundary Element 
Method 7 (BEM). The Boundary Element Method facilitates calculation of surface electric fields 
(which limit the emission of photoelectrons and secondary electrons) without the need to grid up 
the space surrounding the spacecraft. It also enables Nascap-2k to anticipate electric field 
changes due to surface charging, resulting in a smoother and more stable charging simulation. 

Nascap-2k uses a high-order, finite-element representation for the electrostatic potential that 

8 

ensures electric fields are strictly continuous throughout space. The electrostatic potential solver 
uses a finite element/conjugate gradient technique to solve for the potentials and fields on the 
spacecraft surface and throughout the surrounding space. Space charge density models presently 
include Laplacian, Linear, Non-linear, Frozen Ions, Consistent with Ion Density, Full PIC 
(Particle in Cell), and Hybrid PIC (appropriate to the several microsecond timescale response to 
a negative pulse). The input file defining the initial conditions and computational parameters for 
the potential solver is generated through the user interface. 

Particle tracking is used to study sheath currents, to study detector response, or to generate space 
charge evolution for dynamic calculations. Nascap-2k generates macroparticles (each of which 
represents a collection of particles) at either a sheath boundary, the problem boundary, at user- 
specified locations, or throughout all space. Particles are tracked for a specified amount of time, 
with the timestep automatically subdivided at each step of each particle to maintain accuracy. 

The current to each surface element of the spacecraft is recorded for further processing. The 
input files defining the initial conditions and computational parameters for both particle creation 
and tracking are generated through the user interface. 

The Results tab of the Nascap-2k user interface is used to obtain numerical values and time 
histories of potentials and surface currents. The Results 3D tab is used to generate graphical 
output illustrating such quantities as surface potentials, space potentials, particle positions, and 
particle trajectories. Contour levels and other plotting attributes are modified through the user 
interface. 

The computational modules of Nascap-2k use a database manager. The database manager is a 
library of routines capable of making large arrays of infonnation contained in disk files 
accessible to computational modules. It features a programmer-friendly language for defining 
data types and for retrieving and storing data, and an API accessible through C++, Fortran, or 
Java. This strategy enables Nascap-2k to be operable on, and portable among, modem high- 
power workstations, which have proven to be more cost effective than supercomputers for this 
type of code development and analysis. 

The user interface is written in Java, the science modules are written in C++ and Fortran, and the 
utility routines are written in C. All infonnation is stored in the multi-file database or as XML. 
The modules communicate using XML files, keyword text input files, direct subroutine calls 
(Dynamic Link Library (DLL) import/export), Java Native Interface (JNI) subroutine calls, and 


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6 



the proprietary database. XML files and text input files can be manually edited with a text editor 
or XML editor. 

2.1 Units 

The Nascap-2k user interface specifies the units of all input parameters. In general, Nascap-2k 
operates internally in the SI (Systeme International) or MKS system of units. Electrostatic 
potentials are internally stored in volts, and electric fields in volts per meter. Magnetic fields are 
always in tesla (webers per square meter). Particle energy or plasma temperature is usually in 
electron volts. Charge density in coulombs per cubic meter is often divided by the permittivity of 
free space (so), so that it has the units of volts per square meter. 

2.2 Limits 

The maximum values for various parameters are shown in Table 1. 


Table 1. Nascap-2k Limits 


Quantity 

Limit 

Characters in prefix name 

80 

Surface elements 

4095 

Nodes 

4095 

Conductors 

25 

Materials 

999 

Time Steps 

Unlimited 

Particle Types (species) 

99 

Grids 

50 

Grid nodes per grid 

10 8 

Macroparticles per particle type 

3 x 10 8 

Special elements 

16393 

Additional points/special element 

100 

Centroids per special element 

70 

Triangles/special element 

150 

Macroparticles per volume element 

1000 


The spacecraft model is described by a finite-element representation of surface elements and 
nodes. Each surface element has a conductor index and a material name. Building an object is 
described in Section 9. 

In the database, a separate particle type is created for each species used in a calculation and for 
each species tracked for visualization. 

The solution of potentials in space or particle tracking requires gridding of the space external to 
the object. Section 10 describes the construction of grid systems. A grid system consists of a 
main grid and up to 49 subgrids. The number of nodes in each grid is the product of one plus the 
number of grid units in each direction: (NX+1)(NY+1)(NZ+1). 


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Volume elements that are not empty or completely filled by the object or contained within a 
subgrid are special elements. The Embed Object in Grid computational module produces finite- 
element matrices for special elements that couple surface element potentials and fields to those 
on volume nodes. Subgridding should be used to divide up special elements that are too complex 
to be easily resolved (i.e., too many points, centroids, or triangles). 

3 Formatting Conventions 

Table 2 lists the formatting conventions used in this manual. Italic font is also used for emphasis. 


Table 2. Formatting Conventions 


Text Style 

Meaning 

Italics 

Names of software, variable portion of filenames and input 

Boldface 

Names of menus, dialog boxes, tabs, script commands, and computational modules 

“Quotation Marks” 

Text on interface, including menu items, text box labels, etc. 

Lucida Sans Font 

Filenames, folder names, web addresses 

Monotype Font 

Large quantities of text that represent computer output 


4 Installation 
4.1 Requirements 

■ Computer: 

- Pentium 4 processor or higher, 512 MB memory or higher 

- Available hard drive space: at least 1 GB 

■ Operating System: 

- Supported: 

• Windows Vista, Windows 7 

- Not supported: 

• Windows 98, Windows 98SE, Windows ME, Windows NT4, Windows 2000, Windows 
XP, Lindows, Linux, Macintosh, UNIX 

■ Video Display: 

- 1024x768 or higher resolution 

- Color set to 32 bit. 

■ Note: 

- Only members of the Administrators Group for the computer (and Computer 
Administrators) can install software. 

- We strongly recommend that all updates from http://windowsupdate.microsoft.com be 
installed. 

- Object Toolkit and GridTool can be run on other Java platforms (e.g. Linux or Solaris), 
but database access is unavailable. 


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4.2 Nascap-2k Installation 


To install the 64-bit version of Nascap-2k, open Setup.exe in the x64 folder on the installation 
disk. To install the 32-bit version, open Setup.exe in the x86 folder on the installation disk. The 
Nascap-2k user interface, the auxiliary programs Object Toolkit and GridTool, and several DLLs, 
along with documentation and example files, are installed. The various files that are installed are 
listed in Appendix A. Of particular note is the folder Nascap-2k/Materials containing files of 
material properties measured by Utah State University. 

Nascap-2k versions 4.1 and 4.2 have a new database that allows larger problems to be run. 
Projects created using earlier versions of Nascap-2k can still be used; however, the results saved 
in the database will not be accessible. To examine data generated by earlier versions of 
Nascap-2k the earlier version of the software will need to be used. 

Nascap-2k 4.2 and earlier versions may be simultaneously installed, as long as they are installed 
in separate folders. 

4.3 Java Installation 

Nascap-2k 4.2 requires the Java 2 Standard Edition 7.0 (J2SE 7.0) runtime environment (version 
1.7.0 or higher), including the Java3D extension (version 1.5.1 or higher). The Nascap-2k 
installer does not automatically install Java or Java3D. 

Before Installing Java 

Before a user installs Java, we strongly recommend that the user first go to “Control Panel | Add 
or Remove Programs” and remove any Java 3D versions that appear. Then remove any versions 
of Java 2 SDK and/or Java 2 Runtime Environment. 

Java (J2SE) 

Either the Java runtime environment (JRE) or the larger developer kit (JDK) can be installed. 
Java 7 or higher is required. The released version of this code was tested with Java SE 7 update 
25. The runtime environment is included on the Nascap-2k installation disk in the Java Installs 
folder. To install, open jre-7u67-windows-i586.exe (for 32 bit) or 7u67-windows-x64.exe (for 64 bit). 
In addition, both are available from 

http://www.oracle.com/technetwork/java/javase/downloads/index.html. 

Both 32-bit and 64-bit versions of Nascap-2k are available. The appropriate version of Java is 
required. Note that the 32-bit (i586) version of Java can coexist with the 64-bit version on 
Windows. 

Java3D 

Java3D is needed to display the active three-dimensional images in Nascap-2k. The code does 
not run without it. The latest version is 1.5.2 and is available on the install disk and from 

http://www.softpedia.com/progDownload/Java-BD-Download-l 629B7.html. 

To install, openj3d-l_5_2-windows-i586.exe (for 32 bit) orj3d-l_5_2-windows-amd64.exe (for 64 
bit). 


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9 



Make sure that Java3D is installed into the correct copy of the jre and/or jdk. (This usually 
happens by default on Windows, but has been known to fail, particularly on dual-boot machines.) 

On some computers, it is necessary to copy the files in 

C:\Program Files\Java\Java3D\1.5.2\lib\ext to C:\Program Files\Java\jre7\lib\ext and the files in 
C:\Program Files\Java\Java3D\1.5.2\bin to C:\Program Files\Java\jre7\bin (and the equivalent in 
the 32-bit \Program Files (x86)\ directories). (These paths may be different on your computer and 
for different versions of Java.) Administrator privileges are generally needed to alter the Java 
directory. This may need to be done every time Java is updated. 


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II USING NASCAP-2K 


5 Basic Approach 

The Nascap-2k user interface is designed to help less-experienced users easily solve moderately 
complex plasma-interactions problems, while also allowing plasma interactions specialists to 
perfonn realistic analyses with direct application to engineering problems. 

To perfonn a Nascap-2k calculation, proceed as follows: 

1. Create the geometry, specify the surface materials, and define any new materials using 
Object Toolkit. 

2. Open a new Nascap-2k proj ect. 

3. Load the object into Nascap-2k. 

4. Specify the problem by making selections on the Problem tab and defining a grid (if 
needed) using GridTool. 

5. Review all the values on the available tabs, changing the specifications and adding 
parameters as needed. 

6. On the Script tab, build the default script. Examine it to make sure it carries out the 
appropriate procedures using the desired parameters. Edit the script if necessary. For 
complex problems it is generally appropriate to divide the problem into steps. 

7. Run the script. 

8. View the results using the Results tab, the Results 3D tab, and the output files as 
appropriate. 

9. Make adjustments and repeat or continue. 

The best way to become familiar with Nascap-2k is to step through either the Spacecraft 
Charging in a Tenuous Plasma (Section 18) or the Current Collection in a Low-Earth-Orbit 
Plasma (Section 19) example in Part III, Examples. The appropriate sections of Part II, Using 
Nascap-2k can be consulted while performing the example calculations to become familiar with 
the variety of options available and their appropriate use. 

When the code behaves unexpectedly, consult the Common Gotchas and Frequently Asked 
Questions section. 


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6 Creating or Opening a Project 


The opening screen of Nascap-2k (Figure 3) provides the user with the choice of creating a new 
project (Figure 3, left side) or opening an existing project (Figure 3, right side). Each project is 
identified by a “ prefix ” used to name the files created and optionally used as a directory in which 
the files are stored. Appendix A describes the files. To re-create a project (e.g., to make a copy or 
re-create a corrupted database) requires the prefix Project.xml and prefix Object.xml files along with 
the optional prefix. grd, pre/7xPlume.xml, and pref/xPhoto.xml files. 



Figure 3. Opening Screen of the Nascap-2k User Interface 


^ Open Project 


& New Project 


Project Prefix: | NewProject _ 

Location: C:\MyCalculations\NewProjectt 

0 Create New Folder 


Set Location... 


|Geo1Project.xml 


r Type: Project File (*Project.xml) 


MGeol 

- 

n My Computer 

- 

03% Floppy (A:) 


^ Local Disk (C:) 


n MyCalculations 

= 

l~1 Manuals 


QGeol 

— 

^ Removable Disk (D:) 


@ Audio CD (E:) 

- 




Open 


Figure 4. Opening a New (left) or Existing (right) Project in Nascap-2k 


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7 Main Menus 


The main menus in Nascap-2k allow the user to perform a number of top-level, project-related 
functions such as loading and saving the project. The View menu is used to change the 
appearance of the display area on the Results 3D tab. The Materials menu allows users to edit 
the material properties. For additional information on material properties see Section 13.4. 

Note: When a material is changed from a conductor to an insulator or from an insulator to a 
conductor, Nascap-2k should be closed and restarted. 

The Nascap-2k online Help menu provides basic infonnation and descriptions of the parameters 
that appear on the interface. Table 3 describes the main menu options. 


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13 



Table 3. Nascap-2k Menu Options 



File 


New Project 

Create a new project. 

Open Project 

Open existing project file. 

Save Project 

Save existing project file. 

Save Project As 

Save new or existing project file under a new name. 

Load Object 

Import existing Object Toolkit object file into current project for the 
computation of the resulting potentials. An object must be loaded before the 
options on the Problem tab are enabled. 

Load Plume 

Import a plume map file into current project for the computation of the 
resulting potentials. See Section 14. 

Load Script 

Import a saved script file into current project. See Section 16. 

Import SEE Handbook Materials 
File 

Import material definitions from a file in the format saved by SEE 

Interactive Spacecraft Charging Handbook. See Section 13.4. 

Export Script... 

Save the current script to a file. See Section 16. 

Export Tecplot... 

Save the current object and surface potentials to a Tecplot data file. 

Exit 

Exit the Nascap-2k user interface. 

View 

Enabled when Results 3D tab is displayed. 

From X, Y, Z, -X,-Y,-ZAxis 

Reorient view of object so that it is from specified coordinate axis. 

From Sun 

Reorient view of object so that it is from the sun direction. 

From RAM 

Reorient view of object so that it is from the direction the object is headed. 

From Specified Direction 

Reorient view of object so that it is from a user specified direction. 

Timestep to Display 

Display results for the specified timestep. 

Display Special Components 

Turn display of special components defined in Object Toolkit off or on. 

Set Background Color 

Set background color of 3D display area to black or white. 

Set Outline Color 

Set color of lines outlining surface elements to black or white or do not 
display lines (off). 

Color Scale Direction 

Set color scale so that white or black is most positive. 

Rescale View 

Scale view of object to fit within display area. 

Perspective 

Turn perspective adjustment on or off. 

Mouse Position 

Show or hide pop-up window that displays the position of the mouse in 
meters from the center of the grid. Useful for determining an appropriate cut 
plane position or tracking limit. Turns off perspective. 

Legend Font Size 

Increase or decrease font size used in legend on Results 3D tab. 

Edit 

Not implemented. 

Materials 

Edit properties of existing materials, including photoemission spectra. 
Materials are defined in Object Toolkit. See Section 13.4. 

Help 


Nascap-2k Help 

Display online help file. 

About Nascap-2k 

Display Nascap-2k version, copyright, and contacts information. 


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8 Defining the Problem (Problem Tab) 

Figure 5 illustrates the options in the Problem tab. Table 4 lists the parameter definitions. 


Nascap2k - C:\MyCalculations\Manuals\bipolar\leocharging\bipolarProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging [ Space Potentials Particles Script j Results 


S®1) 


Results 3D j 


Problem Type- 

0 Surface Charging 

O Analytic Currents 
(§) Tracked Particle Currents 
O Tracked Ion & Analytic Electron Currents 
O Custom Current Module 
[^Potentials in Space or Detector Analysis 
<D Analytic Space Charge 
O Self-consistent with Ion Trajectories 
O Consistent with Plume Ion Densities 
0Surface Currents 

□ Time Dependent Plasma 

® Fixed Surface Potentials 
O Self-consistent Surface Potentials 
® Tracked Particle Currents Only 
O Tracked Ion & Analytic Electron Currents 

□ Deep Dielectric 


Figure 5. Problem Tab in Nascap-2k 

The available values for “Environment” and “Problem Type” depend on the availability of an 
object and a grid. The object, if not already loaded, is loaded using the “Load Object” choice on 
the File menu. The grid is automatically loaded if a prefix.g rd file is present. 

Some “Problem Types” are not available for some choices of “Environment.” 

Choices of “Environment” and “Problem Type” govern the available and default options on 
subsequent tabs and the contents of automatically generated scripts. This functionality has been 
tailored to facilitate running certain standard problems, such as those provided in this manual as 
examples. The ability to edit the actual script and its parameters either within the user interface 
or externally using a text or XML editor, together with the ability to edit the generated text input 
files for the various modules, allows advanced users to extend Nascap-2k , s capabilities beyond 
the standard problems while continuing to work within the user interface. 

The Problem tab also contains buttons that can be used to launch Object Toolkit (“Edit 
Object...”) and GridTool (“Edit Grid...”). 


- Environment- 

O Geosynchronous 
® LEO or Plume 
O Auroral 
O Interplanetary 

O Radiation Belt 



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Table 4. Input Parameters for the Problem Tab 


PROBLEM 


PARAMETER 


DEFINITION 


Environment 

Specification of spacecraft environment type. 

Geosynchronous 

Geosynchronous Earth orbit (altitude -36,000 km) substorm environment: High- 
energy isotropic tenuous plasma. 

LEO or Plume 

Low Earth orbit (altitude 100-1000 km) or plume environment: Cold, dense 
isotropic plasma. 

Auroral 

Auroral (altitude >100 km): Low energy (<1 eV) electrons and streaming ions 
along with high-energy precipitating electrons. 

Interplanetary 

Solar Wind: Tenuous, moderate energy (-10 eV) electrons and streaming (-1 keV) 
protons. 

Radiation Belt 

(Altitude >1000 km near the equator, lower at high latitude.) High-energy electrons 
of up to a few MeV and protons of up to several hundred MeV energy. (Not yet 
implemented.) 


Problem Type 

Specifications for type of calculation and model to be used. 

Surface Charging 

Charging of surfaces due to the space environment. 


Analytic Currents 

Surface currents calculated analytically using formulation appropriate to specified 
environment. (LEO charging assumes flowing Maxwellian, appropriate only for 
Debye length comparable to or longer than the object size.) 


Tracked Particle Currents 

Surface currents taken from particle tracking results. (LEO only.) 


Tracked Ion &Analytic 

Electron Currents 

Electron surface currents calculated analytically using formulation appropriate to 
specified environment and ion currents taken from particle tracking results. 

Potentials in Space or Detector 
Analysis 

Electrostatic potentials and particle tracking in the space surrounding the 
spacecraft. (Requires a grid.) 


Analytic Space Charge 

Use analytic formulae for charge density distribution. (All environments.) 


Self-consistent with Ion 
Trajectories 

Solve iteratively until electric potentials and ion charge densities are consistent with 
governing equation(s). (LEO and Auroral only. Not available with surface 
charging.) 


Consistent with Plume Ion 
Densities 

Use ion densities imported from a plume map file with or without a contribution 
from Nascap-2k calculated charge exchange particles. See Appendix E. (Not 
available with surface charging.) 

Surface Currents 

Compute surface currents using particle tracking. (LEO and Auroral only. Requires 
a grid.) 

Time Dependent Plasma 

Dynamic plasma calculation using particle tracking. (LEO only. Requires a grid.) 


Fixed Surface Potentials 

Use surface potentials set as specified on Applied Potentials tab. 


Self-consistent Surface 
Potentials 

Determine surface potentials using tracked currents only or tracked currents plus an 
analytic model of electron currents. 

Deep Dielectric 

Fields due to charge deposited (e.g., by radiation-belt electrons) within dielectric 
layers. (Not yet implemented.) 


Object Status 

Indicates whether a geometric model has been imported into the project. 

Edit Object 

Launch Object Toolkit to create or edit a geometric model. Model is automatically 
loaded into the project on return from Object Toolkit. 

Grid Status 

Indicates the existence of a grid (.grd) file for the project. 

Edit Grid 

Launch GridTool to create or edit a spatial mesh surrounding the model. Grid 
automatically loaded (if saved) on return from GridTool. 


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9 Creating a Spacecraft Model 

The first step in a Nascap-2k project is to construct a geometrical model of the spacecraft. Object 
definition for Nascap-2k is perfonned using Object Toolkit. The use of Object Toolkit is fully 
described in the Object Toolkit User s Manual. 

Object Toolkit is used to create finite-element representations of spacecraft surfaces. It also has 
materials editing capability, and can import a finite-element representation from aPATRAN 
neutral file or a NXI-DEAS TMG ASCII VUFF file. The XML output file contains the finite- 
element specification of the object surfaces, the recipe for re-creating/reassembling the object, 
and the properties of the default and used materials. Object Toolkit can be customized to create 
geometric models for other analysis codes. Presently it is also used to define spacecraft for 
EPIC. 5 

The user interface for Object Toolkit is shown in Figure 6. 



Figure 6. Object Toolkit Screen Showing Standard Components 
9.1 Object Requirements 

Nascap-2k performs analyses for potentials and electric fields on surface elements and in space 
using the Boundary Element and Finite Element Methods. The objects (i.e., spacecraft models) 
defined using Object Toolkit and the grids defined using GridTool determine the geometry of 
Nascap-2k problems. The surface and spatial geometry must confonn not only to the strict 
requirements of the Boundary Element and Finite Element Methods, but also to Nascap-2k 


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specific requirements, as well as to standards that are not strictly required, but which are needed 
to avoid pathological results. Note that other Object Toolkit client applications may use different 
computational methods, resulting in very different object definition requirements. 

9.1.1 General 

Objects are defined by points in space (called “Nodes”) and elemental surfaces (called “Surface 
Elements” or “Elements”), which are defined using the Nodes as vertices. All physical quantities 
and results focus on the surface elements. Thus, each surface element is assigned “attributes” 
such as material name, conductor number, and initial potential. A calculation assigns physical 
results such as electrostatic potential, electric field, and incident current density to each surface 
element. In calculating these results, each surface element is assumed to consist of either exposed 
metal or metal with an exposed thin dielectric coating. This, as well as the plasma interactions of 
the surface element, is detennined by properties associated with the material name. 

9.1.2 Material Name Attributes 

Each surface element has a string attribute indicating material name. Properties associated with 
the material name determine whether the surface element is metal or dielectric coating, the 
conductivity and capacitance (if a coating), and the electron emission stimulated by incident 
electrons, protons, or sunlight. Note that material names are case-insensitive in Nascap-2k. 

9.1.3 Conductor Number Attributes 

Each surface element has an integer (1-25) attribute indicating “Conductor Number.” These 
assignments may be used for purely diagnostic purposes or as a basis for internal spacecraft 
circuitry. Conductor number 1 is considered “spacecraft ground.” Higher numbered conductors 
are biased relative to ground or floating. 

9.1.4 Closed Surfaces 

The assembled surface elements are required to fonn one or more disjoint closed surfaces in 
three-dimensional space. Equivalently, any point in three-dimensional space must be 
unambiguously identifiable as being inside the object, external to the object, or (if ambiguous) on 
the object surface. 

9.1.5 Surface Elements 

Individual surface elements may be either triangles or quadrilaterals. A quadrilateral element 
should be as nearly planar as possible (i.e., should not be grossly non-planar). In general, 
quadrilaterals are preferred to triangles. Each element is described by three or four vertices listed 
in counterclockwise order (as viewed from exterior space). If possible, the aspect ratio 
(length/width) of the element should be no greater than two. Also (if possible) the area of an 
element should not be grossly different from that of its neighbors. For calculations that use a 
grid, element dimensions should be within about a factor of two of the local grid spacing. 

9.1.6 Resolution 

The geometric resolution of the calculation is detennined by the surface element size (and the 
grid spacing for gridded calculations). The geometric model should have the overall shape of the 


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object (spacecraft) of interest, approximately correct conductor and insulator areas, and represent 
the distribution of insulators and conductors across the surfaces. Typical models have from 
several hundred to about 2000 surface elements. An excessive number of surface elements slows 
the calculation and, in some cases, reduces the accuracy of the result. The best resolution is 
typically a few percent of the overall object size, and it is generally impractical to resolve 
features smaller than a fraction of a percent. So for a commercial communications spacecraft 
with dimensions in the 10 m range, the resolution should be on the order of 10 cm, with coarser 
resolution on large, uninteresting or conductive areas, and finer resolution on areas of potential 
interest. While zones need not be perfectly square, high aspect ratio zones (greater than 3:1) 
should be avoided as much as possible. 

Large flat areas should generally be 5 to 9 elements across in the short direction. Additional 
elements can be used to resolve fine electric field structure from complex geometry, and should 
have at least 2 to 3 spatial zones across the feature. Large panels (e.g., solar panels) should be 
modeled with thickness a substantial fraction of the surface resolution, even if the actual panels 
are much thinner. Conductor patterns may be used on solar panels to mimic the string layout on a 
gross scale. 

Beyond these general guidelines, the model geometry should be driven by the question of 
interest. Features of particular concern should be well represented. It is sometimes necessary to 
separately model fine structure (such as a probe, antenna, or detector), either with a separate 
“coupon” model of the detailed structure, or with the detailed model mounted on a large brick, 
cylinder, or other simple structure representing the remainder of the spacecraft. 

9.1.7 Compatibility (Edge) 

An “Edge” is the line joining an adjacent pair of vertices of a surface element. The compatibility 
requirement states that each edge must be traversed exactly once in each direction (i.e., in the 
forward direction by the surface element in which we first found it, and in the reverse direction 
by a neighboring element). Equivalently, each edge must have exactly one element on its right 
and exactly one on its left. Edges that violate the compatibility requirement are drawn in red in 
Object Toolkit. 

The reason for this requirement is that its violation leads to discontinuous surface potentials. For 
example, in Figure 7, point B, as a vertex for one of the dark-blue surface elements, may be 
assigned a potential different from the potential that would be obtained by linear interpolation 
between the ends of the edge of the light-blue element that goes from A to C. We would then 
have a sudden jump in potential across the edge. 


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Figure 7. Example Showing Incompatible Edges and their Repair 

To repair this problem, (1) subdivide the offending light-blue element (as at top left); (2) delete the 
three offending small elements; and (3) construct two new elements from the free edges of the 
small element to the free long edges, fonning the pattern seen to the right of the dark-blue area. 

9.1.8 Special Objects (Ion Thrusters, Neutralizers, Magnetic Dipoles) 

The locations and directions of ion thrusters and neutralizers used in a “Consistent with Plume Ion 
Densities” calculation are defined in Object Toolkit. The properties of the thrusters and neutralizers, 
as well as the background neutral density, are defined in the imported plume map file. (See 
Appendix A.) Presently, only one plume map file (and thus one type of thruster) is allowed. A 
thruster is a source of energetic ions, neutrals that effuse unifonnly through its grids, and 
(optionally or initially) charge exchange ions. Charge exchange ion densities may be taken from 
the plume map file or generated and tracked self-consistently in Nascap-2k. Thrusters may be 
temporarily turned on or off or gimbaled from the Nascap-2k interface. A neutralizer is a source of 
neutrals that may undergo charge exchange with the energetic ions. Nascap-2k automatically 
attenuates the main beam ion densities (as specified in the plume map file) due to charge exchange 
interaction with the background neutral density. 

The locations (meters relative to object center) and moments (A m") of spacecraft-generated 
magnetic dipoles are defined in Object Toolkit. The resulting magnetic field is calculated (from 
the dipole values stored in the database) and used when computing particle trajectories. 
Nascap-2k reads new or revised dipole moments and locations on startup or object load, and 
saves them to the database when the Project is saved, either explicitly or due to running a script. 

Note that thrusters, neutralizers, and dipoles are defined by their locations, and are not associated 
with object surfaces. 

9.1.9 Emitters, Detectors, and Injection Points 

Emitters, Detectors, and Injection Points (for Transverse Surface Current calculations) are 
defined in Object Toolkit. These properties are defined by assigning an Emitter, Detector, or 
Injection Point name to a surface element. Injection Points require no additional properties. The 
properties of Emitters and Detectors are defined in Object Toolkit and can be modified on the 

Particles tab and Particle Advanced dialog. 


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10 Creating a Grid System Around the Spacecraft 

A system of arbitrarily nested cubic grids is used to calculate electrostatic potentials and fields, 
store charge densities, and track charged particles in the space external to the spacecraft. 
Electrostatic potential and electric field are defined at each grid point, leading to strictly 
continuous electric fields. (More commonly used finite-element systems only define potential at 
each grid point. This leads to continuous potentials, but it also leads to electric fields that are 
discontinuous across grid cell boundaries.) 

10.1 GridTool 

Nascap-2k , s GridTool is used to define an arbitrarily nested grid structure about the object. 
GridTool allows the user to define a grid structure for an object created by Object Toolkit. A grid 
is needed to compute potentials in space, to track particles, or to compute wake structure. 

GridTool has the following capabilities: 

• Create and modify a primary grid around an object. 

• Add and modify a child grid. 

• Delete a grid and all its child grids. 

• Import an existing grid structure. 

• Graphically display the current grid structure. 

GridTool can be launched either directly or by clicking the “Edit Grid” button on Nascap-2k' s 
Problem tab. The File menu can be used to open an existing database or an Object Toolkit 
geometric model. An existing grid definition can also be read in. If no grid definition exists, the 
grid definition process starts by selecting “New Primary Grid” from the Grid menu, and then 
varying the parameters presented in the grid definition dialog. 

A simple example of a 3-level grid is shown in Figure 8. 


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Figure 8. Grid in Space Generated Using GridTool 

Using the Tree View on the right, the user can select the parent grid or any of the child grids to 
modify or delete, and/or add a new child grid. In Figure 8, the second-level child grid has been 
chosen for modification. The dialog box for the definition of a child grid is shown in Figure 9. 
The user specifies the subdivision ratio and the minimum and maximum indices within the 
parent grid coordinate system. 



Figure 9. Child Grid Dialog Box for Defining or Modifying a Child Grid in GridTool 

Grid files are saved with the extension “.grd.” The file format is described in Appendix A. 


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10.2 GridTool Menu Options 

GridTool s menu options and movement/orientation tools and their usage are listed in Table 5. 

10.3 Grid Requirements 

GridTool is used to construct a grid system about an object. The outermost or primary grid 
encloses the entire computational space and should have all its boundaries sufficiently far from 
the object that the near-object fields are not perturbed. GridTool is then used to add nested child 
grids to achieve adequate resolution near the object and in other regions of interest. See 
Sections 19, 20, and 21 for examples. 

10.3.1 Parameters Defining a Grid 

A grid is defined by its extent in the three coordinate directions (NX, NY, NZ), its subdivision 
ratio (relative to its parent) and the resultant grid spacing, and its origin in its parent and the 
resultant origin in the primary grid. The number of grid points in each direction is greater by one 
than the number of grid elements. Positions in grid coordinates range from 1 to NX+1 (etc.), so 
that the center of the grid is located at ((NX+2)/2, (NY+2)/2, (NZ+2)/2). 

10.3.2 Grid Size 

It is recommended that the extents for each individual grid—NX, NY, NZ—be even numbers, 
leading to odd numbers of grid points in each direction, NX+1, NY+1, NZ+1. Each dimension 
must be at least 2, with typical values in the range of 16 to 40. There is no set maximum, but 
dimensions in excess of a few hundred are not recommended. 

10.3.3 Object Placement 

GridTool allows the position of the object to be adjusted within the grid structure. By default, the 
center of the object’s bounding box coincides with the center of the primary grid. In general, the 
object placement and main grid spacing should be chosen so that spacecraft components are not 
coincident with grid planes with two exceptions. Flat panels, such as solar arrays, are best placed 
to coincide with grid planes (so as not to subdivide volume elements). In addition, booms are 
best placed so that they lie along grid lines (so as not to pierce the faces of volume elements). 

The object position may be adjusted so that low-capacitance objects (e.g., a small instrument on 
a long boom) lie closer to the grid boundary than high-capacitance objects (e.g., the spacecraft’s 
body or solar panels). 

10.3.4 Subdivision Recommendations 

It is recommended that the subdivisions in a child grid be a factor of two finer than those of the 
parent grid. Subdivision by factors of three or four may be used with caution. Subdivision by 
factors greater than four should be avoided. Sudden changes in resolution can lead to unphysical 
results. 


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Table 5. GridTool Menu Options 


GRIDTOOL MAIN MENU AND MOVEMENT/ORIENTATION TOOLS 


PARAMETER 


DEFINITION 


| File 

Open Database 

Open existing database fde. 

Import Object 

Import object fde (•'.xml ) created with Object Toolkit. 

Import Grid 

Import existing grid fde (*.grd). 

Save Grid 

Save newly created or modified grid. As the object dimensions are stored in 
the grid fde, the object must be present for the grid fde to be valid. 

Exit 

Exit GridTool. 

| Edit 

Undo/Redo 

Not implemented. 

Cut 

Not implemented. 

Copy 

Not implemented. 

Paste 

Not implemented. 

View 

Enabled when Results 3D tab is displayed. 

Display special objects 

Turn display of special objects defined in Object Toolkit off or on. 
When the object is read by selecting “Open Database” on the File 
menu special objects never appear. 

Set background color 

Set background color of 3D display area to black or white. 

Set outline color 

Set color of lines outlining surface elements to black or white or do 
not display lines (off). 

| Grid 

New Primary Grid 

Create a new primary grid. 

Add Outer Grid 

Create a new outer grid with twice the linear dimension of the current 
primary grid, and modify the existing grid structure accordingly. 

New Child Grid 

Create a new child of the selected grid. (Enabled when a grid is selected in 
the right-side panel.) 

Delete Grid 

Delete selected grid. (The primary grid cannot be deleted.) 

Edit Grid 

Edit selected grid. (Enabled when a grid is selected in the right-side panel.) 

Move Object 

Specify location (meters) of object center relative to grid center. (Requires 
that an object be present.) 

1 Help 

GridTool Help 

View GridTool help fde. 

About GridTool Application 

Display GridTool version, copyright, and contacts information. 

| View tools 

■ 

nr 

V) 


Set Cursor Tools to rotate and translate the view. 

XY 

xz 

3 

-XY 

-XZ -ZY 

View from specific direction. 

tsE 

d 


Translate Left/Right, Up/Down. 

CJtJ 


Zoom In/Out. 

GDEJ 

\5i 



Rotate about axis. 

EJHJ 


In-plane rotation. 


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10.3.5 Child Grid 


A child grid is fully contained within its parent. A child of the primary grid may not touch the 
primary grid boundary. A child of a non-primary grid may touch the boundary of its parent for 
the purpose of sharing a boundary plane with a cousin grid. Examples of correct and incorrect 
subdivision are shown in Figure 10. The left-hand figure shows two child grids properly meeting 
at a common boundary. The center figure shows two child grids (cousins) properly touching the 
boundaries of their respective parents for the purpose of sharing a common boundary. The right- 



hand figure shows two examples of child grids improperly touching their parents’ boundaries. In 
the egregious case (red) the twice-subdivided grid shares a boundary of its parent with the 
primary grid. In the subtle case (burgundy) the twice-subdivided grid shares a boundary with a 
coarser grid that is not its parent. 


Figure 10. Examples of Correct (Left and Center) and Incorrect (Right) Subdivision 


10.3.6 Grid Overlap 

Sibling grids (i.e., children of a common parent) may not overlap. However, they may touch (i.e., 
share a common boundary plane). 

10.3.7 Boundary Plane Resolution 

The resolution of the boundary between two grids is the coarser (parent) resolution (i.e., the grid 
points belonging only to the finer grid are assigned values interpolated from the coarser grid). 
This is necessary to maintain continuity of potentials and electric fields. As an exception, the 
boundary between two abutting grids of equal mesh spacing is fully resolved. 

10.3.8 Grid Resolution 

It is recommended that the grid resolution near the object be comparable to the size of the 
object’s surface elements. It is recommended that the grid resolution in the “sheath region” be as 
few Debye lengths as possible. (Two Debye lengths is ideal, but a few tens of Debye lengths is 
more common.) 


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11 Specifying the Environment (Environment Tab) 

Presently, Nascap-2k supports geosynchronous, low Earth orbit or plume, auroral, and 
interplanetary environments. Common to all four are the options to specify the local magnetic 
field vector, the direction toward the sun, the (relative) sun intensity at the location of the 
spacecraft, and mass, charge, and percent of plasma density for up to one-hundred species of 
particles. Note that the intent of these differing environment specifications is not to restrict 
Nascap-2k to particular classes of orbits, but to provide the choice of parameters commonly used 
to describe the plasma environments in those orbits. 

11.1 Geosynchronous Earth-Orbit Environment 

The tab for definition of a geosynchronous environment is shown in Figure 11. For the 
geosynchronous environment, four predefined environments are available. These environments 
are as follows: 


• Worst Case: The standard NASA “worst-case” charging environment defined in 
Reference 9. 

• ATS-6: Double-Maxwellian approximation to an environment once measured by the 
ATS-6 spacecraft. 

• Sept. 4 th 1997: Double-Maxwellian approximation to an environment measured on the 
specified day by the Fos Alamos Magnetospheric Plasma Analyzer. 

• SCATHA-Mullenl : Double-Maxwellian approximation to the environment which 
produced the worst vehicle charging ever measured by SCATHA (April 24, 1979, 0650 
UT, as given in Mullen et al, 1981 10 ). 


The values for the predefined environments are summarized in Table 6. Additionally the user 
may select “User Defined.” “User Defined” environments can be parameterized as Single- 
Maxwellian, Double-Maxwellian, Kappa, or Measured. The second column available for 
specifying density and temperature is for cases in which a Double-Maxwellian distribution for 
electron and/or ions is used. 


The differential flux (m 2 s 1 cV ') for the Single-Maxwellian, Double-Maxwellian, and Kappa 
distribution functions are given by the following formulas: 


Single Maxwellian 


Double Maxwellian 


Kappa Distribution 


F(E) = . 

f(e )= 1 
f(e)= 


e E 
2jr0m 0 

e E 


f e/ 


nexp 


V oy 


27i9im Oj 


- n | exp 


( _E A 
V 0 17 


+ 


27T02m 0; 


-n 2 exp 


f _E A 

v 0 2; 


27tK0m K0 


-n 


f \ 

r(t +1) 


r k- 


f TJ X K 1 


1 + - 


K0 


( 1 ) 

( 2 ) 

(3) 


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Where n, 9, and, k are the density, temperature, and kappa parameter, e and m are the electron 
charge and charged particle mass. A kappa distribution is similar to a Maxwellian, but with a 
superthennal tail. Kappa must be greater than 1. At large values of kappa (of order 10), the 
Kappa distribution reduces to a Maxwellian. 

The ionic composition is assumed to be 100% H + . 

The lower energy component of a double Maxwellian environment should be specified in the 
first column. 

Table 7 summarizes the list of input parameters for the Geosynchronous Environment tab. 



Figure 11. The Environment Tab for Studies in a Geosynchronous Plasma 


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Table 6. Predefined Geosynchronous Charging Environments 



WORST CASE 

ATS-6 

SEPT. 4 th 1997 

SCATHA- 

MULLEN1 

Electron Density (m 3 ) 

l.lxlO 6 

1.2X10 6 

3x10 s ; 2x10 s 

2.3x107; 2xl0 6 

Electron Temperature (eV) 

1.2X10 4 

1.6X10 4 ; 1000 

4000;7000 

2.48X10 4 ; 400 

Ion Density (m 3 ) 

2.4X10 5 

2.4x10 s ; 8820 

3x10 s ; 2x10 s 

1.3X10 6 ; 1.6X10 6 

Ion Temperature (eV) 

2.95X10 4 

2.95X10 4 ; 111 

4000;7000 

2.82X10 4 ; 300 

Electron Current (A/m 2 ) 

3.3xl0" 6 

4.1xl0" 6 

9.6X10' 7 

9.8x10 s 

Ion Current (A/m 2 ) 

2.5xl0" 8 

2.5xl0" 8 

2.2X10' 8 

1.5xl0e" 7 

Distribution 

Single Maxwellian 

Double Maxwellian 

Double Maxwellian 

Double Maxwellian 


Table 7. Input Parameters for the Geosynchronous Environment Tab 


GEOSYNCHRONOUS ENVIRONMENT 

PARAMETER 

DEFINITION 


| GEO Environment Plasma 

Drop-down list 

Options: User Defined, Worst Case, ATS-6, Sept 4th, 1997, and 
SCATHA-Mullenl (see Table 6). Plasma parameters available for editing only 
if “User Defined” is selected. 

Drop-down list (hidden in 
Figure 11) 

Options: Maxwellian, Double Maxwellian, Kappa, Measured. (Some of the 
following parameters are only available for specific options.) 

Electron Density 

Number density for the ambient electrons (m 3 ). 

Electron Temperature 

Temperature of the ambient electrons (eV). 

Ion Density 

Number density for the ambient ions (nT 3 ). 

Ion Temperature 

Temperature of the ambient ions (eV). 

Electron Kappa 

Kappa parameter for electron distribution. 

Ion Kappa 

Kappa parameter for ion distribution. 

Edit Measured... 

Specify tables of values of differential flux as a function of energy. 

Electron Current 

Electron thermal current (Am 2 ). 

Ion Current 

Ion thermal current (Am' 2 ). 

| Magnetic Field 

| Bx, Bx, Bz 

Components of the ambient magnetic field vector (tesla). 

| Sun 

Sun Direction (X, Y, Z) 

Direction toward the sun in the spacecraft frame of reference. 

Relative Sun Intensity 

Ratio of sun intensity at the spacecraft over the 1 AU value. 

Use photoemission spectra 

See Section 11.5. (Enabled only if at least one material has a photoemission 
spectrum defined.) 

Particle Species 

Specification of particle species through their mass, charge, and percentage of 
the total plasma density. Note that these species are used for particle tracking 
purposes only. 


Using Measured Spectra 

It is occasionally desirable to specify the incident electron and ion flux using a table of values. 
Clicking the “Edit Measured...” button on the Environment tab brings up the Measured 


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spectrum editor dialog box. ANascap-2k tabular definition of the incident charged particle 
spectra consists of a sequence of energy values in electron volts (lower bin boundary energy) and 
the differential flux in particles per m -sec-eV within the energy bin. The electrons and the ions 
are specified separately. As it is unused (due to unspecified upper bin boundary), the last value in 
the flux columns should be zero. Figure 12 shows the lower energy portion of a spectrum 
specification. 


Extreme caution should be used when using the “Measured” environment option, as inadequately 
characterized environments can lead to numeric instabilities or unphysical results. 



Figure 12. Measured Spectrum Editor Dialog Box 


11.2 Low-Earth-Orbit or Plume Environment 

The tab for definition of a low Earth orbit or plume environment is shown in Figure 13. The 
plasma density and temperature are specified. The Debye length is computed from the density 
and temperature. If the user changes the Debye length, the density is recomputed to be 
consistent. Both the spacecraft velocity vector and the particle species are specified here. Table 8 
summarizes the parameters that appear on the LEO or Plume Environment tab. 


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Nascap2k - C:\MyCalculations\Manuals\bipolar1\bipolarProject.xml 


File Edit View Materials Help 


Problem Environment Applied Potentials ~|" Charging Space Potentials Particles Script Results Results 3D 


LEO or Plume Environment 


Figure 13. The Environment Tab for Studies in a Low-Earth-Orbit or Plume Plasma 


- Direction to Sun ' 


X: 1.000 


V: 0.0 


Z: 0.0 


Relative* Sun Intensity] 1.0 00 _| 

*1 'value at Spacecraft) / (value at Earth Orbit) 


~ Particle Species 



- LEO Environment Plasma- 

Density °QQ e12 I 

Temperature (eV):| o.10Q | 

Deliye Length (m):[2 .351E-3 
Electron Current (Am 2 ): 8.477E-3 
Ion Current (Am" 2 ): 4.964E-5 

- Magnetic Field (T)- 

BxJ o.Q j Bjcl o.Q j Bz:| o.Q 

- Spacecraft Velocity (m/s)- 

VxJ o.Q j Vjcl o.o j Vz:| o.Q 


Table 8. Input Parameters for the LEO or Plume Environment Tab 


LEO ENVIRONMENT 

PARAMETER 

DEFINITION 


| LEO Environment Plasma 

Density 

Number density of the ambient plasma (m 3 ). 

Temperature 

Temperature of the ambient plasma (eV). 

Debye Length 

Debye length of the ambient plasma (m). 

Electron Current 

Electron thermal current (Am 2 ). 

Ion Current 

Ion thermal current (Am' 2 ). 

| Magnetic Field 

Bx, By, Bz 

Components of the ambient magnetic field vector (tesla) in the 
spacecraft frame of reference. 

| Spacecraft Velocity 

Vx, Vy, Vz 

Components of the spacecraft velocity vector (m/s). (Used for 
computing ram ion and wake effects.) 

| Sun 

Direction to Sun (X,Y,Z) 

Direction toward the sun in the spacecraft frame of reference. 

Relative Sun Intensity 

Ratio of sun intensity at the spacecraft over the 1 AU value. 

Particle Species 

Specification of particle species through their mass, charge, and 
percentage of the total plasma density. 


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11.3 Auroral Environment 


The tab for definition of an auroral environment is shown in Figure 14. The low energy plasma is 
defined by a Maxwellian with the ion species defined in the “Particle Species” box. The high- 
energy electrons are defined by a Fontheim 11 distribution. It has three high-energy components, 
specified by the net current in each component. The Maxwellian component describes a broad 
electron distribution, the Gaussian component describes the “inverted-V” part of the spectrum, 
and the Power Law component describes the secondary and backscattered electrons from 
interactions between the Gaussian beam and the rest of the plasma. The Power Law component 
only contributes at energies between specified lower and upper cutoffs. The density of each 
component is calculated based on its current and distribution function and displayed in the 
dialog. The electron differential flux (m s eV ) is specified by 


Flux(E): 


1 2710m. 0 


nexp 


^C m ax EeX P 


V ®max J 


■< s auss E eXp 


f 

f E 

F ^ 

2> 


gauss 



V 

<i 

) 

/ 




( 4 ) 


where n and 0 are the density and temperature of the low-energy ionospheric plasma, e and m e 
are the electron charge and mass, and the C, s, 9 max , E gau ss, A, and a are constants. Table 9 
summarizes the parameters of the Auroral Environment tab. 



Figure 14. The Environment Tab for Studies in an Auroral Environment 


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Table 9. Input Parameters for the Auroral Environment Tab 


AURORAL ENVIRONMENT 


PARAMETER 


DEFINITION 


Auroral Environment Plasma 

Low Energy 


Density 

Number density of the low energy (< 5eV) plasma (m' 3 ). 

Temperature 

Temperature of the low energy (< 5eV) plasma (eV). 

Debye Length 

Debye length of the ambient plasma (m). 

Electron Current 

Electron thermal current (Am 2 ). 

Ion Current 

Ion thermal current (Am' 2 ). 

Maxwellian 

Contribution to high energy auroral electron spectrum described by a 
Maxwellian. 


Electron Current 

Current of Maxwellian component of flux (Am' 2 ). 

Temperature 

Qmax in equation above (eV). 

Density 

Partial number density due to Maxwellian component of flux (m 3 ). 

Coefficient 

Cmax in equation above. 

Gaussian 

Contribution to high energy auroral electron spectrum described by a 
Gaussian. 


Electron Current 

Current of Gaussian component of flux (Am 2 ). 

Energy 

E S auss in equation above (eV). 

Width 

A in equation above (eV). 

Density 

Partial number density due to Gaussian component of flux (m 3 ). 

Coefficient 

Q>auss in equation above. 

Power Law 

Contribution to high-energy auroral electron spectrum described by a 
Power Law. 


Electron Current 

Current of Power Law component of flux (Am' 2 ). 

1 st Energy 

Minimum energy at which the Power Law portion of the flux equation 
contributes (eV). 

2nd Energy 

Maximum energy at which the Power Law portion of the flux equation 
contributes (eV). 

Exponent 

a in equation above. 

Density 

Partial number density due to Power Law component of flux (m' 3 ). 

Coefficient 

Cpower in equation above. 

Magnetic Field 


Bx, By, Bz 

Components of the ambient magnetic field vector (tesla) in the 
spacecraft frame of reference. 

Spacecraft Velocity 

Vx, Vy, Vz 

Components of the spacecraft velocity vector (m/s). (Used for 
computing ram ion and wake effects.) 

Sun 

Sun Direction (X,Y,Z) 

Direction toward the sun in the spacecraft frame of reference. 

Relative Sun Intensity 

Ratio of sun intensity at the spacecraft over the 1 AU value. 

Particle Species 

Specification of particle species through their mass, charge, and 
percentage of the total plasma density. 


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11.4 Interplanetary Environment 

The tab for definition of an interplanetary environment is shown in Figure 15. The plasma is 
taken to be a streaming Maxwellian. The density and temperature for the electrons and ions are 
defined. The ions species are specified in the table. The solar wind streaming velocity is the 
negative of the spacecraft velocity with respect to the plasma. By default, the ion current to 
surface elements facing in the velocity direction that are shadowed by other surface elements is 
zero. This behavior can be changed by changing the shadowlons attribute within the 
Environments folder of the Charge Surfaces command in the script (See Section 16.2 and 
Table 21). Table 10 summarizes the parameters of the Interplanetary Environment tab. 



Figure 15. The Environment Tab for Studies in Interplanetary Space 


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Table 10. Input Parameters for the Interplanetary Environment Tab 


INTERPLANETARY ENVIRONMENT 


PARAMETER 


DEFINITION 


Interplanetary Environment Plasma 

Electron Density 

Number density of the ambient electrons (m' 3 ). 

Electron Temperature 

Temperature of the ambient electrons (eV). 

Ion Density 

Number density of the ambient ions (m 3 ). 

Ion Temperature 

Temperature of the ambient ions (eV). 

Electron Thermal Current 

Electron thermal current (Am 2 ). 

Ion Thermal Current 

Ion thermal current (Am 2 ). 

Magnetic Field 

Bx, By, Bz 

Components of the ambient magnetic field vector (tesla) in the spacecraft 
frame of reference. 

Spacecraft Velocity 

Vx, Vy, Vz 

Components of the spacecraft velocity vector (m/s). (Used for computing ram 
ion and wake effects.) 

Sun 

Direction to Sun (X,Y, Z) 

Direction toward the sun in the spacecraft frame of reference. 

Relative Sun Intensity 

Ratio of sun intensity at the spacecraft over the 1 AU value. 

Use photoemission spectra 

See Section 11.5. (Enabled only if at least one material has a photoemission 
spectrum defined.) 

Particle Species 

Specification of particle species through their mass, charge, and percentage of 
the total plasma density. 


11.5 Using Photoemission Spectra 

Spacecraft in the solar wind or in a very tenuous plasma normally charge to positive potentials (a 
few volts to tens of volts) to balance the emitted photoelectron current with a very low current of 
ambient electrons. Determining just how positive a spacecraft charges requires knowledge of the 
high-energy portion of the photoemission spectrum. (This is not required for geosynchronous 
charging, in which surfaces never achieve positive potentials of more than a few volts.) 

Clicking the “Edit Photoemission...” button on the Material definition dialog box brings up the 
Photoemission Spectrum dialog box. The Material definition dialog box is discussed in 
Section 13.4. For Nascap-2k to realize that the explicit photoemission spectrum should be used, 
the user must at least view the default spectrum, even if she/he does not want to change it. 

ANascap-2k tabular definition of a photoemission spectrum consists of the total emission and a 
sequence of energy-value pairs, where the value indicates the fraction of the photoemission 
spectrum lying above the energy. As an example, Figure 16 shows a single spectrum based on 
data from the WIND spacecraft. Alternatively, the spectrum may be specified by an analytic 
formula, which gives the photocurrent above an energy as a sum of thermal components. The 
spectrum is scaled to give the specified total photoemission. The default analytic spectrum, taken 
from the paper of Nakagawa et al. 12 , is J = 53e~ E/16 + 21e~ E/3 + 4e~ E/89 . 


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The spectrum for each material must be set separately. In addition, for the Charge Surfaces 
module to use the specified photoemission spectrum, the script must include the second-level 
command “ReadPhotoemission.” If no spectrum is specified, the photoemission spectrum is 
assumed to be a 2 eV Maxwellian. However, note that tenuous plasma calculations that use a 
2 eV Maxwellian for the photoemission spectrum fail to predict the charging to tens of volts of 
positive potential that is commonly observed. 



Figure 16. Photoemission Spectrum Dialog Box 


Both close (~0.1 AU) to the sun where photoemission is high and on a very large spacecraft (e.g., 
Solar Sail) for which divergence is low, the density of photoemitted electrons can be so high that 
they fonn a space charge barrier to their escape. The barrier reduces the net photocurrent and 
lowers the surface potential. This problem was studied analytically by Guernsey and Fu, and, 
more recently, numerically by Ergun et al . 14 When the second level script command 
“SetParameters” with the argument “SpaceChargeLimitedPhotoemission” set to “On” is included 
in the script, a preliminary Nascap-2k model is used to compute the barrier height and reduce the 
net photocurrent and the secondary electron current. The model depends on the plasma density, 
the photoemission current, the spacecraft shape, and an assumed shape of the photoemission 
spectrum. Additional details are in Nascap-2k Scientific Documentation. 

12 Specifying Potentials on Surfaces (Applied Potentials Tab) 

Figure 17 shows the Applied Potentials tab for a two-conductor problem. This tab is used to 
specify applied and initial potentials on conductors and insulating surface elements. The top 
portion is used to specify if each conductor is (1) held at a fixed potential, (2) allowed to float, or 
(3) held at a fixed bias with respect to chassis ground (conductor 1). (A time-varying bias 


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potential can be specified directly in the script. See Section 16.2.) Potentials on conducting 
elements are assigned by specifying the value of the potential in the last column (“Initial 
Potential”). In Figure 17, the potential of conductor 1 is specified to be floating with respect to 
the environment with an initial value of 0 V, and conductor 2 is biased by -50 V from conductor 
1. Insulating surface elements not specified on the bottom portion of this tab are assigned the 
initial potentials of their underlying conductor. 

The lower portion of this tab is used to specify the initial potential on insulating surface 
elements. Elements are selected by material name, conductor number, and sunlit or dark 
condition. 

NOTE: When a material is changed from a conductor to an insulator or from an insulator to a 
conductor, Nascap-2k should be closed and restarted in order to update the materials available 
in this portion of the tab. 

Individual elements may also be specified by number. Presently, only fixed potential boundary 
conditions can be specified. In Figure 17, the potential of all the insulating elements of conductor 
1 are specified to be initialized to -100 V, and the potential of all the insulating elements of 
conductor 2 are specified to be initialized to +100 V. Table 11 summarizes the options on the 

Applied Potentials tab. 



Figure 17. Potential Initialization for Objects in a Two-Conductor Problem 


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Table 11. Input Parameters for the Applied Potentials Tab 


APPLIED POTENTIALS 


PARAMETER 


DEFINITION 


Conductor Potentials & Electrical Connectivity 

Conductor 

Specified by a numerical identifier (1, 2, etc.) during the definition of the 
object. 

Type 

Specifies the potential boundary condition on the conductor. Available options 
are Floating Potential, Fixed Potential (conductor 1 only), and Bias Potential 
(relative to conductor 1). 

Initial Potential 

Specifies the initial value of the conductor potential (V). Double-click field to 
edit. 


Insulating Surface Potentials 

Material 

Select surface elements of specified material. 

Conductor 

Select surface elements of specified underlying conductor. 

Sunlit/Dark 

Select surface elements by orientation with respect to the sun (facing toward 
or away). 

Surfaces 

Select specific surface element by number. 

Type 

Specifies the potential boundary condition on the specified surface elements. 
Fixed Potential is the only option at present. 

Initial Potential 

Specifies the initial value of the insulator potential (V). 


13 Surface Charging (Charging Tab) 

13.1 Background 

Spacecraft surface charging is the accumulation of charge on spacecraft surfaces. As illustrated 
in Figure 18, several different current components can contribute to the charging. 9,15,16,17 The 
high-energy incident electrons of the geosynchronous and auroral environments generate 
secondary electrons and backscattered electrons from surfaces. High-energy incident ions also 
generate secondary electrons. The current density of low-energy electrons generated by solar 
ultraviolet radiation normally exceeds that of the net plasma current in geosynchronous orbit and 
in interplanetary space. While, in low-Earth orbit (equatorial and polar), the incident low-energy 
particles dominate the current. 

Charging simulations are complicated by the fact that the rest of the spacecraft influences the 
potential of each surface. In order to compute surface potentials, spacecraft geometry, surface 
materials, and environment must all be considered. Each insulating spacecraft surface interacts 
separately with the plasma and is capacitively and resistively coupled to the frame and other 
surfaces. Nascap-2k uses this information to compute the time history of the surface potentials 
and fluxes. 


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Electrons 


/ 

/ 


Secondary, Backscattered, Photo Electrons 


Figure 18. High Negative Potentials Can Result from the Accumulation of Charge on Spacecraft 

Surfaces 

Figure 19 shows a circuit diagram for a spacecraft with one insulating surface element and 
exposed conducting surfaces. The widely differing capacitances of the surface to infinity, Ca, and 
of the surface to spacecraft ground, Cas, make this a complex numeric problem. 


— « — x 10 7 Farad 
d 2 



( 5 ) 


C A « C s « 47is 0 r« r xlO 10 Farad 


( 6 ) 


where k, d, and S are the dielectric constant, thickness, and surface area of the insulating surface 
element, r is the radius of an equivalent sphere, and s 0 is the permittivity of vacuum. The 
potentials as a function of time are computed using implicit time integration of the charging 
equations, which relate the derivative of the potential, <X>. with time to the current, I. 



(V) 


Insulating surface 

Cas v s Cs 


// 
Spacer 
chassis c 



V=0 


Plasma ground 


All conductive surfaces 


Figure 19. Circuit Model of a Spacecraft with One Insulating Surface Element 


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The multisurface problem is solved by linearizing the currents and inverting the matrix. 

CO> = l(0>) (8) 

13.2 Numerical Approach and Implementation in Nascap-2k 

Among the difficulties of developing accurate and robust algorithms for spacecraft charging has 
been the inability to calculate accurate electric fields, let alone predict how electric fields change 
as a result of surface potential changes. Nascap-2k uses the Boundary Element Method 7 to 
calculate accurate electric fields and as the basis for implicit charging equations. 

The Boundary Element Method is a means for relating fields and potentials in a region to sources 
on the region’s boundary. It is comparable to a sum over the coulomb fields of all the charges in 
a region rather than an iterative field solution. In our case, the region is the space exterior to a 
spacecraft and the boundary is the spacecraft surface. Also, we assume the “free space Green’s 
function.” i.e., the potentials in the region obey Laplace’s equation. 

The Charging tab shown in Figure 20 is used to specify the time-stepping parameters used in 
calculations of surface charging. The parameters are summarized in Table 12. If the Results tab 
display indicates that potentials are unphysically bouncing up and down from one timestep to the 
next, taking more (shorter) timesteps may reduce or eliminate the problem. The “Start Time” and 
“End Time” allow specification of a sequence of changing environments for specified time 
intervals. 


A reasonable timestep is x = — A(J>, where j is the maximum surface current density, c is the 

c 

appropriate capacitance per unit area, and Acf) is an approximate change in potential during the 
timestep. The appropriate capacitance is either the capacitance to space for overall charging or 
the capacitance to the underlying conductor for differential charging. In denser plasmas, the 
timesteps should be set much shorter than the default values. As the Boundary Element Method, 
used to determine the system capacitance, assumes no plasma, the calculated chassis charging 
rate in dense plasmas is generally unrealistically fast. However, the steady-state solution, which 
is detennined by current balance, and the differential charging rates, detennined by surface-to- 
chassis capacitance, is correct. 

Script options (see Section 16) are used to specify whether the environment currents are given by 
analytic expressions or by the most recent tracked particle currents. When the environment 
currents are specified analytically, the values are given by the orbit-limited current from the 
specified environment, which is usually correct for the repelled species but not for the attracted 
species, especially in dense plasma. The LEO and Solar Wind plasmas are taken to be flowing 
Maxwellians. The low energy component of the auroral plasma is also taken to be a flowing 
Maxwellian. For dense plasma with a Debye length short compared with the system size, this 
assumption may significantly overestimate the environment current. In a long Debye length 
plasma, this assumption overestimates the environment current to cavities and other shielded 
regions. 

The environment specified in the script is used to determine the secondary and backscattered 
yields even if the environment currents are computed by particle tracking. 


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File Edit View Materials Help 

| Problem ~| Environment Applied Potentials Charging Space Potentials | Particles ~j Script [ Results | Results 3D 


Charging Time - 


Start Time (sec):l o.Q 


End Time (sec):l 300 0~ 


Min Timestep (sec):l o.1QQ~ 


Max Timestep (sec)j 60.00~ 


Number of Timesteps*:|45 


Figure 20. Charging Tab: Specifying Parameters for Spacecraft Charging Calculations 
Table 12. Input Parameters for the Charging Tab 


CHARGING 


PARAMETER 


DEFINITION 


Start Time 

Time (sec) to start charging calculation (usually zero). 

End Time 

Time (sec) to end charging calculation (usually real-time duration). 

Min Timestep 

Shortest (first) timestep (sec) during charging calculation. 

Max Timestep 

Longest (final) timestep (sec) during charging calculation. 

Number of Timesteps 

Total number of timesteps used during the charging calculation. Same quantity as 
“Number of Iterations” on the Space Potentials tab. 


13.3 Monitoring the Calculation 

When a charging calculation is launched, the Script Running Monitor indicates the progress of 
the calculation. The monitor shown in Figure 21 is for a sample charging calculation of a 
spacecraft in a geosynchronous-type environment. The monitor displays, among other 
information, the simulated time, the clock time, and the minimum and maximum spacecraft 
potentials at the present timestep. 


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Figure 21. Script Running Monitor Showing Charging Calculation 


13.4 Materials 


A material name is associated with each surface element of the Nascap-2k object. Each material 
name is in turn associated with a set of material properties than can be edited, either in Object 
Toolkit or Nascap-2k, using the Materials menu. Nascap-2k uses these properties to determine if 
each element is an insulator or a conductor and then to compute each of the components of the 
net current to each element and through each element to the underlying conductor. The Material 
dialog box is shown in Figure 22. The “Reset to Default Properties” button restores material 
property values to their default values for the displayed material. 


£ile Edit VMaterials Help 
Problem Envi Edit Npaint... 


als Charging Space Potentials Script Results Results 3D 


Interplane I 


I Edit Graphite... 

I Edit Teflon... 

I Edit Kapton... 

Edit Aluminum... 
Edit Gold... 

I Edit OSR... 

I Edit Black Kapton... 


Magnetic. 

BxjPQ 


wm Edit Solar Cells.. 

H Edit Nextel... 

H Edit Columbium. 
M Edit Composite.. 
M Edit Radiator... 
le Edit Quartz... 
M Edit Anodized... 
Edit AZ93... 

I Edit HotNextel... 


Interplanetary Environment 





J lJl-000E8 




_I ByfocT 


Spacecraft Velocity with Respe 

Vxj 2 768E5 j Vyj -2768 


Name: Solar Cells 


Reset to Default Properties 


Dielectric Constant 3 800 


Proton Yield: 0 244 


Thickness(m): 1 500E-4 
Bulk Conductivitvtohms~ 1 m' 1 >:! 1 000E-10 | 


Proton Max(eV): 230 0 


Atomic Number: 10 00 


Photoemission(A m' z l:| 2 000E-5 
Surface Resistivity(ohms/square): j 1 000E19 


Delta Max: 5 800 


Atomic Weight(amu): 20.00 


E-Max(keV): 1 000 


Densityfkg m 3 ):|2660 


Range 1 (A): j 77 50 


Exponent 1:| o 450 


Not Used 1:|l7_00 
Not Used 2: ll8.00 


Range 2(A): j 1 56 1 


Rad. Cond.:;1 000E-18 


Exponent 2: 1 730 


Transparency: 0 0_ 


Edit Photoemission... 


Figure 22. Nascap-2k Materials Menu Showing Material Property Editing Dialog Box 


The “Import Materials from SEE Handbook” option on the File menu allows users to import 
material property files in the format created by the SEE Interactive Spacecraft Charging 
Handbook. We recommend the SEE Handbook as an aid to the determination and preliminary 
assessment of material property sets. To use material definitions from the SEE Handbook in 


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Nascap-2k, first define the materials in the Handbook. Save the Handbook parameters by 
clicking the “Save” button along the top and note where the file is saved. In Nascap-2k, select 
“Import SEE Handbook Materials File...” on the File menu and browse to the saved file. 

A folder of material properties measured by Utah State University in this format is placed in the 
installation folder (Nascap2k_4/Materials) during the Nascap-2k installation. 

The meaning and use of each of the material properties are listed in this section. Additional 
details of the yield models are in Nascap-2k Scientific Documentation. 

Dielectric constant. This property is the relative dielectric constant for an insulating material 

(9) 

where s is the absolute dielectric constant and s 0 is the dielectric constant of free space, k is 
dimensionless. It is ignored for conductors. 

Thickness. This property is the thickness of a dielectric film covering an underlying conductor 
in meters. It is ignored for conductors. 

Bulk conductivity. This property is the bulk conductivity of the surface material in ohms' 1 m. 

A negative value indicates that the material is a conductor. If the bulk conductivity is in excess of 
10" 4 Q' 1 m' 1 , the material should be defined as a conductor (value of-1). NOTE: When a material 
is changed from a conductor to an insulator or from an insulator to a conductor, Nascap-2k 
should be closed and restarted. 

Atomic number. This property is the atomic number for pure elements or the mean atomic 
number for chemical compounds; e.g., polyethylene (CH 2 ) n has a mean atomic number of (6 + 1 
+ \)H> = 2.7. This value is used to compute the electron backscatter yield. 

Secondary yield (“Delta-Max” and “E-Max”). These properties give the size and location of 
the maximum in the secondary electron yield curve. The secondary yield is the current of 
secondary electrons emitted over the incident electron current. The secondary yield curve is a 
plot of secondary yield for normally incident electrons, against the incident energy of the primary 
electron E. This is shown in Figure 23. 8 max is unitless and E max is in keV. 


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Figure 23. Electron Secondary Yield as a Function of Incident Energy 

Electron range (“Range 1,” “Exponent 1,” “Range 2,” “Exponent 2”). Part of the secondary 
electron emission fonnulation requires an analytical form for the “range” of electrons in the 
material. The range is the depth to which the electrons can penetrate the material as they are 
continuously slowed down by losing energy to the material lattice. Nascap-2k uses a bi¬ 
exponential form. If bi, qi, ly, and q 2 are the four properties, the range R is given by 


R = b!E qi +b 2 E q2 


( 10 ) 


where the bs are the “Range” parameters and the qs are the “Exponents.” The four parameters are 
obtained from fits to stopping power data. The range is determined in angstroms. If no reliable 
stopping power data or four parameter fits are available, the range may be estimated from 
Feldman’s formula automatically by assigning -1 to Range 1. In this mode these properties are 
assigned as follows: 


Range 1 
Exponent 1 
Range 2 
Exponent 2 


-1 

null 

"5 

material density (g cm ) 
mean atomic weight (AMU) 


Ion-induced secondary emission (“Proton Yield” and “Proton Max”). Secondary emission of 
electrons due to ion impact is treated using a two-parameter fit. “Proton Yield” is the yield for 
1 keV normally incident protons and “Proton Max” is the proton energy in keV that produces the 
maximum electron yield. The secondary emission properties due to the impact of ions other than 
protons are assumed to be identical to the proton values for the same energy. 


Photoemission. This property contains the yield of photoelectrons from the surface material 
exposed to a normally incident solar spectrum in amperes per square meter. 

Surface resistivity. This property gives the intrinsic surface resistivity in “ohms per square.” 
This rather odd unit is used to distinguish the resistivity coefficient from the actual surface 
resistance (in ohms). Consider two points in a plane A and B, a distance Li apart. If L 2 is the 
“width” of the plane 


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surface resistance = surface resistivity x -p- 

L 2 

i.e., ohms = (ohms per square) x dimensionless geometrical factor 


i 

1-2 

Li 

A * 

* B 

r 


Figure 24. Illustration of Surface Resistivity 

Nascap-2k uses the surface resistivity per square times and the surface geometry to detennine the 
surface resistance between two adjacent surface elements or between a surface and a grounding 
element. The intrinsic surface conductivity is due to the migration of electrons along the surface 
layer, possibly aided by adsorbed impurities and defects. A negative value indicates that the 
material is a conductor. 

Transparency. This property is used to model current collection of transparent surfaces, such as 
wire meshes. The fraction of the incident current (analytic and tracked) collected by each surface 
element is (1 -t), where t is the transparency. Caution should be exercised when using non-zero 
values with tracked currents, as all particles are stopped by the surface element—leaving some of 
the current unaccounted for. 

Other properties. The “Atomic Weight,” “Density,” and “Rad. Cond” values are not used at 
present by Nascap-2k. 

13.5 Surface Conductivity 

Nascap-2k can include surface conductivity in charging calculations. Surface conductivity 
operates between insulating surface elements of a common material and with a common edge, 
thus covering transport over a wide expanse of such material. The material can be grounded by a 
strip at a surface element edge or by a circular contact located at a node. Grounding edges and 
nodes are specified within Object Toolkit by selecting the “Conductivity” option on the Mesh 
menu. Grounding elements can be specified only for primitive components, because other types 
of components frequently have their meshes re-created. A grounding edge establishes 
conductance to ground from each of the two neighboring elements of L/Dk , where L is the 
length of the edge, D is the distance from the center of the surface element to the center of the 
edge, and k is the surface resistivity of the material. A grounding node establishes conductance to 

Q 

ground from each of the neighboring elements of —-———-, where Q is the angle the element 

(ln(D/r)Kj 


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subtends at the node, D is the distance from the element center to the node, and r is the user- 
specified node radius. 

14 Calculating Electric Potentials in Space (Space Potentials Tab) 

To compute space potentials, the user checks “Potentials in Space or Detector Analysis” on the 
Problem tab. There are many reasons why calculation of the potential structure in the 
surrounding space might be desired, including the generation of sheath currents and the study of 
charged particle trajectories. 

A number of space charge formulations are available in Nascap-2k for solving Poisson’s 
equation, — V 2 c() = p/s 0 , for the electrostatic potential about the object. Space charge may be 
computed either fully by particles, fully analytically, or in a hybrid manner, and with flexible 
boundary conditions on the object and at the grid boundary. Figure 25 shows the Space 
Potentials tab, which is used to select a charge density model and specify parameters for the 
potential solution. The available charge density models are described in Section 14.1. The input 
parameters that appear on the Space Potentials tab are listed in Table 13. 



Figure 25. Space Potentials Tab, Used to Specify Options and Parameters for Calculation of 

Potentials in Space 


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Table 13. Input Parameters for the Space Potentials Tab 


SPACE POTENTIALS 


PARAMETER 


DEFINITION 


Charge Density Model 

The charge density models that are available depend on “Problem Type” parameters 
selected on the Problem tab. 

Laplace 

Zero space charge. 

Linear (Debye Shielding) 

Linear (Debye) shielding. 

Non-linear 

Standard equilibrium space-charge formula for high-density plasmas. 

Frozen ion 

Ion density equal to the ambient plasma density everywhere. Electron density is nxexp(<|)/0) 
for negative potentials, and n(l + 6/0) for positive potentials. 

Barometric 

Ion density equal to the plasma density decreased by the wake factor. Electron density 
is nexp(6/0) for negative potentials, and nx(l + 6/9) for positive potentials. 

Full Trajectory Ions 

Space charge from ion trajectories. Electron density is nxexp(6/0) for negative potentials, 
and n x (l + 6/0) for positive potentials. Used to calculate potentials in space self- 
consistent with ion trajectories. “Non-linear” used for initialization. 

Plume Ion Density 

Use ion density computed by summing the contributions from the thruster plumes in full 
trajectory ions expression for charge density. Requires imported plume map. 

Hybrid PIC 

Ion density from tracking of macroparticles. Electron density is nxexp(6/0) for negative 
potentials, and n x (l + 6/0) for positive potentials. Only available for time-dependent 
plasma calculations. “Non-linear” used for initialization. 

Full PIC 

Ion and electron densities from particle tracking results. Only available for time-dependent 
plasma calculations. “Frozen ion” used for initialization. 


Geometric Wake 
Initialization 

Compute wake of the (uncharged) object (Neutral Approximation), using the “Spacecraft 
velocity” (as specified on the Environment tab). The calculation is only done in a “New” 
potential run (iteration 0). (Option is only available in dense plasmas: LEO and auroral.) 

Species 

Mass of the selected species is used to compute geometric wake. (Mass is defined on the 

Environment tab.) 

Target Average (RMS) 
Error 

Root mean square error below which the potential is considered converged. 

Minimum Density (m' 3 ) 

Reference density n min for “Full Trajectory Ion” or “Plume Ion Density” calculation. 


Iteration 

Relevant only for iterative (“Self-consistent with Ion Trajectories,” “Consistent with Plume 
Ion Densities,” and “Charging” with “Tracked Particle Currents”) and “Time-dependent” 
calculations. 

Number of iterations 

Number of times to iterate using preexisting solution. 

Fraction old potential 

Fraction of potential solution from previous iteration of the potential solver to use in new 
iteration. 

Fraction old density 

Fraction of density solution from previous iteration of the particle tracker to use in new 
iteration. 


Ion Plumes 

Relevant only for calculations involving an ion thruster plume. 

On 

Indicates if thruster plasma is included in potential solution. 

Thruster 

Name of thruster as defined in Object Toolkit. 

Location 

Location of origin of thruster in meters in coordinate system used by Results 3D tab. 

Direction 

Direction of Z-axis of thruster coordinate system. 


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14.1 Available Space Charge-Density Models 

Additional infonnation on the charge density models can be found in Section 1.4.1 of Nascap-2k 
Scientific Documentation. 

Laplace. The Laplacian space charge option specifies that the charge density is zero, i.e., charge 
exists only on object surfaces and external boundaries, as detennined by the boundary 
conditions. “Space charge” iterations may still be required, however, due to the treatment of 
surface electric fields. 

Linear (Debye Shielding). The Linear space charge option solves the Helmholtz or Debye- 
Hiickel equation: 


_V 2 (j) = A = _^y (11) 

£ o k D - 

Non-Linear. The Non-linear space charge option is appropriate for most low Earth orbit type 
plasmas. It accounts for space charge acceleration and convergence in a manner based on 
spherical collection (Langmuir-Blodgett problem). 

Frozen Ion. The frozen ion fonnulation is intended for short timescale (typically sub¬ 
microsecond) problems for which it is a good approximation to assume that ions remain 
stationary and at ambient density (“ion matrix” approximation), but electrons achieve barometric 
equilibrium. 


Barometric. This algorithm is for cases in which all the surfaces are at potentials comparable to 
or below the plasma temperature and there is a region of low density, such as a plasma wake. The 
ion density is given by the plasma density decreased by the wake factor and the electrons are 
treated as barometric. In a dense, short Debye length plasma, the requirement that the ion and 

^ n ion ( x )^ 


electron densities be nearly equal gives strictly barometric potentials, § = 01n 


which 


V n J 

are negative in regions of ion depletion. In plasmas with a longer Debye length, the wake 
potential will be considerably less negative. The barometric fonnulation is not appropriate for 
problems in dense plasma with well-formed space charge sheaths. 


Full Trajectory Ions. Ion densities are calculated from steady-state ion trajectories. Electrons 
are barometric. This algorithm is typically used for steady-state calculations in which geometric 
or angular momentum considerations limit the access of ions to portions of the computational 
space. Minimum density should be set 4 to 6 orders of magnitude less than ambient. 


Plume Ion Density. Ion densities are computed from the imported plume map file. Electrons are 
barometric. After the initial iteration, the ion density is computed by summing the main beam 
contribution from the thruster plumes and the charge density contribution from tracking particles. 
Tracked particles are assumed to be charge exchange ions. Additional infonnation is available in 
Appendix E. Minimum density should be set to the ambient value. 


Hybrid PIC. This algorithm is used for timescales (typically sub-millisecond) on which it is 
practical to treat ion motion, but electrons may be considered in barometric equilibrium. The 
total charge density is the sum of the tracked ion and barometric electron charge densities. 


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47 



Full PIC. For this option, it is assumed that both the electron and ion-charge densities were 
obtained by particle tracking. 

14.2 Grid Boundary Conditions 

For choices of space charge density model in which potentials are substantially screened within 
the computational space, the nodes on the outermost grid boundary are set to zero. If the space 
charge density is taken to be zero (the “Laplace” option) the boundary potential is determined by 
matching an inverse radial falloff outside the grid. If the “Linear” option is chosen, the boundary 
potential matches a screened inverse radial falloff outside the grid. 

14.3 Advanced Potential Solver Parameters 

Users have a variety of options to control the potential solver. For most calculations, the default 
values work well. Figure 26 shows the available parameters on the Advanced Potential Solver 
Parameters dialog box. Table 14 provides descriptions of all the parameters. 



Figure 26. Advanced Potential Solver Parameters Dialog Box 


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Table 14. Input Parameters for the Advanced Potential Solver Parameters Dialog Box 


ADVANCED POTENTIAL SOLVER PARAMETERS 


PARAMETER 


DEFINITION 


Debye Scaling 

Specifies if “DebLim” parameter is applied based on the local grid spacing or on the 
primary grid spacing. 

Timer Level 

Specifies how often the time since Windows started is output. 

Convergence 

For the nonlinear space charge formulation, estimate convergence of attracted particle 
trajectories using local electric field. 


Wake 

Parameters used to compute geometric wake. 

NADD 

Number of extra vertices to add to compute object shadow for geometric wake 
calculation. 

NPHI 

Number of polar angle divisions in geometric wake calculation. 

NTHETA 

Number of azimuthal angle divisions in geometric wake calculation. 


Convergence Criteria 

Normally only the parameters “Maxits” and “RDRmin” are varied from their default 
values. 

Maxits 

The maximum number of major or “space charge” potential iterations to be performed. 

RDRmin 

The value of the “RDotR” parameter below which the potential is considered 
converged. 

Maxitc 

The maximum number of minor iterations within each conjugate gradient solution. 

PotCon 

The number of orders of magnitude that the RDotR parameter drops within each 
conjugate gradient solution before it is considered converged. 

DebLim 

The number of Debye screening lengths allowed per volume element. The various space 
charge formulas limit the amount of space charge in an element in accordance with this 
parameter. 


Grid 

It is possible to apply the potential solver to a subset of the Nascap-2k grids. 

Low/High 

Minimum and maximum grid numbers defining the range of grids in which potentials 
are to be computed. Only useful for special diagnostics calculations. 


Save Results 


Save to fdes every 

How often potentials are saved in time-dependent problems, 

iterations starting with 

starting at this iteration. 


Diagnostics 

These parameters govern optional diagnostics output from various portions of the 
potential solver. Level 1 (least) through 5 (most) for each phase of potential calculation. 

Initial 

Print initial potential values. 

Final 

Print final potential values. 

SCG 

Scaled conjugate gradient details. 

Screen 

Space charge screening details. 

Special 

Custom routines. 

Interf 

Grid interface details. 

Wake 

Geometric wake details. 


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14.4 Monitoring the Calculation 

This section discusses the operation of the potential solver from the point of view of monitoring 
its progress. In Nascap-2k the Script Running Monitor displays progress of the calculation of 
potentials in space, and an output file records the potential solution’s progress in detail. 



Figure 27. Script Running Monitor Showing “Potentials in Space” Calculation Progress 

A potential solver run consists of an initialization phase, a number of major (space charge) 
iterations of the potential solution, and a brief exit phase. In the initialization phase, the input 
parameters are read and echoed, and the database information is processed. Grid information 
(mesh size and sheath potential) are written to the output file. The grid interface pairs list is 
fonned and written out. Conductor potentials are also written out. 

At the beginning of each major potential iteration, the space charge function and its derivative 
are evaluated volume element by volume element, and the conjugate gradient process is 
initialized. The “Initial RDotR” is a measure of the current error in the potential solution. For 
many cases the “Initial RDotR” decreases monotonically beyond the first few major iterations, 
but lack of such behavior is common and does not indicate an error. 

During the conjugate gradient process, the “RDotR” parameter is displayed for each minor 
iteration. This parameter should generally decrease, but for most cases does not decrease 
monotonically. The conjugate gradient process is deemed converged when the “PotCon” 
convergence criterion is satisfied. 

The most time-consuming task of the exit phase is to calculate and update surface electric fields 
This requires a full matrix operation, as the electric field value is related to the residual for the 
corresponding potential. The differences between the new and previous potential solutions are 
expressed as root-mean-square (RMS) errors. If the root-mean-square errors remain constant, 
solution-mixing may ameliorate or solve the problem. The potential solver concludes when the 
requested number of major iterations has been performed or when the RMS error has been 
reduced below its requested value. 

15 Calculations Using Particles (Particles Tab) 

In Nascap-2k macroparticles may be generated and tracked for the purposes that include: 

■ Studying and/or displaying representative particle trajectories 

■ Calculating surface currents arising from sheath currents 


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50 






■ Studying wake structure 

■ Calculating steady-state, self-consistent charge densities 

■ Calculating time-dependent charge densities and surface currents. 

As not every electron or ion can be treated individually, the individual charged particles are 
collected into macroparticles. Each macroparticle is then treated as a single particle. Henceforth, 
references to generating and tracking “particles” in Nascap-2k refer to macroparticles. 

The Particles tab is used to specify parameters for the particle generation and tracking. The 
Create Particles module defines the particle species and generates particles as appropriate to the 
present problem, which may be throughout a volume, along a sheath surface, along a contour 
line, at problem boundaries, at surface elements, or in accordance with external input. The Track 
Particles module computes the motion of all or a subset of the particles for a maximum time, 
recording surface currents, accumulating steady-state charge density, or calculating the new 
charge density at the updated time. After the particle tracker executes, the particle files are left 
with updated particle positions and velocities, and the time and cycle number is updated in the 
database. Plotting trajectories is addressed in Section 17.2. 

The Particles tab has three subtabs (see Figure 28 to Figure 30), which are enabled depending on 
the choice of “Problem Type” defined on the Problem tab. Table 15 summarizes the parameters 
on the Particles tab. 


File Edit View Materials Help 

Problem [ Environment j Applied Potentials (Charging f 1 ' Space Potentials | Particles | Script [ Results ] Results 3D | 


Surface Currents \ Ion Densities [^Time-Dependent 


Potential Value (V)j 1.724 

Number per zone: 


Charged particles used for surface current calculation 

Initial Particle Distribution- 

<D Sheath 
O B Field 
O Boundary * 

O Charge Exchang 
G Surface* 

G None of above 
□ External File 


’Additional 


ters on advanced screen 

- Particle Species- 

Electron 
■ Oxygen 


Figure 28. Surface Currents Subtab for Generation and Tracking of Surface Currents 


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SM® 


Nascap2k - C:\MyCalculations\ManualsVChaws\Withlterations\ChawsProject.xml 


File Edit View Materials Help 

Problem j Environment Applied Potentials If Charging Space Potentials Particles | Script Results Results 3D ( 

Surface Currents Ion Densities ] Time-Dependent | _ 


Ions used to self-consistently compute ion density and potentials 
- Initial Particle Distribution- 

O B Field Number per zone: ]4 

® Boundary (Additional parameters on advanced screen.) 

Cross SectionOO 20 M 2 ): 

O None of above 

□ External File Filename: Browse 


“ Particle Species 
Oxygen 


Advanced 


Figure 29. Ion Densities Subtab for Generation and Tracking of Particles for Potentials that are 

“Self-Consistent with Ion Trajectories” 



Figure 30. Time-Dependent Subtab for Generation and Tracking of Time-Dependent Plasma 


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15.1 Generating Particles 

The choices of initial particle distribution are as follows: 

Contour. Generate particles at the intersection of a cut plane and a constant potential surface 
(such as a sheath). This option is available for visualization only. (See Section 17.2.) 

Sheath. Generate particles representing sheath currents at a sheath surface of specified potential. 
The current density created at a specific sheath section is the plasma thennal current adjusted to 
account for the ambient magnetic field and the velocity. 

Care must be taken when choosing the sheath potential, particularly in cases of high surface 
potential (compared to temperature) and short Debye lengths (compared to the mesh size). In a 
highly resolved problem, the appropriate sheath edge potential would be 91n2, where 9 is the 
plasma temperature in eV. However, this value must be adjusted at high potentials as Nascap-2k 
limits the rate at which space charge can cause the potential to drop. The Potentials in Space 
module writes the appropriate value to use for each grid to its output file. See Section 17.3.2. The 
following discussion describes how this value is determined. 

The distance in which a specified potential is screened to zero, known as the Child-Langmuir 
distance, D C l, is expressed in terms of the potential, (j), and the Debye length, A, De bye> as follows: 

D CL =1.255|(^/9| 3/4 k Debye (12) 

Equating the above equation to the meshing spacing, L, gives 

<|> x =5.1xl9“ 6 L 4/3 9 1,3 n 2/3 =9.74(L/k Debye ) 4/3 9 (13) 

for plasma density n. The potential (j) x may be interpreted as the potential below which 
Nascap-2k underestimates screening. At best, beyond the (j) v contour, the potential drops about 
one order of magnitude per volume element. For 9 = 9.1 eV, n = 19 m' , and L = 9.2 m, we find 
(j) x = 6 V. If the 6 V contour is correctly placed, the 9.6 V contour lies at least one element beyond 

(at the approximate sheath location), and 91n2 (9.97 V) is yet another element farther. This would 
produce a sheath area that is too large. The suggested criterion for the sheath boundary potential is 

4>SB =Max(9hi2,exp(- D iimH x ) (14) 

where exp(-Di im ) is the planar screening per element allowed by Nascap-2k. Note, however, that 
(j) x depends strongly on the grid in which the sheath is found, so that if an increase in object 

potential moves the sheath from grid 3 to its parent, grid 2, a corresponding larger value of cJ) SB 
should be used. The choice of the sheath boundary potential for a specific example is illustrated 
in Section 19.3.2. 

B Field. This option is used to generate particles where magnetic field lines enter the 
computational space. The particles have weights reduced by the cross product of the boundary 
nonnal and the magnetic field direction. The number of particles per volume element must be a 


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53 



square (1, 4, 9,...) as the particles are emitted in a square array from the surface of the boundary 
elements. The user interface displays the square root of the number of particles per element. 

Boundary. Generate a thermal distribution of particles at the problem boundaries. Additional 
parameters are available on the Advanced Particle Parameters dialog box (Section 15.3). 


Charge Exchange. Generate particles throughout space with current given by the product of the 
charge exchange cross section, the neutral density, and the main beam ion density. The main 
beam ion density is determined from the plume. Each component of the initial velocity is given 


by C 


2e0.3448 


m ; 


, where 0.3448 is 4000 K in electron volts and C, is a random number between 


-1 and 1. 


The neutral density is either specified in the plume map file or is the sum of the un-ionized 
propellant from the thrusters, the gas flowing through the neutralizers, and the background gas. 

At each point in space, the contribution from the thruster is given by the solid angle subtended by 
the thruster grid, the flow rate and the temperature. The contribution from the neutralizers is 

given by the flow rate, the temperature, and a factor of-—. The quantity vp is the angle 

Tir 2 

between the neutralizer axis and the line of sight from the neutralizer to the point of interest and r 
is the distance from the neutralizer. 

The parameters used to compute the neutral density appear in the plume map file described in 
Appendix A. 

Uniform. For time-dependent problems (Figure 30), a uniform distribution is available for 
initialization. If the “split” option is chosen, each particle is split into eight outwardly moving 
particles so as to approximate a thennal distribution. Each new particle has a temperature (to be 
used for possible later splitting) equal to one-half of the original temperature, with the remaining 
thennal energy appearing as the kinetic energy of the particles. The velocities have components 

of ±O.7O7^/e0/m along each axis in a randomly oriented coordinate system. The splitting is 
done in the plasma frame of reference in order to simulate the correct momentum and energy 
distribution for a drifting Maxwellian when transformed back to the spacecraft reference frame. 

Boundary Injection. For time dependent problems, particles can be created at the problem 
boundaries to represent the plasma thennal current. These particles can be split in the same 
manner as described above for a uniform distribution to account for their thennal distribution. 
Alternatively, a thennal distribution can be created in the same manner as for Boundary particles 
above. 


Surface. Particles can be created at surface elements to model either charged particle emission 
from a surface or collection by a detector. 

Emitter: The user specifies the emitted cunent density, the range of angles, and range of kinetic 
energies at the surface. The emission current is associated with the surface (not the underlying 
conductor) for charging purposes. Tracked particles returning to spacecraft surfaces are counted 


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54 



as incident tracked particle current, so the emitter facility can be used to study the distribution of 
the returning emitted particles. 

Detector: The detector facility provides a means to accurately sample the environment current to 
a single surface. The reverse trajectory technique, which takes advantage of the Liouville 
theorem that the distribution function is constant along a trajectory, is used. In the reverse 
trajectory approach, particles are created at the detector and tracked backwards to determine 
where they originated. Trajectories that leave the problem space are assumed to connect to the 
environment, while trajectories that strike object surfaces or become trapped do not. The current 
is given by an integral over the distribution of the incident charged particles. 19 

The reverse trajectory method outlined above is in sharp contrast to the sheath current method 
that is used to calculate the total current to an object and its distribution over the surface. The 
sheath current method works well when (a) the environment is dense enough to have a sheath, 
and (b) the object potentials are large compared with the environment temperature. Additionally, 
it only works for attracted species currents, and due to coarse sampling gives only a crude 
estimate of the current to any individual surface. It fails completely for surfaces whose current 
comes from low phase space density portions of the environment. By contrast, the reverse 
trajectory method can be made to give very accurate results provided care is taken that the high 
phase space density portion of the ambient environment is well sampled. 

External File. When the aforementioned options are inadequate, an external file can be used to 
specify initial positions and velocities. (See Figure 31 for sample file.) The file fonnat is: 

LOCATION x y z 

DIRECTION dx dy dz 

WEIGHT weight 

ENERGY energy 
LOCATION ... 

where the location is in meters relative to the grid center, the direction need not be nonnalized, 
the weight is in amperes, and the energy is kinetic energy in electron volts. Alternatively, the 
keyword “ETOTAL” may be used to give the total particle energy. Each such four-line 
sequence results in definition of a particle. If the “Weight” keyword does not appear, a unit 
particle weight is assigned. Lines that start with “Comment” are ignored. The user has the option 
of typing in the filename or browsing to the file. Values for location, direction, weight, and 
energy that are more than fifteen characters long are read incorrectly. 

Particles created from an external file for time dependent problems can be split to account for 
their thennal distribution. If the initial kinetic energy is less than the temperature, the particles 
are split in the same manner as described above for a uniform distribution. Otherwise, each 
particle is split into nine with additional velocity components nonnal to the initial particle 
velocity only. There is one zero-velocity central particle and two particles with velocity 

±O.866^/e0/m in each of the two randomly oriented coordinate directions normal to the initial 
particle velocity. 


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55 



50eVfan.txt 


Location 1.001 

0.0 

0 

0 

Direction 5 -5 

-5 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 -4 

-4 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 -3 

-3 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 -2 

-2 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 -1 

-1 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 1 0 

0 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 1 

1 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 2 

2 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 3 

3 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 4 

4 



Weight 0.100E 

-03 



E_Total 50. 




Location 1.001 

0.0 

0 

0 

Direction 5 5 

5 



Weight 0.100E 

-03 



E_Total 50. 




END 





Figure 31. Sample External File for Specifying Initial Particle Distribution 

Particle generation can be monitored during execution using the Script Running Monitor 
shown in Figure 32. 


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Figure 32. Script Running Monitor Showing Progress in Particle Generation 
15.2 Tracking Particles 

Once an initial distribution of particles has been generated, “TrackParticles” is used to track 
each one of them. Each particle is tracked for a maximum of the “Tracking time per timestep” 
(on the Advanced Particle Parameters dialog box, Figure 34 in Section 15.3). For each 
timestep, which might be 1 second long for full trajectory tracking, the particle is tracked in 
substeps that can be no longer than the “Distance a particle can go in one substep” (on the 
Advanced Particle Parameters dialog box, Figure 34), generally 0.1 local mesh units. 

Each particle is tracked until one of the following conditions occurs: 

(1) The particle strikes the object. 

(2) The particle exits the computational space. 

(3) The trajectory time reaches the requested particle tracking time. 

(4) The number of substeps exceeds the maximum substep number. 

When tracking is complete, Nascap-2k writes out the total current to the object and a table 
apportioning that current by material and conductor in a file with a name like 
pref/x_tracker_traj_/feraf/on#_out.txt. Also, a Hit file is created, listing each particle that struck the 
object with its vital statistics that may be used for additional processing. Tracking can be 
monitored during execution through the Script Running Monitor shown in Figure 33. 



Figure 33. Script Running Monitor Showing Progress in Particle Tracking Calculation 


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Table 15. Input Parameters for Generating and Tracking Particles 


PARTICLES 

PARAMETER 

DEFINITION 

| Particle Creation/Initial Particle Distribution for Trajectories 

Contour 

Generate particles at the intersection of a cut plane specified in meters from the 
grid center and a constant potential surface (such as a sheath). (Visualization only, 
see Section 17.2.) 

Sheath 

Generate particles representing sheath currents at a constant potential surface. 


Potential Value 

Potential defining the “sheath” surface at which particles are generated (V). 

(Sheath or Contour particles only.) 

B Field 

Generate particles where magnetic field lines enter the computational space. Only 
appropriate for electrons. 

1 

Number per cell 

Square root of the number of particles emitted on each boundary element surface. 

Boundary 

Generate a thermal distribution of particles at the problem boundaries. 

Charge Exchange 

Generate particles throughout space to represent charge exchange ions. 


Cross-section 

Charge exchange cross section. 

None of the Above 

Used when all particles come from an initial uniform distribution, boundary 
injections, or from an external file. 

Uniform 

Generate a uniform distribution of particles throughout the grid at problem 
initialization. (For time dependent problems.) 


Split particles 

Divide each newly created particle into eight with velocities that represent the 
thermal distribution. 

| Boundary Injection 

Generate particles at the problem boundaries. (For time dependent problems.) 


Split particles 

Divide each newly created particle into eight with velocities that represent the 
thermal distribution. 

| Surface 

Generate particles at surface elements. 


Emitter/Detector 

Specification of surface elements at which particles are created. Particles created at 
a detector are for the computation of currents to those surface elements using the 
reverse trajectory approach. Particles created at an emitter may be used to study 
the distribution of the escaping and return currents of the emitted particles. 


Current Density 

Emitted current density (Am' 2 ). (For emitters only.) 

| External File 

Particle position and velocity information specified in an external file. 


Filename 

File used to specify particle position and velocity. (20 characters maximum.) 


Split particles 

Divide each newly created particle into eight with velocities that represent the 
thermal distribution. 

Particle Species boxes 

Select species to be generated and tracked. Use <control select> to pick multiple 
species and to unselect species. Double click to change color of trajectory on 

Results 3D tab. Species are defined on the Environment tab. 

Particle Species 

Select species to be generated. 

Particle Species for External File 

Select species to be generated as specified in an external file. Only applies if 
external file is specified. 

Particle Species for Boundary 
Injection 

Select species to be generated at the problem boundary. Only applies to time 
dependent problems and if boundary injection is specified. 

Tracking time per timestep 

The maximum time (sec) a particle is to be tracked. For time-dependent problems 
without a charging step, the time variable is incremented by this amount. 

Advanced 

Open Advanced Particle Parameters dialog box. 


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15.3 Particle Advanced Parameters 

There are two main sections on the Advanced Particle Parameters dialog box: “Particle 
Generation” and “Tracking.” Under “Particle Generation” there are three subsections: “Boundary 
particle parameters”, “Surface particle parameters”, and “Diagnostics”. The “Boundary particle 
parameters” are for particles generated with a “Boundary” initial particle distribution. The 
“Surface particle parameters” are for particles generated at a surface element for an emitter or 
detector. Under “Tracking” there are two subsections, “General” and “Diagnostics.” To change 
the value of a diagnostic parameter, click the button until the desired value appears. Table 16 
describes the parameters on the Advanced Particle Parameters dialog box. 

Particles generated using the “Boundary” specification represent particles (typically ram ions) 
entering the grid from the external space. Particles generated using the “Boundary Injection” 
specification represent particles thermally flowing into the grid from the external space in time- 
dependent problems. For each emission point, the thermal distribution of the entering particles 
may be sampled. For “Boundary Injection” this sampling can be done either by particle splitting 
or using the distribution parameters. The “Fraction of distribution” parameters specify how the 
Maxwellian distribution of velocities in each of the three coordinate directions is to be divided. 
For example, the sequence (0.1, 0.4, 0.5) specifies three particles representing respectively 10% 
of the distribution on the negative tail, 40% of the distribution constituting the bulk of the 
negative velocity particles, and the half of the particles with positive velocity. The mean velocity 
(e.g., ram ion velocity) is added to the thennal velocity. (Note that the number of particles may 
add up fast: 4 divisions in each of VX, VY times 3 divisions in VZ gives 48 particles per 
emission point.) 

The density of particles generated along the problem boundaries is specified by the default 
subdivision ratio. Boundary elements are subdivided by the specified factor and particles are 
generated at the center of the exterior surface of each boundary subelement. For example, if the 
primary grid is 14 grid units in the Z-direction and a default ratio of “2” is specified, particles 
would be created for the element (3,4,14) at the four emission points (3.25, 4.25, 15), (3.75, 4.25, 
15), (3.25, 4.75, 15), and (3.75, 4.75, 15). The code knows to weight the particles by the cosine 
of the incident angle, and to omit particles whose velocities point out of the grid. 

In the “Surface particle parameters” section, the emitter or detector at which particles are created 
is specified. The range and number of values of the kinetic energy of the particles at the surface 
is specified. The “Theta” and “Phi” rows refer to the polar and azimuthal angles of the field of 
view. The range of the azimuthal angles is always 2n. Particles with the specified range and 
number of speeds, theta, and phi values are emitted from the specified number of locations. The 
code may create particles at fewer or additional locations depending on the details of the surface 
element shape. The number of particles created should be adequate to capture the shape of the 
distribution function and resolve any shadows or other structure. The total number of particles 
created is the product of the four values in the “Number” column. 

The “split” option under tracking is used to request that each particle be split when it reaches a 
subgrid boundary. This is to avoid having heavy particles in well-resolved regions. The particle 
is split only if it carries more charge than a similar particle that has been created in the subgrid 
and if it has a temperature greater than 0.05 eV. Since the temperature is halved each time a 
particle is split, this limits the number of times a particle is split. 


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Figure 34. Advanced Particle Parameters Dialog Box 


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Table 16. Input Parameters for the Advanced Particle Parameters Dialog Box 


PARTICLE GENERATION AND TRACKING ADVANCED PARAMETERS 

PARAMETER 

DEFINITION 

Particle Generation 

Boundary Particle Parameters 


Fraction of Distribution 

PVX, PVY, and PVZ 

Fraction of distribution in each orientation that each particle represents. 

Default subdivision ratio 

Ratio by which to subdivide boundary elements before generating 
particles at centers if no specific value is specified in the table below. 

| Surface Particle Parameters 


Emitter/Detector 

Name of emitter or detector. (Display only.) 

Energy (Min, Max, Number) 

Minimum and Maximum speed of particles at surface and Number of 
speed values at which to create particles. 

Theta (Min, Max, Number) 

Minimum and Maximum polar angle in radians and Number of polar 
angles at which to create particles. 

Phi (Number) 

Number of azimuthal angles at which to create particles. 

Location (Number) 

Number of locations on each emitter/detector surface element at which 
to generate particles. 

| Diagnostics 


PartGen Diag, 

Dyna Diag 

Govern optional diagnostic output from various portions of the particle 
generation process. Level 1 (least) through 5 (most) for each phase of 
the calculation. 

Timer Level 

The frequency of CPU time monitoring. 

Tracking 

General 


Tracking time per timestep 

Maximum time (sec) a particle is to be tracked. For time-dependent 
problems, the time variable is incremented by this amount. 

Maximum number of substeps 

Maximum number of substeps per particle per iteration. 

Distance a particle can go in 
one substep 
(local mesh units) 

Maximum distance (in local grid units) a particle moves during a 
substep. Substep distances may be less than this value. Electrons 
gyrating in a magnetic field move only for a fraction of the cyclotron 
period. Slow ions may move less than “Max Dx” in the tracking time. 

Split at subgrid boundaries 

Turn “off’ or “on” splitting each particle when it reaches a subgrid 
boundary. 

Deposit charge each substep 

Turn “off’ or “on” depositing charge to the grid at each substep in time- 
dependent problems. If “Off,” the entire charge is placed on the nodes 
of the volume element in which the particle is located at the end of the 
timestep. 

Save to fdes every 

How often charge densities are saved in time-dependent problems, 

iterations starting with 

starting at this iteration. 

Tracking limits 

Limits (specified in meters from the center of the grid) of initial particle 
locations. Particles originating outside these limits are ignored. 

| Diagnostics 


Tracker Diag, 

Dyna Diag 

Govern optional diagnostic output from various portions of the tracking 
process. Level 1 (least) through 5 (most) for each phase of the 
calculation. 


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16 Generating and Executing a Script (Script Tab) 

The Script tab is used to specify and execute the steps of the calculation. There are two subtabs, 
Run Script and Edit Script. The script specifies the steps and some of the calculation 
parameters. This tab is used to construct, view, edit, and run the script. 

16.1 Run Script Subtab 

Figure 35 shows the Run Script subtab with a typical script for a geosynchronous charging 
calculation followed by the computation of potentials in the space about the spacecraft. The 
script consists of commands (preceded by a capital “C”), folders (proceeded by a folder icon), 
and attributes (proceeded by a capital “A”). Attributes are data associated with the command. 
Each folder contains a set of related attributes. 


I File Edit View Materials Help 

Problem ] Environment Applied Potentials ~|" Charging \ Space Potentials \ Particles Script j Results j Results 3D 
Run Script | Edit Script | 



Figure 35. Run Script Subtab for a Typical Geosynchronous Charging Problem with Computation 

of Potentials about Spacecraft 


The bottom of the tab displays a message, a checkbox, and three buttons. Clicking the “Build 
Script” button generates a default script from the “Environment,” “Problem Type,” and 
parameters specified on the previous tabs. If relevant parameters have changed since the script 
was last built, the “The Script is out of date!” message appears, suggesting that the user may 
want to rebuild the script. Clicking the “Run Script” button instructs Nascap-2k to successively 
execute the script commands. During script execution, the button text changes to “Running.” 

Four of the top-level commands have input and output files. During preprocessing, the code uses 
information on the various tabs to construct the text input files and write them to disk. Then it 
starts the computational modules. Each module reads its input file, executes using the parameters 


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specified in the input file, and writes a text output file in addition to writing its results into the 
database. These text output files are discussed in Section 17.3. 

If needed, these input files can be edited by the user. The meaning of each of the keywords 
included in these files is provided in Appendix A. Clicking the “Save Files” button on the bottom 
of the tab writes out the input files without actually doing the calculations. Unchecking the 
“Automatically Overwrite Files” checkbox ensures that previously edited input files are not 
automatically overwritten. The checkbox also applies to the files used when generating particle 
trajectories for visualization. 

16.2 Script Commands 

There are several top-level commands available for inclusion in scripts: Loop, Read Object, 
Append Object, Initialize Potentials, Charge Surfaces, Embed Object in Grid, Potentials in 
Space, Static A Field, Create Particles, Track Particles, and Save Files. 

Loop. Execute the enclosed commands the specified number of times, substituting the iteration 
number for the character “?” in any input or output filename, iteration keyword argument, or 
directory name. 


Table 17. Attributes of Loop Command 


KEYWORD 

DEFINITION 

Iterations 

Number of iterations 

StartAt 

Iteration number for first iteration 


Read Object. Reads the XML text file defining the object geometry, materials, initial surface 
potentials, and other parameters and places the information in the Nascap-2k database for use by 
other commands. Initializes surface potentials. 

Table 18. Attribute of Read Object Command 


KEYWORD 

DEFINITION 

| FileName 

Relative path to XML file | 


Append Object. The Append Object command adds a second object specified in an XML file to 
the object in an existing database. See Appendix D for further information. 


Table 19. Attributes of Append Object Command 


KEYWORD 

DEFINITION 

FileName 

Full path name of XML file to be appended. 

X 

X offset (m) of appended object. 

Y 

Y offset (m) of appended object. 

Z 

Z offset (m) of appended object. 


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Initialize Potentials. The Initialize Potentials command can be used to reset the surface 
potentials to their initial values without rereading the object into the database. 

Charge Surfaces. Compute time evolution of surface potentials. This command is used to 
perfonn surface charging calculations. This module requires that the object had been previously 
read into the database by the Read Object command. Charge Surfaces has several second-level 
commands and no input or output fde. Some of the second-level commands, such as 
“Setlllumination,” set parameters needed for surface charging calculations. Some second-level 
commands, such as “DoTimeSteps,” specify the various steps of a surface charging calculation. 
Other second-level commands, such as “UseTrackedlons,” are instructions to the charging code 
regarding which algorithm to use. Table 20 specifies how each of the available commands is to 
be used. The “DoTimeSteps,” “DoOneTimeStep,” and “DoTrackTimeStep” commands are the 
only ones that write results into the database. Two of the commands, “DoTimeSteps” and 
“SetEnvironment,” require an additional child element (folder of attributes). The command 
“SetConductorBias” has an optional folder of attributes as a child element. 


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Table 20. Second-Level Commands of the Charge Surfaces Command and their Attributes 


COMMAND/ATTRIBUTE 

DEFINITION 

Setlllumination 

Set sun intensity and direction for surface-charging calculation. 

Value 

Ratio to solar intensity at Earth’s orbit (1 AU). 

X 

X component of sun vector. 

Y 

Y component of sun vector. 

Z 

Z component of sun vector. 

SetEnvironment 

Set an environment for surface-charging calculation. Requires at least 
one “Environment” folder. 

SetCustomCurrentDLL 

Specifies that surface currents for surface charging calculation are to 
be obtained from a custom DLL. See Appendix D. 

FileName 

Name of custom DLL. 

ReadPhotoemission 

Read photoemission spectral data for surface-charging calculation. 

FileName 

File in which photoemission spectrum is specified, generally 

pre/7xphoto.xm 1. 

SetVelocity 

Set spacecraft velocity in meters per second. 

X 

X component of spacecraft velocity. 

Y 

Y component of spacecraft velocity. 

Z 

Z component of spacecraft velocity. 

SetBField 

Set value of ambient magnetic field in tesla. 

X 

X component of magnetic field. 

Y 

Y component of magnetic field. 

Z 

Z component of magnetic field. 

SetVXBPotentials 

Sets vxB potentials on conducting surfaces. Set time to zero. 

Value 

Initial value of maximum potential in volts. 

SetlnitialConductorPotential 

Set initial value of the potential of a conductor. 

Index 

Index of conductor. 

Value 

Initial value of conductor potential in volts. 

FixGroundPotential 

Fix ground potential to a specified value throughout charging 
calculation. 

Value 

Value of ground potential in volts. 

SetConductorBias 

Set fixed bias value for a conductor. 

Value 

Value of bias potential in volts. 

Index 

Index of biased conductor. 

lndex2 

Index of reference conductor. 

FourierComponent 

Folder specifying the amplitude (V), frequency (Liz), and phase 
(degrees) of time varying components of bias value. Multiple folders 
specifying multiple Fourier components are allowed. 

Emit Current 

Add additional current source to charging calculation. 

Index 

Conductor number from which current is emitted. 

Current 

Current emitted in amperes. 

UseTrackedCurrent 

Use currents generated by particle tracking in computation of surface 
currents. 

UseTrackedlons 

Use currents from tracked ions in addition to an analytic expression for 
the election current in computation of surface currents. 


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COMMAND/ATTRIBUTE 

DEFINITION 

SetParameters 


FieldsFromFile 

If “On”, use surface electric fields from database in computing limiting 
of secondaries and photoelectrons. Generally used after Potentials in 
Space, so that the electric fields calculated by Potentials In Space are 
used rather than those computed by the Boundary Element Method, 
which do not account for any plasma. 

SpaceChargeLimitedPhotoemission 

If “On”, use the preliminary model for the space charge barrier height 
due to photoemitted electrons. Appropriate for near sun environments. 
See Nascap-2k Scientific Documentation. 

TransverseC urrent 

If “On”, after each timestep, compute transverse currents along 
surfaces need to achieve change in surface charge density. 

ZeroCurDeriv Algorithm 

If “On”, perform explicit charging calculation. 

ZeroTotCurAlgorithm 

If “On”, following a charging timestep, attempt to adjust the overall 
potential in order to achieve zero net current to the spacecraft. 

DoTimeSteps 

Perform surface charging calculation for multiple timesteps using time 
parameters provided. Requires at least one “TimeParams” folder. Uses 
parameters (surface potentials, environment, and algorithms) set by 
previously executed commands. Writes surface potentials to database 
at end of execution. 

DoOneTimeStep 

Perform one timestep of a surface-charging calculation. Uses 
parameters (surface potentials, environment, and algorithms) set by 
previously executed commands. Writes surface potentials to database 
at end of execution. 

Timestep 

Timestep duration in seconds. 

DoTrackTimeStep 

Perform one timestep of a surface-charging calculation. Uses 
parameters (surface potentials, environment, and algorithms) set by 
previously executed commands. Writes surface potentials to database 
at end of execution. 

Timestep 

Timestep duration in seconds. Same value as “Tracking Time per 
Timestep” on Particles tab/Time-dependent subtab. 


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Table 21. Attributes Contained in “Environment” Folder 


Attribute 

Value 

Type 

Allowed values are “GEO,” “LEO,” “Auroral,” “SolarWind,” “Tabular,” and “Custom.” 

Nel 

Density (m' 3 ) of electrons of first Maxwellian component of environment. (GEO, LEO, 

Auroral, SolarWind, Custom.) 

Tel 

Temperature (eV) of electrons of first Maxwellian component of environment. (GEO, LEO, 
Auroral, SolarWind, Custom.) 

Nil 

Density (m' 3 ) of ions of first Maxwellian component of environment. (GEO, SolarWind, 
Custom.) 

Til 

Temperature (eV) of ions of first Maxwellian component of environment. (GEO, Auroral, 
SolarWind, Custom.) 

Ne2 

Density (m' 3 ) of electrons of second Maxwellian component of environment. (GEO (Double 
Maxwellian only), Custom.) 

Te2 

Temperature (eV) of electrons of second Maxwellian component of environment. (GEO 
(Double Maxwellian only), Auroral, Custom.) 

Ni2 

Density (m' 3 ) of ions of second Maxwellian component of environment. (GEO (Double 
Maxwellian only), Custom.) 

Ti2 

Temperature (eV) of ions of second Maxwellian component of environment. (GEO (Double 
Maxwellian only), Custom.) 

Ke 

Kappa parameter for electron Kappa distribution function. (GEO) 

Ki 

Kappa parameter for ion Kappa distribution function. (GEO) 

Curmax 

Current (A) in second Maxwellian component of auroral environment. (Auroral.) 

Curgaus 

Current (A) in Gaussian component of auroral environment. (Auroral.) 

Egaus 

Center energy (eV) of Gaussian component of auroral environment. (Auroral.) 

Widthgaus 

Width (eV) of Gaussian component of auroral environment. (Auroral.) 

Curpower 

Current (A) in Power Law component of auroral environment. (Auroral.) 

El power 

Minimum energy (eV) of Power Law component of auroral environment. (Auroral.) 

E2power 

Maximum energy (eV) of Power Law component of auroral environment. (Auroral.) 

Ratepower 

Rate used in Power Law component of auroral environment. (Auroral.) 

Mass# 

Mass (kg) of ion species number #. (LEO, Auroral, SolarWind.) 

Fraction# 

Fraction of total density in ion species number #. (LEO, Auroral, SolarWind.) 

NumSpecies 

Number of ion species. (LEO, Auroral, SolarWind.) 

electronEnergy# 

Energy bin lower edge value. (Tabular) 

electronFlux# 

Differential flux between electronEnergy# and electronEnergy(#+l) 

numEFluxes 

Number of electron flux values, and one less than the number of energy values. 

ionEnergy# 

Energy bin edge value. (Tabular) 

ionFlux# 

Differential flux between ionEnergy# and ionEnergy(#+l) 

numIFluxes 

Number of ion flux values, and one less than the number of energy values. 

Shadowlons 

Set to zero current to sun facing surfaces that are shadowed by other surfaces. Allowed values 
are “yes” and “no”. (SolarWind) 

Begintime 

Beginning time of this environment for time-varying environment. 

FileName 

For “Custom” environment only. Name of custom DLL used to compute charging currents. 

See Appendix D. 


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Table 22. Attributes Contained in “TimeParams” Folder 


ATTRIBUTE 

VALUE 

Begintime 

Timestamp at beginning of timestep sequence. (Default 0 or previous endtime.) 

Endtime 

Timestamp at end of timestep sequence. (Default 1.) 

Nsteps 

Number of timesteps. (Default 1.) 

Mindt 

Duration of first timestep. (Default 0.1.) 

Maxdt 

Maximum allowed timestep duration. (Default is no maximum.) 


Table 23. Attributes Contained in “FourierComponent” Folder 


ATTRIBUTE 

VALUE 

Amplitude 

Amplitude of Fourier component of conductor bias in volts. 

Frequency 

Frequency of Fourier component of conductor bias in hertz.) 

Phase 

Phase of Fourier component of conductor bias in degrees.) 


Embed Object in Grid. Construct matrix elements used to solve Poisson’s equation for 
potentials in space. The Embed Object in Grid module requires that the object had been 
previous read into the database by the Read Object command and that a grid file, prefix. grd, 
exists. It creates the prefixes and prefix. NME files and writes into the prefix. NDB file. This 
module must be rerun every time either the grid or the object geometry is changed. While the 
user is not required to delete existing files before execution, strange results are often eliminated 
when all the database files are deleted before executing this module. 


Table 24. Attributes of Embed Object in Grid Command 


KEYWORD 

DEFINITION 

InputFileName 

File in which parameters used by module are stored. 

OutputFileName 

File written by module containing results and diagnostic information. 


Potentials in Space. Solve Poisson’s equation for the potential at each grid point using object 
potential boundary conditions and specified charge density model. This module requires matrix 
elements computed by Embed Object in Grid. It writes into the prefix. NDB and prefix. NTM files. 


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Table 25. Attributes of Potentials in Space Command 


KEYWORD 

DEFINITION 

InputFileName 

File where parameters used by module are stored. 

OutputFileName 

File written by module; contains results and diagnostic information. 

Iteration 

Integer used to determine the value of some of the parameters written into the input file. 

Iteration “0” specifies that a geometric wake initialization is performed if the checkbox on the 
Space Potentials tab is checked. 

Iteration “0” specifies that the space potentials are to be initialized. Therefore, if the requested 
charge density model is “Full PIC” or “Hybrid PIC,” “Laplace” should be used. Also, if the 
requested charge density model is “Full Trajectory Ions,” “Non-linear” should be used. 

Any value other than “0” specifies that previously computed space potentials are to be used as 
an initial condition. 

The value also identifies which “Fraction old potential” specified on the Space Potentials tab 
is to be used. 


Static A Field. Use the transverse surface currents computed by Charge Surfaces, the volume 
ion currents computed during particle tracking, and the volume electron currents saved in the 
database by an external code to compute the magnetic field, the vector potential, and the rate of 
change of the vector potential from these currents. See the Nascap-2k Scientific Documentation 
for additional details. 


Table 26. Attributes of Static A Field Command 


KEYWORD 

DEFINITION 

OutputFileName 

File written by module; contains results and diagnostic information. 

Timestep 

Timestep at which source current values were saved. 

Components 

Folder of commands that specify which source current terms to use. 


Table 27 specifies the attributes contained in the “Components” folder. 

Table 27. Attributes Contained in “Components” Folder 


ATTRIBUTE 

VALUE 

Electron 

If value is “True,” include transverse surface currents as a source in magnetic field and vector 
potential calculation. 

Ion 

If value is “True,” include volume ion currents as a source in magnetic field and vector potential 
calculation. 

Transverse 

If value is “True,” include volume electron currents as a source in magnetic field and vector 
potential calculation. 


Create Particles. Create particles for tracking. This module requires the potentials created by the 
Potentials in Space module. The particles are stored in prefix.NPTnn files. Each species has its 
own file. 

This module is also used to create particles tracked for visualization on the Results 3D tab. 

When used for visualization, the only relevant attributes are the input and output file names, 
which are fixed. The user can edit the input file and view the output file. Particles created for 
visualization are kept in separate files from those used in calculations. 


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Table 28. Attributes of Create Particles Command 


KEYWORD 

DEFINITION 

InputFileName 

File where parameters used by the module are stored. 

OutputFileName 

File written by module; contains results and diagnostic information. 

Track mode 

Allowed values are “Surface Currents,” “TimeDependent,” and “ton Density.” Specifies 
from which subtab of the Particles tab the parameters for these particles are to be drawn. 

Creation mode 

Allowed values are “Uniform,” “External,” or “Regular.” Specifies if the particles created by 
this command are to be uniformly distributed, specified by an external file, or as indicated by 
the radio buttons on the relevant subtab. 

Species 

Name of species to be created. Mass and charge specified on Environment tab. 

ExecuteEvery 

Integer value. Allows for conditional execution. If the iteration step number is evenly divisible 
by this value, the Create Particles command is executed. Only applies within loop. 


Track Particles. Compute particle trajectories to determine surface currents and volume charge 
density. This module requires that the initial positions and velocities have already been created 
by Create Particles. The particle positions and velocities are updated in the prefix.NPTrm files. 
Surface currents and charge densities in volume elements are saved in the prefix .NDB file. 
Historical values are saved in the prefix .NTM file 

This module is also used to track particles for visualization on the Results 3D tab. When used for 
visualization, the only relevant attributes are the input and output file names, which are fixed. 

The user can edit the input file and view the output file. 


Table 29. Attributes of Track Particles Command 


KEYWORD 

DEFINITION 

InputFileName 

File where parameters used by the module are stored. 

OutputFileName 

File written by module; contains results and diagnostic information. 

Iteration 

Integer that identifies which “Fraction old density” specified on the Space Potentials tab is to 
be used. Ignored if “0.” 

Track mode 

Allowed values are “Surface Currents,” “TimeDependent,” and “Ion Density.” Specifies 
from which subtab of the Particles tab the parameters for these particles are to be drawn. 

UpdateTime 

Allowed values are “Yes” and “No.” Indicates if the time should be updated each timestep. 

ElectronsOnly 

Allowed values are “Yes” and “No.” Indicates if resulting charge and current are to be stored 
in arrays for electron charge and current, for possible use in computations involving both ions 
and electrons. 

ExecuteEvery 

Integer value. Allows for conditional execution. If the iteration is evenly divisible by this 
value, the command is executed. Only applies if within loop. 


Save Files. Save a copy of all the project files to a specified directory. This command can be 
useful for plotting or in order to resume the calculation from that point in case of a subsequent 
error. The relative path name is specified. 


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Table 30. Attributes of Save Files Command 


KEYWORD 

DEFINITION 

Directory 

Directory into which the project fdes are to be copied. 

ExecuteEvery 

Integer value. Allows for conditional execution. If the iteration is evenly divisible by this value, the 
command is executed. Only applies if within loop. 


16.3 Edit Script Subtab 

The Edit Script subtab, shown in Figure 36, is used to modify the script. Caution should be 
exercised during any script editing. There are no checks to ensure that the resulting script 
performs as the user intended. 



Figure 36. Edit Script Subtab: Making Problem Changes by Directly Modifying the Script 

A list of available commands appears in the listbox at the left of the tab, and the script appears on 
the right. The user can use the buttons to add, delete, and reorder the commands. The value of 
any attribute may be modified by double-clicking the line and then typing over the old value. The 
attributes of the first occurrence of each of the “Setlllumination,” “SetEnvironment,” and 
“DoTimeSteps” commands are the values shown on the Environment and Charging tabs. 
Changing the value on the Script tab changes the value on the other tab and vice versa. 


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The script can be saved to or read from an external XML file by using the “Save Script” or 
“Load Script” selections on the File menu. These commands require that the file name is of the 
form *Script.xml. Adventurous users can edit this file using a text or XML editor. 

Table 31. Elements on the Script Tab 


SCRIPT 


COMMAND USE 


Run Script subtab 


Script is out of date! 

Informs user if any relevant parameters may have been changed since the script was last 
built. 

Build Script 

Construct a default script based on the “Environment,” “Problem Type,” and parameters 
specified on other tabs. 

Save Files 

Save the input files for all instances of Embed Object in Grid, Potentials in Space, 
Create Particles, and Track Particles that appear in the script without actually running 
the script. 

Automatically 
overwrite files 

Overwrite existing input files without querying the user prior to executing a script. 

Should not be checked if user has edited any of the input files outside the interface. 

Run Script 

Execute the script. During execution, the button text changes to “Running.” 

Edit Script subtab 

Used for script editing. 

Add Commands 

Add highlighted command to script. 

Delete Item 

Delete highlighted line in script pane. 

Duplicate Item 

Duplicate highlighted line in script pane, including any second-level commands and 
attributes. 

Up 

Move highlighted line up one place in the script pane. 

Down 

Move highlighted line down one place in the script pane. 


17 Viewing Results 

17.1 Time-Dependent and Numerical Results (Results Tab) 

The Results tab is used to obtain the present values and time histories of surface potentials, 
normal electric fields, and currents. Generally these quantities vary smoothly with time; shorter 
timesteps can often smooth out any numeric jitters. Time history plots and numeric values may 
be obtained for groups of surface elements, single surface elements, and conductors using the 
top, middle, and bottom sections, respectively, on the left side of the tab (Figure 37). Numeric 
values of the plotted results appear on the Text subtab, suitably formatted for copy-and-paste to 
another plotter or analysis tool. 

In the upper left corner of the tab, a drop-down list is used to specify the quantity to be 
displayed: charging currents, tracked currents, potentials, normal differential potential, electric 
field, internal electric field or transverse currents. The internal electric field is the differential 
potential divided by the material thickness. Only available quantities are included in the drop¬ 
down list. 


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Figure 37. Results Tab: Plotting Minimum, Maximum, and Average Values of Elements with 

Specified Conductors and/or Materials 

Each line in the first section specifies a group of surface elements. All elements matching the 
specification are included in the group. The selection of elements can be narrowed by specifying 
that only elements of a single conductor or a single material be included. Elements facing a 
certain direction can be specified by nonnal vector and tolerance angle. An element is included if 
the angle between the nonnal and the specified vector is less than the specified tolerance. (Thus 
an angle of 180° includes all orientations.) The selection of elements can also be narrowed by 
orientation with respect to the sun. In Figure 38 the potential of all the elements were plotted as a 
function of time. Because all elements are included in this specification, the minimum, 
maximum, and average potential values of the elements are displayed. By checking the second 
row, the user would analyze only those elements pointing away from the sun direction. The third 
row would produce minimum, maximum, and average potential values for all sunward-facing 
OSR elements. 

Time histories of specific surface elements are plotted using the middle section of the tab as 
shown in Figure 38. Elements #37 and #62 are shown but not checked. Therefore, they are not 
plotted. Note that the third and fourth columns automatically display the corresponding 
conductor number and material. The last column displays the value at the end of the calculation, 
in this case at t=300 seconds. 

The bottom section of the tab may be used to plot values for a specific conductor. The value 
shown in the last column is the value after the final timestep. 


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The Settings subtab can be accessed to control the axes scales and legend. The Text subtab 
(Figure 39) provides the numerical values that are plotted, which can be copied and pasted into a 
spreadsheet or other program for further manipulation. The “Display surface numbers of Min and 
Max” checkbox on the Settings subtab specifies that the surface number of the surface with the 
minimum and the maximum value at each timestep is included in the table on the Text sub tab. 


File Edit 


Materials Help 


Surface Element Groups 

Plot 

Condu Material 

Norma 

X 

Y 

Z Sunlit 


(Any Any 

180 0 

0.0 

00 

O.OAny 


Any 'Any 

180 0 

00 

0.0 

0 0 Any 


Any iOSR 

180 0 

00 

o.o| 

0 0|Any 


Plot 

Element 

Conductor 

Material 

Potential (V) 

0 

147 

1 

Teflon 

-4095 

0 

378 

1 

Solar Cells 

-3278 


Individual Surface Elements 


Conductors 

_ Plot 


Potential (VO 


Graph Settings Te> 

1000- 

0- 

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CaatrcMfOOOO 0S3* 4170$) 


-El«m«nt#378 
Conductor #1 


Figure 38. Results tab: Plotting Values at Surface Elements 



Figure 39. Text Output in the Results Tab 

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17.2 Three-Dimensional Results (Results 3D Tab) 


The Results 3D tab displays results in three dimensions. The View menu (see Table 3 in 
Section 7) can be used to globally adjust the appearance of the display area. As in Object Toolkit 
and GridTool, the object may be viewed from a variety of angles and positions using the cursor 
tools and Direct Movement and Rotation buttons in the same manner as in Object Toolkit and 
GridTool (see Table 5 in Section 10.2). As shown in Figure 40, information associated with a 

specific surface element is displayed using the Surface Element Infonnation tool, IlLJ. The 
components of the charging current are not always available. If the ion current is determined by 
tracking particles, the value used is not always displayed. 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging Space Potentials 


Script Results Results 3D 


Spacecraft - 


Display: Potential 


View: Standard 


Hide Spacecraft 


Display^ 


; Z | New 


View: Standard ▼ 
Hide Cutplane 


Trajectories- 


Specify Trajectories... 


• Linear O Log 

Mind-7241 


Max; 14 92 


Replot 


r E3GD frSriLJfcJ E?"' 1 


Direct Movement & Rotation 


Surface Element 294 Info 



Surface Element Number 294 
Material: Nextel 
Conductor 1 
Potential (V):-63.57 


Charging Current Density (Am 
Incident Electrons (Am 
Backscattered Electrons (Am 
Electron Secondaries (Am 
Incident Ions (Am 
Ion Secondaries (Am 
Photocurrent (Am 
Tracked Current Density (Am 
Tracked Electron Current Density (Am' 


2 ):-1 204E-8 

■^i.assE-? 
2 ):2.356E-9 
2 ):9 894E-8 
■*):2.655E-« 
2 ):9.992E-9 
**0.0 
‘ 2 >:0 0 
''poo 


Transverse Current (A/m): Not available 
Electric Field (Vm' 1 ):^ 95 
Differential Potential (V):-48 38 
Internal Electric Field (Vm' 1 ):-! 935E5 
Sunlit Dark 
Area (m z ):5 241E-2 
Normal: (0.0.0.0.1000) 

Centroid: (-9 353E-4. -1.310.0.316) 


rr 


Figure 40. Results 3D tab: Displaying Potentials on a Plane through the Center of the Box, Together 

with Results for a Selected Surface Element 


A “Show/Hide” button specifies whether the object is to be displayed or not. The “Display” 
drop-down list specifies if surface elements are color-coded by surface potential (Figure 41), 
material, conductor number, charging current, tracked current, differential potential, internal 
electric field, or normal electric field. Only quantities available are shown in the drop-down list. 
The “View” drop-down list specifies if the object is to be displayed with a solid color fill with 
black outlines along element boundaries or with a colored wire frame along element boundaries. 

Figure 40 also shows the cut plane capability in the Nascap-2k user interface. The specified 
quantity along surfaces of constant X, Y, or Z can be displayed. The possible quantities are 
shown in Table 32. Only quantities computed and stored in the database for the selected timestep 
are shown in the drop-down list. The magnitude and each component of vector quantities may be 
plotted separately. Values of some quantities are not displayed in special elements (next to the 


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object). Many of the quantities listed in the table are only computed in specialized calculations, 
such as thruster plume or dynamic PIC. 


Table 32. Quantities in Contour Plots 


CONTOUR QUANTITIES 

QUANTITY 

NODAL OR 
ELEMENT- 
CENTERED 

SCALAR 

OR 

VECTOR 

MEANING 


Potentials 

Nodal 

Scalar 

Potentials computed by “Potentials in Space” 
calculation. 

Neutral Wake 

Element-Centered 

Scalar 

Geometric wake density. Ambient density is 1. 

Electric Field 

Nodal 

Vector 

Electric field computed by “Potentials in Space” 
calculation. 

Ion Plume Density 

Element-Centered 

Scalar 

Density of high-energy main-beam ions from 
thruster used in thruster plume calculation. 

Neutral Plume Density 

Element-Centered 

Scalar 

Density of neutral atoms from unused propellant 
from the thrusters and neutralizers used in 
thruster plume calculation. 

Charge Exchange Density 

Element-Centered 

Scalar 

Density of ions created by charge exchange 
computed during tracking. 

Ion Density 

Element-Centered 

Scalar 

Density computed during particle tracking. 

Electron Density 

Element-Centered 

Scalar 

Density computed during particle tracking. 

Ion Current Density 

Element-Centered 

Vector 

Current density computed during particle 
tracking. 

Electron Current Density 

Element-Centered 

Vector 

Current density computed during particle 
tracking. 

Ion Density (Nodal) 

Nodal 

Scalar 

Density computed during particle tracking. 

Electron Density (Nodal) 

Nodal 

Scalar 

Density computed during particle tracking. 

Current Density (Nodal) 

Nodal 

Vector 

Ion current density computed during particle 
tracking. 

E Current Density (Nodal) 

Nodal 

Vector 

Electron current density computed during particle 
tracking. 

A Field 

Element-Centered 

Vector 

Vector potential from transverse surface and 
particle currents. 

B Field 

Element-Centered 

Vector 

Magnetic field from transverse surface and 
particle currents. 

dAdt 

Element-Centered 

Vector 

Rate of change of the vector potential form the 
transverse surface and particle currents. 

Poynting 

Element-Centered 

Vector 

Poynting vector from cross product of the rate of 
change of the vector potential and magnetic field. 


Nodal quantities, such as potentials, are Gouraud shaded. The color of each volume element for 
element-centered quantities is unifonn within the element. The cut plane is specified by the axis 
to which it is normal and its position, measured in meters, from the center of the grid. The cut 
planes may be displayed using a Standard view (e.g., as in Figure 40), Wire Frame (e.g., as in 
Figure 79), or Points. The wire frame view of the contours shows the lines used to construct the 


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76 

































plot. Each face of an empty volume element is divided into four squares and additional lines are 
used to specify the contour levels. 

Clicking the “Show/Hide” button specifies that trajectories of selected particles are to be 
computed and displayed. Clicking the “Specify Trajectories” button opens the Particle 
Visualization dialog box, where the selected particles are specified. This dialog box, shown in 
Figure 42, is similar to the Particles tab with an additional option for specifying the initial 
particle distribution. “Contour” specifies that particles are to be generated at the intersection of a 
cut plane and a constant potential surface element (such as a sheath). The color of the trajectory 
is set by double-clicking the species name. Either trajectories or particle positions can be 
specified. If “Trajectories” is selected, new particles are created and tracked solely for the 
purpose of visualization. If “Particles” is selected, the present positions of the particles in the 
database are shown. The plotting limits are the limits within which particles or trajectories are 
plotted. If not set (all zeroes) no plot is produced. The tracking limits constrain initial particle 
locations. Particles originating outside these limits are ignored. If not set (all zeros) all particles 
are tracked. Table 15 in Section 15.2 lists the input parameters for this dialog box. Figure 43 and 
Figure 44 are examples of displayed trajectories and particles, respectively. Additional 
illustrations are provided in Part III. 

The code can only display a reasonable number of trajectory segments and stops when there are 
too many. This can lead to trajectory segments at the outer edge of the grid that are difficult to 
see. The same problem can occur when plotting particle locations. The “Tracking Limits” 
parameters can be used to constrain the region of space in which particle trajectories begin. 

The “Color Scale” box provides control of scale range, linear or log, and plotting limits 
(minimum and maximum). Table 33 summarizes the options on the Results 3D tab. 

Note that running a script deletes any cut plane and trajectory plot objects. 


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77 




Figure 41. Results 3D: Displaying Potential on the Surface Elements 



Figure 42. Particle Visualization Dialog Box 


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HUM 


Nascap2k - C:\MyCalculations\Manuals\Chaws\WithlterationsYChawsProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging \ Space Potentials Particles | Script Results Results 3D 



kEfJGlU EEJEEEE) 


Cursor Tools 


Direct Movement & Rotation 




“Trajectories- 

, Specify Trajectories... | 

Hide Trajectories 

“Color Scale- 


<§) L 
Min: 

Max: 

near O Loq 

-2000. 

0.0 


Replot 




Potentials 



Figure 43. Selected Particle Trajectories (O+) in “CHAWS” Example 



Figure 44. Particle Distribution During Time-dependent Ion Collection by a Negatively Biased 

Cube 


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Table 33. Input Parameters for Displaying Results on the Results 3D Tab 


RESULTS 3D 

PARAMETER 

DEFINITION 

| Spacecraft 

Display 

Choice of result to display. 

View 

Standard: display with a solid color fill. 

Wire Frame: display with colored frame along surface element boundaries. 

Points: display using colored points. 

Show/Hide 

Display or hide results on object surfaces. 

| Cut Plane 

Display 

Choice of result to display. 

View 

Standard: display with a solid color fill. 

Wire Frame: display with colored frame along contour boundaries. 

Points: display using colored points. 

Plane 

Specifies axis to which the cut plane is normal, and its position (meters) from the 
center of the grid. 

Show/Hide 

Display or hide results on a plane in space. 

| Trajectories 

Specify Trajectories 

Open the Particle Visualization dialog box (Figure 42). 

Show/Hide 

Display or hide particle trajectories. Disabled until trajectories are specified. 

Color Scale 

Plotting control of scale (options are linear or log) and limits. 


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80 























Table 34. Additional Input Parameters for Displaying Particles. Also See Table 15 


PARTICLES 

PARAMETER 

DEFINITION 

Plot 

“Trajectories” or “Particle Present Positions.” If “Trajectories,” generate 
and display trajectories for the specified initial particle distribution. If 
“Present Particle Positions,” display the positions of existing particles— 
usually for particle-in-cell calculations—and ignore the initial particle 
distribution portion of the dialog box. 

| Initial Particle Distribution for Trajectories 

Contour 

Generate particles at the intersection of a cut plane (specified in meters 
from the grid center) and a constant potential surface (such as a sheath). 

Plotting Parameters 


Plotting limits 

Set the region of space (specified in meters from center of grid) for which 
trajectories or particle positions are shown. If no plotting limits are set (all 
zeroes) no trajectories are generated. 

Tracking limits 

Limits (specified in meters from the center of the grid) of initial particle 
locations. Particles originating outside these limits are ignored. 

Buttons 


OK 

Accept displayed parameters and return to Results 3D tab. 

Apply 

Accept displayed parameters. 

Cancel 

Return displayed parameters to previous values. 


17.3 Output Files 

Four of the computational modules, Embed Object In Grid, Potentials in Space, Create 
Particles, and Track Particles, have input and output files. These modules write a text output 
file in addition to writing results into the database. These output files contain useful information, 
both computational results and diagnostic information. The amount of diagnostic information is 
controlled by the diagnostic levels set on the Advanced Potential Solver Parameters and 
Advanced Particle Parameters dialog boxes. If a calculation goes awry, the information 
contained in these files can help diagnose the problem. A description of the most widely used 
information follows, and a more extensive description is in Appendix A. 

17.3.1 Embed Object in Grid 

The output file from the execution of the Embed Object In Grid module (N2kDyn_out.txt) is 
primarily useful for identifying possible problem areas. 

Normal completion is indicated by the following lines at the end of the file. 

WptTri Called xxxxxxx Times; 

WptQud Called yyyyyyy Times. 

***TIMER*** Total Elapsed User Time =111957.203 Seconds. 

***TIMER*** Total Elapsed User Time =111957.250 Seconds. 

The presence of error messages, indicated by the presence of the string “Error” in the file, may or 
may not indicate problem regions. The potential solution in volume elements in which error 


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81 






























messages occur should be checked for possible problems and the grid modified (usually by 
additional subdivision) if necessary. 

17.3.2 Potentials in Space 

Nonnal completion is indicated by the following lines at the end of the file. 

(prefix, potent./feraf/on#_out.txt.) 

About to close input - unit 5 
End Potential Solver. 

***TIMER*** Total Elapsed User Time = 8118.583 Seconds. 

About to return from PSMAIN 

The appropriate potentials to use for the sheath boundary for each grid appear near the beginning 
of the output file. 

Sheath boundary potentials: 

Grid # 1 Ymesh= 1.000000 meters. SthPot= 4.344533 volts. 

Grid # 2 Ymesh= 0.500000 meters. SthPot= 1.724129 volts. 

Grid # 3 Ymesh= 0.250000 meters. SthPot= 0.684221 volts. 

Grid # 4 Ymesh= 0.250000 meters. SthPot= 0.684221 volts. 

Grid # 5 Ymesh= 0.125000 meters. SthPot= 0.271533 volts. 

Grid # 6 Ymesh= 0.125000 meters. SthPot= 0.271533 volts. 

The most important information in the output file from execution of the Potentials in Space 
module is diagnostic infonnation regarding the convergence of the potential solution. The “RMS 
Error” and “RDotR” infonnation displayed on the monitor are also written to the file. A complete 
discussion of these values and other convergence infonnation is in Appendix A. The overall 
convergence is given by the differences between the new and previous potential solutions, which 
are expressed as root-mean-square errors and are listed grid by grid. 

RMS Error for Grid # 1 = 7.0608E-03 

RMS Error for Grid # 2 = 8.3624E-01 

RMS Error for Grid # 3 = 3.3420E+00 

RMS Error for Grid # 4 = 9.5733E-02 

RMS Error for Grid # 5 = 3.5733E+00 

RMS Error for Grid # 6 = 1.7358E+00 

PSMAIN -- space charge iter= 18 rmserr= 2.1303E+00 

If the root-mean-square errors fail to decrease to an acceptable level, solution-mixing may 
ameliorate or solve the problem. (See end of Section 14.4.) A particularly large “RMS Enor” for 
a particular grid may or may not indicate a problem in obtaining a solution. 

17.3.3 Create Particles 

Nonnal completion is indicated by the following lines at the end of the file. 

Exiting Particle Generator. 

***TIMER*** Total Elapsed User Time = 64241.121 Seconds. 

A line near the end of the file indicates how many particles were created. 

GenPa2: found 8005 ELECTRON particles spanning 9 pages. 


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82 



17.3.4 Track Particles 


Normal completion is indicated by the following lines at the end of the file 
(/;rc//x_t rac k c r_t raj _/ terati on #_out. txt). 

Exiting Particle Tracker. 

***TIMER*** Total Elapsed User Time = 64B79.781 Seconds. 

A table of the current to each material and to each conductor appears near the end of the file. 
Each entry in the table indicates the current (amperes) collected by the surface elements of the 
specified material and conductor during the current thnestep. 


Cond. 

ALUM 

KAPT 

CRAP 

GOLD 

Total 

1 

-1.3E-07 

-1.3E-08 

0.0E+00 

0.0E+00 

-1.465E-07 

2 

0.0E+00 

0.0E+00 

0.0E+00 

-1.1E-01 

-1.141E-01 

3 

0.0E+00 

-6.8E-07 

-1.1E-05 

0.0E+00 

-1.204E-05 

4 

0.0E+00 

0.0E+00 

-2.8E-06 

0.0E+00 

-2.847E-06 

5 

0.0E+00 

0.0E+00 

-1.9E-06 

0.0E+00 

-1.855E-06 

6 

0.0E+00 

0.0E+00 

-5.1E-06 

0.0E+00 

-5.101E-06 

7 

0.0E+00 

0.0E+00 

-8.0E-05 

0.0E+00 

-7.951E-05 

8 

0.0E+00 

0.0E+00 

-5.4E-03 

0.0E+00 

-5.422E-03 

Total 

-1.3E-07 

-6.9E-07 

-5.5E-03 

-1.1E-01 

-1.196E-01 


Historical currents, relevant to time dependent calculations, are listed at the very end of the file. 


ITime 

Dt 

Time 

Col 1ected 

Lost 

T rapped 

Other 

Saved 

1 

1.00E-06 

1.00E-06 

7.76E-05 

0.00E+00 

0.00E+00 

0.00E+00 

T 

2 

1.00E-06 

2.00E-06 

1.88E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

3 

1.00E-06 

3.00E-06 

2.31E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

4 

1.00E-06 

4.00E-06 

2.58E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

5 

1.00E-06 

5.00E-06 

2.85E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

6 

1.00E-06 

6.00E-06 

3.09E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

7 

1.00E-06 

7.00E-06 

3.08E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

8 

1.00E-06 

8.00E-06 

3.20E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

9 

1.00E-06 

9.00E-06 

2.91E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

10 

1.00E-06 

1.00E-05 

2.97E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

11 

1.00E-06 

1.10E-05 

3.07E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

12 

1.00E-06 

1.20E-05 

2.44E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

13 

1.00E-06 

1.30E-05 

3.06E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

14 

1.00E-06 

1.40E-05 

2.69E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

15 

1.00E-06 

1.50E-05 

2.68E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

16 

1.00E-06 

1.60E-05 

2.43E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

17 

1.00E-06 

1.70E-05 

2.33E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

18 

1.00E-06 

1.80E-05 

2.61E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

19 

1.00E-06 

1.90E-05 

2.36E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

0 

0.00E+00 

0.00E+00 

0.00E+00 

0.00E+00 

0.00E+00 

0.00E+00 

F 

20 

1.00E-06 

2.00E-05 

2.31E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 


Particle tracking proceeds grid by grid, iterating through all particles that start in each grid. A 
summary of the status of all the particles is listed after every grid. 


Trackr: total of 


8241 new particles. 

2117 were partially tracked. 

591 were dead. 

5110 went off primary grid. 

0 were trapped. 

423 with unknown status. 


Weight: -5.8023E-02 
Weight: -2.3377E-02 
Weight: -9.4114E-03 
Weight: -2.1547E-02 
Weight: 0.0000E+00 
Weight: -3.6869E-03 


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83 








The “new” particles are those that were created since the last time particles were tracked. The 
“partially tracked” particles are those that have not yet been tracked. The “dead” particles are 
those that hit the object. The particles that “went off primary grid” are those that left the 
computational space. The “trapped” category is not used. Particles classified as “unknown” have 
most likely exceeded the maximum number of substeps (e.g., because they are trapped by a 
magnetic field). 

The particle weights generally are proportional to the current they represent. For PIC type 
problems (particles created by “Uniform” and “Boundary Injection”) the weights are 
proportional to their charge. Particles created using “Contour” or “Surface/Detector” have 
weights that are not easily interpreted. The weights of particles read from an external file are 
specified in the file. 


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84 



Ill EXAMPLES 


18 Spacecraft Charging in a Tenuous Plasma (example name: “GeoCharging”) 

18.1 Background 

The basic physics background on spacecraft charging is provided in Section 13. In this first 
example Nascap-2k is used to compute charging of a simple spacecraft at geosynchronous 
altitude. The calculation provides the history of surface potentials and fluxes during charging 
under different conditions in a “Worst Case” geosynchronous environment. 


18.2 Object Definition 


A simple spacecraft is depicted in Figure 45. The sun is taken to be incident on the spacecraft 
from the (0.77, 0.4, -0.5) direction in the spacecraft coordinate system. This is appropriate to a 
spacecraft in geosynchronous orbit at 0° longitude and Universal time of 8 hours, 10 minutes, 
and 0 seconds, on day 360 (December 26) of 2002. (The SEE Interactive Spacecraft Charging 
Handbook computes the incident sun angle for geosynchronous spacecraft at 0° latitude as a 
function of day and time.) The Object Toolkit model of the spacecraft depicting materials and 
conductors as displayed in Nascap-2k is shown in Figure 46. Notice that sun-pointing required a 
33-degree (counterclockwise from the +z-axis) array twist. 



- 7.04 m 


y«- 


-2.00 m- 


| Black Kapton blankets [top & bottom] [_ 

J Solar cells [solar array front] 

| Teflon blankets [most of body] 

J Non-conducting paint [top antenna] 

I | OSR [2/31 of side L 

1 Graphite [antennas] 

I Kapton [booms and solar array back] 



Figure 45. Illustrative Spacecraft for Sample Charging Calculation Using Nascap-2k 


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85 


4.4 m 

































BES® 


Nascap2k - C:\MyCalculations\ManualsYGeoCharging\GeoChargingProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging \ Space Potentials Particles j Script Results Results 3D 



hBrJOU 0EEEEEJ 


Cursor Tools 


Direct Movement & Rotation 



Materials 




Figure 46. Spacecraft Model Used in the “GeoCharging” Example Showing Material (Top) and 

Conductor (Bottom) Definition 


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18.3 Surface Charging Calculation 
18.3.1 Case 1: Charging in Sunlight 

First, we calculate charging when the spacecraft is sunlit. Start Nascap- 2k and click “Create New 
Project.” 

Name the new project “GeoCharging” and load the “GeoCharging” object from the 
Nascap2k_4/Manual/Example Problems/GeoCharging folder (GeoChargingObject.xml). On the 
Problem tab, under “Problem Type,” check “Surface Charging.” Figure 47 illustrates the 
Problem tab as it should now look. 



Figure 47. Problem Tab for the “GeoCharging” Example 

These calculations use the “Worst Case” environment recommended by the 1984 NAS A .Design 
Guidelines for Assessing and Controlling Spacecraft Charging Effects 9 for initial modeling 
during the spacecraft design process. (See Section 11.1.) Click the Environment tab, which 
displays geosynchronous environment parameters. Under “GEO Environment Plasma,” select 
“Worst Case” from the drop-down menu. Make sure the magnetic field, sun-direction, and 
relative sun intensity are as shown in Figure 48. 


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File Edit View Materials Help 

Problem Environme nt j Applied Potentials j Charging \ Space Potentials \ Particles Script j Results j Results 3D 

Geosynchronous Environment 

■ GEO Environment Plasma- 

Worst Case 


Electron Density (m* 3 ): 1 120E6 
Electron Temperature (eV): 1.200E4 
Ion Density (m' 3 ):2.360E5 
Ion Temperature (eV):2.950E4 
Electron Kappa: 

Ion Kappa: 

Electron Current (Am' 2 ):3.289E-6 
Ion Current (Am' 2 ): 2.536E-8 

Magnetic Field (T)- 

Bxj o.Q | Byj o o j Bzlao 


Direction to Sun- 

xj o.770 1 Yj o.400 | zj -0.500 | 


Relative* Sun Intensityj l.OOO 


'(value at Spacecraft) / (value at Earth Orbit) 

□ Use photoemission spectra 


Add Species 







Type 

Mass (amu) 

Charge (C) 

% 

Electron 

5.486E-4 

-1.602E-19 

100.0 


Delete Species 


Figure 48. Geosynchronous Environment Tab for Case 1 of the “GeoCharging” Example 


The initial potentials are set to zero on the Applied Potentials tab as depicted in Figure 49. 



Figure 49. Applied Potentials Tab for the “GeoCharging” Example 


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In Figure 50, the Charging Time parameters are set to allow the spacecraft to charge for 5 
minutes using geometrically distributed timesteps. Typically, the longest a spacecraft would be 
exposed to such a severe environment is 15 minutes. 



Figure 50. Charging Tab for the “GeoCharging” Example 

Click the Script tab. The message “The Script is out of date! ” appears and there is no script on 
the page. Click the “Build Script” button. Once the script is created, sublevels in the “Charge 
Surfaces” script can be opened up by clicking on the particular steps as shown in Figure 51. 


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89 





















File Edit View Materials Help 

Problem }' Environment Applied Potentials | Charging 1 Space Potentials Y Particles \ Script j Results Results 3D 


Run Script Edit Script 


9 Q Read_Object 
A FileName 
9 C Charge_Surfaces 
? Q Setlllumination 
A Value 

Ax 

Ay 

Az 

9 Q SetEnvironment 
9 CJ Environment 
A type 

A nel 
A tel 
Anil 
A til 

A begintime 

9 O SetlnitialConductorPotential 
A Index 

A Value 


GeoChargingObjecLxml 


1.000 

0.770 

0.400 

-0.500 


1.120E6 

1.200E4 

2.360E5 

2.950E4 

0.0 


9 TimeParams 

A nsteps 

0 

A begintime 

0.0 

A endtime 

300.0 

A mindt 

0.100 

A maxdt 

60.00 


Build Script 


E Automatically overwrite files 


Run Script 


Figure 51. Script for Case 1 of the “GeoCharging” Example 


To execute the calculation, click the “Run Script” button. Figure 52 shows a snapshot of the 
Script Running Monitor during the calculation. The monitor’s main purpose is to confirm that 
the calculation is proceeding and indicate its progress. In Figure 52, the calculation has reached 
0.345 seconds out of the requested 300 seconds. As the calculation proceeds the “Total Current” 
should drop a few orders of magnitude from its initial level. 

H 4>\ Script Running Monitor Charge Surfaces 


Prefix: GeoCharging 

Current Command: DoTimeSteps 
Time: 0.345 
Minimum Potential: -3.602 
Maximum Potential: 3.663 
Chassis Potential: -0.281 
Total Current: 1.987e-004 

Elapsed Time: 24.680 



Figure 52. Script Running Monitor During Calculation for Case 1 of the “GeoCharging” Example 

Figure 53 through Figure 56 show the results of the calculation as displayed on the Results tab. 
The drop-down list at top-left enables the selection of potentials, electric field, charging currents, 
or tracked currents. The checkboxes along the left are used to select for which elements the 
desired quantity appears in the graph on the right. The graph is updated each time the “Plot” 
button is clicked. 

In Figure 53, the “Surface Element Groups” portion of the tab is used to compare the history of 
potentials of sunlit and dark surface elements of the cylindrical antenna. Specify groups of 


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elements by selecting the conductor number, material, normal direction, and if the elements are 
sunlit or dark. In the figure, “NPaint” is selected from the drop-down list of materials, while 
“Sunlit” is selected in the first row and “Dark” in the second. (Note that the “sunlit” category 
does not account for shadowing by other surfaces, so that some of the “sunlit” surfaces are 
actually shadowed.) Click the “Add Row” button to create an additional row. When you click the 
“Plot” button, the minimum, maximum, and average surface potentials for each group are 
displayed for each timestep. In this case, all the shaded potentials are equal and coincident with 
the minimum sunlit potential (which is that of the shadowed sun-facing cells). 



Figure 53. Results Tab for Case 1 of the “GeoCharging” Example Comparing Evolution of 
Potential Between Sunlit and Dark Surface Elements on the Cylindrical Antenna 

Potential, electric field, and current-to-individual surface elements may also be compared using 
the “Individual Surface Elements” section of the tab, as shown in Figure 54. Enter the element 
number. (The element number of a specific element can be determined on the Results 3D tab by 
clicking on the element when the cursor is in element select mode). Values are automatically 
added in the “Conductor,” “Material,” and “Potential,” (or “Current” or “Electric field”) fields 
when the checkbox is checked and the “Plot” button is clicked. The “Potential,” (or “Current” or 
“Electric field”) value is that at the end of the calculation. 


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sum 


Nascap2k - C:\MyCalculations\Manuals\GeoCharging\GeoChargingProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging Space Potentials f 1 ' Particles [ Script Results Results 3D 


Plot 

Condu... 

Material 

Norma.. 

X 

Y 

z 

Sunlit 

□ 

Any 

NPaint 

180.0 

0.0 

0.0 

0.0 

Sunlit 

] lAny 

NPaint 

180.0| 0.0 

0.0 

0.0 

Dark 


Individual Surface Elements 


Plot 

Element 

Conductor 

Material 

Potential (V) 

0 

31 

1 

Graphite 

-3971. 

h 

85 

1 

OSR 

-4498. 


Add Row Delete Row 




Potential (V) 


Graph Settings Text 


Potential 



Figure 54. Results Tab for Case 1 of the “GeoCharging” Example Comparing Evolution of 

Potential for Different Surface Elements 


Figure 55 shows the mean charging current density to bare cells of a conductor as a function of 
time. The graph is created by selecting “Charging Current” on the drop-down list and checking 
the checkboxes next to the conductors in the “Conductors” section at the bottom of the tab. The 
value for each conductor at the end of the calculation is displayed. 


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BBS 


Nascap2k - C:\MyCalculations\Manuals\GeoCharging\GeoChargingProject.xmI 


File Edit View Materials Help 


Problem Environment Applied Potentials Charging ~\ Space Potentials \ Particles [ Script j Results Results 3D 


| Charging Current ▼ 


Surface Element Groups 


Plot 

Condu... 

Material 

Norma.. 

X 

Y 

z 

Sunlit 

□ 

Any 

NPaint 

180.0 

0.0 

0.0 

0.0 

Sunlit 

] lAny 

NPaint 

180.0 

0.0 

0.0 

0.0 

Dark 


Add Row 


Delete Row 


Individual Surface Elements 


Plot 

Element 

Conductor 

Material 

Charging C... 

□ 

31 

1 

Graphite 

-1.469E-6 

□ 

85 

1 

OSR 

-1.509E-6 


Conductors 


Plot 


Add Row 


Delete Row 


Conductor 


Charging Current (A/. 


1 -4.006E-7 



Figure 55. Results Tab Showing mean Current density to the Conductor as a Function of time for 

Case 1 of the “GeoCharging” Example 


The Text subtab can be used to obtain the difference between the potentials on insulators and 
those on the underlying conductor(s), as shown in Figure 56. This is an important part of a 
spacecraft charging calculation that leads to assessments of the likelihood of arcing. Table 35 
lists absolute and differential potentials after 300 seconds for Case 1. Because the results are 
displayed in tabular format they can be copied elsewhere (e.g., a favorite spreadsheet program) 
for further manipulation, such as assessing the sensitivity of the results on the choice of number 
of timesteps, as shown in Figure 57. 


Table 35. Absolute and Differential Spacecraft Potentials after 300 seconds for the “GeoCharging” 

Example 



Chassis 

Kapton 

OSR 

Solar Cells 

Teflon 

Non-cond. 

Paint 

Absolute 

Potential (kV) 

-4 

-4.0 to -5.3 

-3.7 to -5.0 

-2.4 to -3.7 

-3.5 to -5.2 

-4.4 to -5.3 

Differential 
Potential (kV) 
(Vi ns — V con( j) 


-0.03 to-1.4 

0.3 to -1.2 

1.7 to 0.3 

0.6 to-1.3 

^t 

i 

o 

o 

1 


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EMg 


O Nascap2k - C:\MyCalculations\Manuals\GeoCharging\GeoChargingProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging Space Potentials f Particles [ Script i Results Results 3D 




Potential 

- 


Plot 

Condu... 

Material 

Norma.. 

X 

Y 

z 

Sunlit 




Any 

Black... 

180.0 

0.0 

0.0 

0.0 

Sunlit 




Any 

Graphi... 

180.0 

0.0 

0.0 

0.0 

Dark 




Any 

Kapton 

180.0 

0.0 

0.0 

0.0 

Any 


✓ 


Any 

NPaint 

180.0 

0.0 

0.0 

0.0 

Any 




Any 

OSR 

180.0 

0.0 

0.0 

0.0 

Any 




Any 

Solar... 

180.0 

0.0 

0.0 

0.0 

Any 




Any 

Teflon 

180.0 

0.0 

0.0 

0.0 

Any 




Individual Surface Elements 


B 


Potential (V) 


TimeSteps, Max3, Avg3, Min3, Element #31, Element #85, Condi 
0 . 0 . 0 . 0 , 0 0 . 0 0 . 0 . 0 , 0 . 0 . 0.0 
0.100, 5.855, 5.279, 5.195, 5.864, 5.839, 5.864 
0.214, 0.465, -1.589, -1.895, -9.758E-2, -0.967, -9.758E-2 


Plot 

Element 

Conductor 

Material 

Potential (V) 


el 

31 

1 

Graphite 

-3971. 



85 

1 

OSR 

-4498. 



Graph ] Settings Text 


0.345, 

0.805,- 

2.469,- 

2.954,- 

0.281,- 

1.638,- 

0.281 

0.495, 

0.133, 

-4.255, 

4.877, 

-1.202, 

-3.004, 

-1.202 

0.667, 

2.258, 

-6.807, 

7.498, 

-2.677, 

-5.152, 

-2.677 

0.863, 

4.992, 

-10.11, 

-10.88, 

-4.745, 

-7.906, 

-4.745 

1.088, 

8.382, 

-14.07, 

-14.91, 

-7.279, 

-11.54, 

-7.279 

1.345, 

13.44, 

-19.94, 

-20.89, 

-11.55, 

-16.16, 

-11.55 

1.640, 

22.40, 

-30.13, 

-31.25, 

-19.96, 

-26.64, 

-19.96 

1.977, 

42.51, 

-52.26, 

-53.70, 

-40.18, 

-46.94, 

-40.18 

2.362, 

57.38, 

-69.79, 

71.62, 

-55.56, 

-65.17, 

-55.56 

2.804, 

68.62, 

-83.42, 

-85.56, 

-66.58, 

-76.29, 

-66.58 

3.309, 

83.97, 

-100.8, 

-103.2, 

-80.92, 

-93.79, 

-80.92 

3.887, 

101.7, 

-121.6, 

124.5, 

-98.37, 

-111.4, 

-98.37 

4.549, 

122.6, 

-145.5, 

-148.8, 

-118.4, 

-136.4, 

-118.4 

5.307, 

145.4, 

-172.0, 

-175.9, 

-140.6, 

-158.7, 

-140.6 

6.174, 

172.0, 

-202.7, 

-207.2, 

-166.2, 

-190.2, 

-166.2 

7.166, 

201.2, 

-237.4, 

-242.6, 

-195.3, 

-219.5, 

-195.3 

8.301, 

235.9, 

-276.5, 

-282.5, 

-227.9, 

-260.2, 

-227.9 

9.601, 

273.5, 

-320.5, 

-327.3, 

-264.4, 

-296.9, 

-264.4 

11.09, 

316.7, 

-370.7, 

-378.6, 

-306.3, 

-349,6, 

-306.3 

12.79, 

366.5, 

-428.3, 

-437.3, 

-354.3, 

-397.8, 

-354.3 

14.74, 

419.1, 

-490.6, 

-501.0, 

-405.9, 

-463.5, 

-405.9 

16.97, 

483.2, 

-562.5, 

-574.2, 

-465.4, 

-523.1, 

-465.4 

19.52, 

553.1, 

-644.2, 

-657.6, 

-533.3, 

-591.2, 

-533.3 

22.44, 

631.3, 

-735.6, 

-750.8, 

-609.0, 

-687.7, 

-609.0 

25.79, 

720.0, 

-838.8, 

-856.2, 

-694.6, 

-773.3, 

-694.6 

29.61, 

818.4, 

-953.2, 

-972.9, 

-789.1, 

-893.7, 

-789.1 

33.99, 

928.6, 

-1082., 

1104., 

-895.5, 

-999.8, 

-895.5 


Figure 56. Results Tab Showing Text Subtab with Tabulated Results 


ro 

*> 

£ 

0 ) 

*-> 

o 

CL 

5 

s_ 

o 

+-* 

o 

3 

T3 

£ 

O 

o 



100 200 

Time (sec) 


300 


Figure 57. Sensitivity of Results on Choice of Number of Timesteps in the Charging Calculation of 

Case 1 of the “GeoCharging” Example 

The Results 3D tab (Figure 58) shows potentials on the spacecraft from two different views. 
Notice that the least negative surface elements are at the end of the solar arrays while the most 


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negative are the shaded boom (Kapton) and Teflon surface elements. Note in particular the high 
negative potential on the portion of the sun-facing face of the spacecraft that is shadowed by the 
antenna. Click the element selection tool (leftmost of the Cursor Tools) and click on one of these 
shadowed cells to verify that it is indeed shadowed. 


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Figure 58. Results 3D Tab for Case 1 of “GeoCharging” Showing Spacecraft Potentials of Sunlit 

(Top) and Dark (Bottom) Surface Elements 


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18.3.2 Case 2: Eclipse Exit 


The night-to-dawn transition is a likely region for surface charging-induced anomalies onboard 
the spacecraft. While in eclipse, the spacecraft may charge negatively to tens of kilovolts. A 
potential sufficient for discharge is easily created when the satellite emerges into sunlight, which 
results in near zero surface potentials due to photoelectron emission. In this example we perform 
an eclipse/sunlight charging calculation. We will calculate potentials at the end of five minutes of 
eclipse to obtain initial conditions for a five minute sunlight calculation. To preserve the earlier 
calculation, exit the code, make a new directory for the new case, copy all the files into the new 
directory, and restart the code, opening the copied project in the new directory. 

To perfonn the consecutive eclipse-sunlit calculation we must edit the script from the Edit 
Script subtab (Figure 59). We begin with the script of Case 1 and repeat the “Setlllumination” 
and “DoTimeSteps” commands immediately following the original “DoTimeSteps” command, as 
shown in Figure 59. To duplicate a command, select it and then click the “Duplicate Item” 
button. Use the “Up” and “Down” buttons to reorder commands. Set the illumination value to 
zero (0) the first time and one (1) the second time, as shown in Figure 60. Make sure the nsteps 
value of each “DoTimeSteps” command is set to 45. All other parameters remain as defined in 
Case 1. (Note that several such steps with varying illumination values could be used to exit 
eclipse at a finite rate.) 



Figure 59. Edit Script Subtab for Case 2 of the “GeoCharging” Example 


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File Edit View Materials Help 

Problem | Environment j Applied Potentials Charging \ Space Potentials \ Particles j Script Results | Results 3D 

Run Script j Edit Script 


■ Commands- 

Loop 

Read_Object 
Append_Object 
lnitialize_Potentials 
Charge_Surfaces 
DoOneTimeStep 
DoTime Steps 
DoT rackTime Step 
EmitCurrent 
FixGroundPotential 
Read Photoemission 
SetBField 
SetConductorBias 
SetCustomCurrentDLL 
SetEnvironment 
Setlllumination 
SetlnitialConductorPotential 
SetParameters 
SetVelocity 
SetVXBPotentials 
UseTrackedCurrent 
UseTrackedlons 
Embed_Object_in_Grid 
PotentialsJn_Space 
Static_A_Field 
Create_Particles 
Track_Particles 
Save_Files 


Script- 

Value 

o- 0 Read_Object 


9 0 Charge Surfaces 


9 C Setlllumination 

A Value 

0.0 

Ax 

0.770 

Ay 

0.400 

Az 

-0.500 

o- 0 SetEnvironment 


o- Q SetlnitialConductorPol 


9 0 DoTimeSteps 


9 CJ TimeParams 


A nsteps 

45 

A begintime 

0.0 

A endtime 

300.0 

A mindt 

0.100 

A maxdt 

60.00 

9 0 Setlllumination 


A Value 

1.000 

A* 

0.770 

Ay 

0.400 

Az 

-0.500 

9 0 DoTimeSteps 


9 £] TimeParams 


A nsteps 

45 

A begintime 

0.0 

A endtime 

300.0 

A mindt 

0.100 

A maxdt 

60.00 



Up 


Build Script 


Save Files 0 Automatically overwrite files Run Script 


Figure 60. Expanded Script for Case 2 of the “GeoCharging” Example 


Once the script is edited, it is executed by clicking the “Run Script” button. The Results tab 
(Figure 61) shows the history of the potential for various surface elements during the 10-minute 
time interval. The two time periods, before and after the eclipse exit, can be seen clearly from the 
Potential versus Time plots. During the eclipse period all the NPaint charges to equally negative 
differential potential with respect to the conductor. After a uniform increase in potential at eclipse 
exit, differential potentials develop among the sunlit NPaint cells. The dark NPaint cells (along 
with the shadowed sun-facing NPaint cells) continue to charge negative together. 


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HIM 


Nascap2k - C:\MyCalculations\Manuals\GeoCharging\GeoChargingProject.xml 


File Edit View Materials Help 


Problem | Environment Applied Potentials Charging Space Potentials - ^ Particles Script Results Results 3D 


Surface Element Groups 


Plot 

Condu... 

Material 

Norma.. 

X 

Y 

z 

Sunlit 

k 


Any 

NPaint 

180.0 

0.0 

0.0 

0.0 

Sunlit 

k 


Any 

NPaint 

180.0 

0.0 

0.0 

0.0 

Dark 


Add Row Delete Row 


Individual Surface Elements 


Plot 1 Element | Conductor | Material | Potential (\Q 


E 


Potential (V) 


Graph Settings ~[ Text 


Potential 



Figure 61. Results Tab for Case 2 of the “GeoCharging” Example 


19 Current Collection in a Low-Earth-Orbit Plasma (example name: “Bipolar”) 

19.1 Background 

A common issue on low Earth orbit spacecraft is the prediction and control of interactions 
between a spacecraft with high-voltage components (ranging from a few volts to kilovolts) and 
the ionospheric environment. Ever since electron guns were first placed on rockets, the voltage 
on the main body necessary to collect ionospheric electrons and complete the circuit has been the 
subject of numerous theoretical and experimental studies. A large-scale effort to address such 
issues was the SPEAR series of experiments. SPEAR-F was designed to measure whether 
Earth’s magnetic field impedes electron collection, SPEAR-II was designed to test pulsed high- 
voltage components, and SPEAR-III was designed to test proposed spacecraft grounding 
mechanisms. The following example illustrates the implementation of Nascap-2k to study the 
physics associated with current collection by the bipolar plasma sheath generated by a 
SPEAR-I/SPEAR-III like object. 

In the following example, a new problem—Bipolar—should be created, and the object “Bipolar” 
should be loaded from the Nascap2k_4/Manual/Example Problems/Bipolar folder 
(BipolarObj ect.xml). 

19.2 Object and Grid Definition 

The object (constructed using Object Toolkit) is shown in Figure 62. It consists of a gold-plated 
cube (Figure 63) mounted on a cylindrical boom (Figure 64). The boom is connected to a 
cylindrical support boom covered with an insulator (Figure 65). This boom is in turn connected 


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to the main (aluminum) rocket body (Figure 66). In SPEAR-I and SPEAR-III this part of the 
rocket was a bushing constructed with graded rings that were connected by resistors. The graded 
boom created a uniform potential gradient from the positively biased cube to payload ground. 

The grid surrounding the object is constructed using GridTool. The example involves calculating 
both electron-collecting (surrounding the cube) and ion-collecting (main body) sheaths that have 
different characteristic scale lengths. Therefore, to resolve the space potentials accurately it is 
necessary to incorporate six grids of different extents and resolution based on the region of space 
in which the potentials are to be computed. The specifications of all the grids are shown in 
Figure 67. The combined grid arrangement with the object embedded is shown in Figure 68. 

To build the problem grid, click “Edit Grid” on the Problem tab. This launches GridTool. On 
GridTooTs File menu, select “Import Object” and import the “Bipolar” object. Under the Grid 
menu, select “New Primary Grid,” and set the grid dimensions and mesh size to those shown in 
the top left dialog box in Figure 67. Click the primary grid folder icon to the right of the 3-D 
object/grid display, and select “New Child Grid” on the Grid menu, setting the limits and 
subdivision ratio as shown in the Child Grid dialog box for grid number 2 in the top right dialog 
box of Figure 67. Make grids 3 and 4 the “children” of grid 2, and make grids 5 and 6 the 
children of grid 3, setting the dimensions as shown. Save the grid to the current project by 
selecting “Save Grid” from the GridTooTs File menu. 


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Elfgfg 


Nascap2k - C:\MyCalculations\Manuals\bipolar\bipolar1 \bipolarProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging | Space Potentials j Particles Script Results Results 3D 



CiEdELLI EUEJEBLIE) 


Cursor Tools 


Direct Movement & Rotation 


_ Spacecraft- 

Display: Material 
View: ) Standard |- 
Hide Spacecraft 



_ T r ajectories- 

Specify Trajectories... 
Show Trajectories 


“Color Scale 


<D L inear O Log 


Min: 

0.0 

Max: 

0.0 


Replot 



Materials 

Aluminum 


Kapton 


Graphite 


Gold 




Figure 62. Object Constructed for the Study of Current Collection from a Bipolar Sheath in a Low- 
Earth-Orbit Environment. Top: Object Materials. Bottom: Object Conductors 


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Figure 63. Specifications of Gold-plated Cube in Figure 62 



Figure 64. Specifications of Graded Boom in Figure 62 


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Figure 65. Specifications of Kapton Support Boom in Figure 62 



Figure 66. Specifications of Main Rocket Body in Figure 62 


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si 


B 


Primary Grid 


Grid Number: 1 


m 


Grid Dimension: 18 


18 


25 


Mesh Size (m): | 1.000 | 


Primary Grid Extents * 
Min. 


X: 

1.000 

19.00 

Y: 

1.000 

19.00 

Z: 

1.000 

26.00 


Apply 


Grid Number: 2 

Parent Grid Dimension: 18 18 

Subdivision Ratio: 2 


25 


r Grid Limits ' 


Min. 

Max. 

X: !s 

I lie 


Y: 5 

J |15 

Z: |7 

1 [23 


■ Primary Grid' 

Min. 


Max. 


X: 

5.000 

16.00 

Y: 

5.000 

15.00 

Z: 

7.000 

23.00 


Apply 


Grid Number: 3 

Parent Grid Dimension: 22 
Subdivision Ratio: 12 


20 


32 


~ Grid Limits' 



_ Primary Grid- 

Min. Max. 

X: 7.000 13.00 

Y: 7.500 12.50 

Z: 13.00 19.50 


Apply 


.= Child Grid 


Grid Number: 4 

Parent Grid Dimension: 22 20 

Subdivision Ratio: 2 


32 


“ Grid Limits' 



Primary Grid" 
Min. 


Max. 


X: 

7.000 

13.00 

Y: 

7.000 

12.50 

Z: 

9.000 

13.00 


Apply 


0 W & Child Grid 


Grid Number: 5 

Parent Grid Dimension: 24 
Subdivision Ratio: 2 


20 


26 


- Grid Limits ' 



_ Primary Grid- 

Min. Max. 

X: 9.250 11.25 

Y: 9 000 11.00 

Z: 15.00 17.75 


OK 


Apply 


Cancel 


Grid Number: 6 

Parent Grid Dimension: 24 
Subdivision Ratio: 2 


20 


26 


- Grid Limits ' 



_ Primary Grid- 

Min. Max. 

X: 9.500 10.00 

Y: 9.750 10.25 

Z: 13.00 15.00 


OK 


Apply 


Cancel 


Figure 67. Grid Specifications for the Parent and Child Grids Used in the “Bipolar” Example 


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Figure 68. Grid Arrangement Showing All Six Grid Levels and Embedded Object for the “Bipolar” 

Example 


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105 



19.3 Case 1: Electron Collection 
19.3.1 Potentials in Space Calculation 

Figure 69 shows the Problem tab with “LEO” checked under “Environment” and “Potentials in 
Space” checked under “Problem Type.” This calculation consists of computing potentials in a 
low Earth orbit environment. We later compute the current collected. We use an analytic space 
charge model in this example. The object and grid must be loaded before these choices are 
available on the user interface. The object is loaded using the “Load Object” choice on the File 
menu. If a grid file with the appropriate name is present, the grid is automatically loaded on code 
start-up and on return from GridTool. If the grid is not loaded, open the grid file (and the object 
file) in GridTool and save the grid to the same directory as the rest of the project files. 



Figure 69. Problem Tab for the “Bipolar” Example 


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10 3 

The Environment tab is shown in Figure 70. The plasma density we use, 5x10 m" , is 
considerably lower than the default value (10 12 m°). We assume 100% oxygen ions by clicking 
the “Add Species” button and changing the name “Unknown” to “Oxygen” (the mass, charge, 
and percentage are already correct). We begin with no magnetic field; all other environment 
parameters remain unchanged for these calculations. 



Figure 70. Environment Tab for the “Bipolar” Example, for Case 1 and Zero Ambient Magnetic 

Field 


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In Case 1, the main body is held at ground potential. The conductor potentials are set as shown 
on the Applied Potentials tab (Figure 71). The gold-plated cube is biased to +10 kV with respect 
to the body, and each of the remaining six conductors is biased positively in 1.5 kV increments. 
Set the type from the drop-down menu, and enter the initial or bias potential by double clicking 
in the “Initial Potential” box and entering the appropriate value. 



Figure 71. Applied Potentials Tab for Case 1 of the “Bipolar” Example 


On the Space Potentials tab, select the “Non-linear” analytic space charge density model as it is 
appropriate for steady-state calculations in low Earth orbit plasmas and is used in this example 
for computing the potential distribution around the object. The model is described in greater 
detail in Section 14.1. Because an analytic space charge formulation is used, no iterations 
between potentials and particles are needed. Considering the kilovolt-level potentials associated 
with the object surfaces (Figure 72), the “Target Average (RMS) Error” is set to 1 V. The choices 
on the Advanced Potential Solver Parameters dialog box (Section 14.1) remain at their default 
values. 


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I 


Materials Help 


Problem ] Environment i Applied Potentials Charging [ Space Potentials [ Particles f Script | Results ] Results 3D | 


Charge Density Model- 

O Laplace O Full Trajectory Ions 

O Linear (Debye Shielding) O Plume Ion Density 
<§) Non-linear □ Self-Consistent CEX 

O Frozen ion 

O Barometric O Full PIC 


— □ Geometric Wake Initializatii 
Species: [~~ 


Target Average (RMS) Error (V)j 1.000 


>rof iterations: 

Frac. old potential 


Frac. old density 


Figure 72. Space Potentials Tab for the “Bipolar” Example 


The actual execution of the calculation is launched from the Script tab (Figure 73). Initially, 
because no script has been generated, the “Script is out of date! ” message appears. To build the 
script, click the “Build Script” button. 


File Edit View Materials Help 


Problem j Environment [ Applied Potentials Charging \ Space Po tentials \ Particles [ Script Results | Results 3D | 


j Run Script Edit Script 


? C Read_Objed 
A FileName 

9 c Embed_Objed_in_Grid 
A InputFileName 
A OutputFileName 
? C Potentials_in_Space 
A InputFileName 
A OutputFileName 
A Iteration 


Value 


BipolarObjedxml 

Bipolar_n2kdyn_in.txt 

Bipolar_n2kdyn_out.txt 

Bipolar_potent_0_in.txt 
Bi p o I ar_p ote nt_0_o ut.txt 
0 


Build Script 

l 1 - 


Save Files [✓] Automatically overwrite files Run Script 


Figure 73. Run Script Subtab Showing the List of Commands and Arguments for Case 1 of the 
“Bipolar” Example 


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Note the text files associated with the arguments for the Potentials in Space script element. 
These files contain input and output information associated with the Potentials in Space module 
and are written when either the “Run Script” or “Save Files” button is clicked. 

We are now ready to compute. Click the “Run Script” button to launch the calculation. The 
electric potential solution is monitored through the Script Running Monitor. Figure 74 shows 
progress on the 7th space charge (SC) iteration at which the RMS error is still 20.14 V. At the 
20th iteration the value is 1.35 V, slightly more than the requested value of 1 V. (The slow 
convergence is related to the high screening in the low potential region into which the sheath is 
trying to expand.) This information is provided at the end of the Potentials in Space output file. 
(Search for the string “rmserr” in the Bipolar_potent_0_out.txt file.) 



Prefix: Bipolar 


Input File Name: Bipolar_potent_0_in.txt 
Output File Name: Bipolar_potent_0_outtxt 
After SC Iteration: 7 

RMS Error 2.014e+001 
After SCG Iteration: 5 

Initial RDotR: 5.371 e+004 
Current RDotR: 6.288e+004 
Elapsed Time: 77.985 


Figure 74. Script Running Monitor Showing Computational Diagnostics at the 10th Space 

Calculation 

Figure 75 shows a Y=0 cut plane of the results of the potential calculation for Case 1. To 
(or hide) the cut plane, click on the “Show (Hide) Cut Plane” button. Note that we have selected 
a log color scale and changed the limits. The electron-collecting sheath surrounds the positively 
biased surface elements of the object while no ion-collecting sheath exists because no negatively 
biased components were defined. As a prelude to calculating current collection by the object, it is 
useful to view electron trajectories. Click the “Specify Trajectories” button on the Results 3D 
tab. The Particle Visualization dialog box appears. The parameters are chosen as shown in 
Figure 76. The minimum Z value of the tracking limits may need to be adjusted slightly to 
eliminate additional trajectories. Click the “OK” button to start the calculation. Note that the 
“Contour” option for the initial particle distribution was chosen (Section 15.1). This option 
requires a value for the desired contour value of the potential. We chose a value of 1.724 V, 
which, as is explained in the next section, is the sheath edge potential. The electron trajectories 
are shown in Figure 77. Note that we have turned off the cut plane. The View menu has options 
such as “Set Background Color” that can be used to tailor the view. 


Charge 

display 


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EHM 


Nascap2k - C:\MyCalculations\Manuals\bipolar\bipolar1 \bipolarProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials If Charging \ Space Potentials Particles ~| Script Results Results 3D 



frSdQILJ EUBEBEEJ 


Cursor Tools 


“ Spacecraft- 

Display: [Potential | 

Vie w: | Standard | ^ 

Hide Spacecraft 

“Contours- 

Display:; Potentials 
New 



“Trajectories- 

Specify Trajectories... 

| Show Trajectories | 


“Color Set 

Ol 

Min: 

le 

near <S> Log 

0.0 

Max: 

1 OOOE4 

Replot | 



Direct Movement & Rotation 


Potentials 

Volts 

1E04.- 


3000 

1000 




Figure 75. Distribution of the Electric Potential on a Y=0 Cut Plane for Case 1 of the “Bipolar” 

Example 



Figure 76. Particle Visualization Dialog Box for Case 1 of the “Bipolar” Example 


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EHM 


Nascap2k - C:\MyCalculations\Manuals\bipolar\bipolar1 \bipolarProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging | Space Potentials Particles Script Results Results 3D j 



Cursor Tools 


“ Spacecraft- 

Display: [Potential | 

Vie w: | Standard | ^ 

Hide Spacecraft 

“Contours- 

Display: Potentials 
V~j New 



“Trajectories- 

Specify Trajectories... 
Hide Trajectories ■ 


“Color Scale- 

C Linear f Log 


Min: 

0.0 

Max: 

1.000E4 

Replot | 



h&JGL HE) EE EE 

Direct Movement & Rotation 

Potentials 

Volts 

1E04.- 


3000 

1000 




Figure 77. Electron Trajectories for Case 1 of the “Bipolar” Example 


19.3.2 Surface Currents Calculation 

In this part of the example, we compute current collection for zero and non-zero magnetic fields. 
Return to the Problem tab, uncheck “Potentials in Space,” and check “Surface Currents.” 

Go to the Surface Currents subtab of the Particles tab as shown in Figure 78. Select the 
“Sheath” option (Section 15.1) and highlight “electron” in the “Particle Species” box to compute 
electron current collection. This option requires the value of the potential at the sheath boundary. 
To determine the appropriate value, use the potential contours figure on the Results 3D tab. 
Using appropriate color scale limits (Min=0 V, Max=10 V), Figure 79 shows that the sheath edge 
lies mostly in Grid #2. (Remember to click “Replot” when changing the plot.) The sheath 
boundary potentials for each grid are given in the bipolar_potent_0_out.txt file as shown in Figure 
80. Using Figure 79 and Figure 80, we chose a value of 1.724 V as displayed in Figure 78. 


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File Edit View Materials Help 

Problem i Environment Applied Potentials^ Charging f Space Potentials \ Particles Script | Results j Results 3D | 


Surface Currents ~\ Ion Densities [^Time-Dependent | 


Charged particles used for surface current calculation 

Initial Particle Distribution- 

(?) Sheath Potential Value (V)j 1.724 


O B Field 
C Boundary* 

O Charge Exchange 

G Surface* 

G None of above 
□ External File Filename: 

’Additional parameters on advanc 


Browse 


Particle Species 

■ Electron 

■ Oxygen 


Advanced 




Figure 78. Parameters on the Surface Currents Subtab Used to Compute the Electron Current 

Collection for the “Bipolar” Example 



Figure 79. Potential Distribution Showing Sheath Edge on Mesh for Case 1 of the “Bipolar” 

Example 


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| Bipolar_potent_0_out.txt - Notepad 


File Edit Format View Help 


PSprep — Mix 0.00 % of old to new solution 
PSprep — surface electric field limited. 


PSprep — lTime= 
sheath boundary 


1 TotTim= 0.00E+00 
potentials: 


nirid# 

1 9 m v 




2 Ymesh= 

TTW??n=- 

Grid # 4 Ymesh= 
Grid # 5 Ymesh= 
Grid # 6 Ymesh= 


0.500000 meters. SthPot= 1. 

U.25UUUU ffl^LW 1 !,. bl!IMUl= U. 

0.250000 meters. SthPot= 0. 
0.125000 meters. SthPot= 0. 
0.125000 meters. SthPot= 0. 


ICLow = 0 

conductor potentials at time= 


icond Type 

1 Fixed_Potential 

2 Fixed_Potential 

3 Fixed_Potential 

4 Fixed_Potential 

5 Fixed_Potential 

6 Fixed_Potential 

7 Fixed_Potential 

8 Fixed_Potential 

VXB = C 0.00E+00, 0.00E+00, 

***timer*** main: iteration 1 
***timer*** Total Elapsed user Time 
pssCG: Begin ... 


0.0000E+00 secs: 
value 
0.0000E+00 
1.0000E+04 
1.5000E+03 
3.0000E+03 
4.5000E+03 
6.0000E+03 
7.5000E+03 
9.0000E+03 
0.00E+00) 


Biased From 
0 
0 
0 
0 
0 
0 
0 
0 


22.776 seconds. 


□ 


724129 volts. 1 

b84221 05 IU. 1 

684221 volts. 
271533 volts. 
271533 volts. 


PCond(volts) 
0.0000E+00 
1.0000E+04 
1.5000E+03 
3.0000E+03 
4.5000E+03 
6.0000E+03 
7.5000E+03 
9.0000E+03 


Figure 80. Partial Contents of the bipolar_potent_0_out.txt File Showing Highlighted Sheath 
Potential for Grid #2 for Case 1 of the “Bipolar” Example 


Go to the Script tab. Notice that “ The Script is out of date !’ ’ message has appeared. Build the 
script and run it. The inputs and results of the surface currents calculations of electron collection 
are in the following text files: bipolar_partgen_Electron_0_in.txt, 
bipolar_partgen_Electron_0_out.txt, bipolar_tracker_trajE_0_in.txt, and 

bipolar_tracker_trajE_0_out.txt. The electron current collected by the various object components is 
in bipolar_tracker_trajE_0_out.txt. As shown in Figure 81, the electron current collected by the 
gold-plated cube is 0.11 amperes, with 0.008 amperes collected by the 9 kV biased section of 
boom next to the cube, and small amounts of current collected by lower potential boom 
segments. 


_/] Bipolar_tracker_trajE_0_out.txt - Notepad 




File Edit Format View Help 

proces: current to object: -1.1456E-01 amps. 

lost current(off grid): -1.3411E-06 amps, 

trapped current : 0.0000E+00 amps, 

other current : -2.8756E-04 amps. 


cond. 

1 

kapt 

-2.9E-05 

tefl 

0.0E+00 

0. 

alum 
0E+00 . 

gold 
n ncxnn 

2 

0.0E+00 

0.0E+00 

0.0E+00 

I-1.1E-01 1 

3 

-2.5E-07 

0.0E+00 

0. 

0E+00 


4 

0.0E+00 

0.0E+00 

0. 

0E+00 

0.0E+00 

5 

0.0E+00 

0.0E+00 

0. 

0E+00 

0.0E+00 

6 

0.0E+00 

0.0E+00 

0. 

0E+00 

0.0E+00 

7 

0.0E+00 

0.0E+00 

0. 

0E+00 

0.0E+00 

8 

0.0E+00 

0.0E+00 

0. 

0E+00 

0.0E+00 

Total 

-2.9E-05 

0.0E+00 

0. 

0E+00 

-1.1E-01 

Summary 

of current 

collected 

after 

2 steps 


osr 

blac 

sola 

grap 

Total 

0.0E+00 

0.0E+00 

0.0E+00 

0.0E+00 

-2.864E-05 

0.0E+00 

0.0E+00 

0.0E+00 

0.0E+00 

-1.066E-01 

0.0E+00 

0.0E+00 

0.0E+00 

-2.2E-06 

-2.446E-06 

0.0E+00 

0.0E+00 

0.0E+00 

-5.1E-06 

-5.060E-06 

0.0E+00 

0.0E+00 

0.0E+00 

-1.9E-06 

-1.858E-06 

0.0E+00 

0.0E+00 

0.0E+00 

-1.8E-06 

-1.805E-06 

0.0E+00 

0.0E+00 

0.0E+00 

-7.9E-05 

-7.873E-05 

0.0E+00 

0.0E+00 

0.0E+00 

-7.9E-03 

-7.865E-03 

0.0E+00 

0.0E+00 

0.0E+00 

-8.0E-03 

-1.146E-01 


Figure 81. Partial Contents of the bipolar_tracker_traj_0_out.txt File Showing Current Collection 

Results for Case 1 of the “Bipolar” Example 


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The next calculation involves electron current collection, but with a non-zero magnetic field. In 
general, the presence of a magnetic field reduces current collection and is particularly important 
in low Earth orbit environments involving large electron sheaths. 

Earth’s magnetic field in the environment chosen for this example is approximately 0.4 G. On 
the Environment tab, in the “Magnetic Field” subsection (Figure 70), we therefore impose 
Bx=0, By=4e-5, Bz=0 in tesla. On the Surface Currents subtab of the Particles tab, the sheath 
potential is once again the sheath edge potential, 1.724 V. Rerun the script. Note that the 
magnetic field orientation is chosen such that it is nonnal to the plane fonned by the boom and 
rocket axis. In this configuration electrons ExB drift around the cube, in a plane with nonnal 
pointing in the same direction as the magnetic field (i.e., Y-direction). Figure 82 shows the 
Results 3D tab illustrating one electron trajectory in the presence of the non-zero magnetic field. 
The second view of the particle is to confinn that the tracked electron is leaving the grid. To view 
this trajectory, change the tracking limits to X=0.1 to 0.15, Y=-9 to 9, and Z=-5 to 0. We find that 
the computed electron current to the cube has been reduced from 106.9 mA to 8.47 mA as can be 
seen in the bipolar_tracker_traj_0_out.txt file. 


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Figure 82. Electron Trajectories Around the Positively Biased Cube when Bx=0, By=0.4 G, Bz=0 for 
Case 1 of the “Bipolar” Example (Bottom is rotated view of top) 


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19.4 Case 2: Ion Collection 

The next sample calculation, Case 2, involves ion current collection. Because the effect of the 
magnetic field on ion motion is negligible in this case, we set all components of the magnetic 
field in the Environment tab to zero. To create an ion-collecting sheath, we fix the body 
potential (conductor 1) to -8 kV as shown in Figure 83. Because the boom is covered with an 
insulating material and therefore has a surface floating potential of near zero, we set the boom 
surface potential to zero using the “Insulator Surface Potentials” portion of the tab. 

As in Case 1, a sheath edge potential value is required before we can compute surface currents. 
Click the Problem tab, check “Potentials in Space,” and uncheck “Surface Currents.” Return to 
the Script tab and rebuild and run the script. Click the Results 3D tab to view the potentials. The 
potential calculation shows the ion sheath extending far beyond the electron sheath, with the first 
almost completely choking off the second (and thus reducing the effective electron-collecting 
sheath area). As illustrated in Figure 84 the sheath edge lies in grid #1, so the appropriate 
potential value to use on the Surface Currents subtab is 4.34 V. (This value is obtained by 
looking in the bipolar_potent_0_out.txt file as in section 19.3.2.) Click the Problem tab to specify 
“Surface Currents,” then click the Script tab to build and run the new script. The ion current 
collected by the aluminum body is 2.156 inA, as seen in bipolar_tracker_traj_0_out.txt. Figure 
85 shows ion trajectories using the sheath edge potential value of 4.34 V for the “Contour Initial 
Particle Distribution.” 


Nascap2k - C:\MyCalculations\Manuals\bipolar\bipolar2\bipolarProject.xml 




File Edit View Materials Help 


Problem | Environment Applied Potentials T Charging [ Space Potentials Particles Script Results Results 3D 


[-Conductor Potentials & Electrical Connectivit 


y 

Conductor 


Initial Potential (V) 


1 

Floating Potential 

-8000 

2 

Bias Potential from Conductor #1 

isi-Ronn non +1 nnnF4 = 2nnn non 


3 

Bias Potential from Conductor #1 

rsi -soon non +1 fioo.ooo = -bsoo.ooo 


4 

Bias Potential from Conductors 

1S1 -8000.000 + 3000.000 = -5000.000 


5 

Bias Potential from Conductors 

1S1 -8000.000 + 4500.000 = -3500.000 


6 

Bias Potential from Conductors 

IS 1 -8000.000 + 6000.000 = -2000.000 


7 

Bias Potential from Conductors 

IS 1 -8000.000 + 7500.000 = -500.000 


8 

Bias Potential from Conductors 

1S1 -8QQQ.QQQ ♦ 9.QQQ.QQQ = 1 QQQ.QQQ 






'Insulator Surface Potentials - 


Material 

Conductor 

Sunlit/Dark 

Surfaces 

Type 

Initial Potential (V) 

Kapton 

Any 

Any 

Any 

Fixed Potential 

0.0 


Figure 83. Applied Potentials on Conductors and Insulators for Ion-current Collection Calculation 

for Case 2 of the “Bipolar” Example 


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Nascap2k - C:\MyCalculations\Manuals\bipolar\bipolar2\bipolarProject.xml 


File Edit View Materials Help 


Problem Environment Applied Potentials Charging Space Potentials Particles Script Results Results 3D 


SB SO fciEdOfJCJEJQEBE 


Cursor Tools 


Direct Movement & Rotation 


- Spacecraft- 

Display; Potential 
View: [standard | ^ 

Hide Spacecraft 

“Contours- 

Display: [ Potentials 1 1 

Y New 



- T rajectories- 

Specify Traje ctorie s... 

| Show Trajectories | 


“Color Scale- 

(D L inear O Log 

Min: [To.OO 

Matc h 0 00 

Replot 




Figure 84. Potential Distribution Showing Ion and Electron Sheath Edges on the Mesh for Case 2 of 

the “Bipolar” Example 



Figure 85. Oxygen Ion Trajectories for Case 2 of the “Bipolar” Example 


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19.5 Case 3: Current Balance 

We can calculate the steady-state rocket body and cube floating potentials, determined by the 
condition of zero net current. As we are again tracking electrons, we make sure that the magnetic 
field is set to (0, 4e-5, 0) tesla on the Environment tab. We use the model for charging using 
“Tracked Particle Currents” as shown on the Problem tab (Figure 86). This consists of 
iteratively calculating space potentials, tracked sheath currents, and surface charging due to those 
currents. The Applied Potentials (showing the change from fixed to floating boundary 
conditions on Conductor #1) and the Charging tabs are shown in Figure 87 and Figure 88, 
respectively. Two microseconds of charging are specified for each iteration of the space potential 
calculation and 100 microseconds for the total charging time. This time does not correspond to 
real time, but must be short for stability. The total number of timesteps is 75, which is also 
displayed on the Space Potentials tab (Figure 89) as the “Number of Iterations.” Also on this 
tab, be sure to update the Target Average (RMS) Error to what is shown. Because both species 
must be tracked, both “Electron” and “Oxygen” are highlighted on the Surface Currents subtab 
of the Particles tab (Figure 90). Notice that the chosen sheath edge potential value is the one for 
ions (4.344 V). For this problem the difference in the electron current using the electron sheath 
potential rather than that of ions is negligible. As it does affect the ion current, we use the value 
for the ion sheath edge. In this version of Nascap-2k, the user interface is not set up to handle 
different sheath potentials for the different species. (It is possible to do this by directly editing the 
input files for the Create Particles module) As usual, rebuild and rerun the script. Note that this 
calculation can take a couple of hours depending on the speed of the computer 



Figure 86. Problem Tab for Case 3 of the “Bipolar” Example 


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QUM 


Nascap2k - C:\MyCalculations\Manuals\bipolar\leocharging\bipolarProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging Space Potentials Particles Script Results Results 3D | 


“Conductor Potentials & Electrical Connectivity' 


Conductor 

Type 

Initial Potential (V) 

1 

Floating Potential 

-8000.0 

2 

Bias Potential from Conductor #1 

r#n -soon non +1 noon non = 2000 non 

3 

Bias Potential from Conductor #1 

r#ii-Roon non +1 son non = -rsoo non 

4 

Bias Potential from Conductor #1 

[#11-8000.000 + 3000.000 = -5000.000 

5 

Bias Potential from Conductor #1 

[#11-8000.000 + 4500.000 = -3500.000 

6 

Bias Potential from Conductor #1 

[#ii-8onn non + fionn non = -2000 non 

7 

Bias Potential from Conductor #1 

[#11 -Ronn non + 7500 non = -500 non 

8 

Bias Potential from Conductor#! 

[#118.Q.Q.Q-Q.Q.Q + 2QQQMQ =1QQ.Q..Q.Q.Q 



-Insulator Surface Potentials 



Figure 87. Applied Potentials Tab for Case 3 of the “Bipolar” Example 



Figure 88. Charging Tab for Case 3 of the “Bipolar” Example 


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File Edit View Materials Help 

Problem Environment j Applied Potentials j Charging ] f Space Potentials j Particles { Script j Results i Results 3D 

Iteration - 


Charge Density Model- 

O Laplace O Full Trajectory Ions 

C Linear (Debye Shielding) O Plume Ion Density 
(?) Non-linear □ Self-Consistent CEX 

O Frozen ion 
O Barometric 


- □ Geometric Wake li 
Species: [(T 


Target Average (RMS) Error (V)j l 000E-2 


L= 


Number of iterations: 75 


Iterations | Frac. old potential [ Frac. old density 


Add Row Delete Row 


On| Thruster | X [ Y | Z | X | Y | ~Z~ 


Figure 89. Space Potentials Tab Showing Number of Iterations for Case 3 of the “Bipolar” Example 



Figure 90. Surface Current Subtab for Case 3 of the “Bipolar” Example 


Figure 91 illustrates a plot on the Results tab of the potential as a function of time for 
Conductors #1 (rocket body only because boom potential has been fixed to 0 V) and #2 (cube). 


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The plots show that steady-state is reached. (The time parameter is nonphysical.) The Settings 
subtab may be used to adjust the graph properties, such as axis limits. The Text subtab may be 
used to transfer the current collection results (in tabular format) to a spreadsheet and plot the 
evolution to current balance as shown in Figure 92. Ion and electron currents are tracked 
separately, so one must alternatively select “Tracked Current” and “Tracked Electron Current” 
on the drop-down list to plot the different values. The equilibrium values of the potentials for the 
body and gold cube are -6.4 kV and 3.6 kV, respectively, as shown in Figure 91. The collected 
values are electron current to cube =1.8 mA, electron current to bushing = 0.26 mA, and ion 
current = 2.1 mA as shown in Figure 92. The potential distribution and trajectories are shown in 
Figure 93 and Figure 94, respectively. 

When interpreting the calculation’s results, it is important to remember that any secondary 
electrons created by the incident 6.7 keV ions are not included in the calculation. For many 
materials, each incident ion generates several electrons, effectively multiplying the incident ion 
current. The extra current source dramatically increases (i.e., makes less negative) the chassis 
potential at which current balance is achieved. 



Figure 91. Results Tab Showing Evolution of Conductor Potentials Toward Current Balance for 

Case 3 of the “Bipolar” Example 


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0.003 


0.002 


1 *********M,yu 11 1111'» 


♦♦♦♦♦ 



0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 

Time (ms) 

Figure 92. Current Collection by Conductors as a Function of Time for Case 3 of the “Bipolar” 

Example 



Figure 93. Potential Distribution at Equilibrium (-Zero Net Current) in the “Bipolar” Example 


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Elfglg 


0 Nascap2k - C:\MyCalculations\Manuals\bipolar\leocharging\bipolarProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials Charging Space Potentials Particles Script [ Results Results 3D 



Cursor Tools 


bEdOU EOBEBEOU 

Direct Movement & Rotation 


" Spacecraft- 

Display; Potential 


View: Standard 


Hide Spacecraft 


r Contours - 


Display; Potentials 


| Y | New 


rJ[0F 


View: Standard ▼ 
Show Cutplane 


'Trajectories - 


Specify Trajectories... 
Hide Trajectories 


Min: 

0.0 

Max: 

0.0 

Replot 1 



Figure 94. Selected Ion and Electron Trajectories at Equilibrium in the “Bipolar” Example 
20 Wake Effects and Current Collection in Low Earth Orbit (example name: “CHAWS”) 
20.1 Background 

When a high-speed spacecraft moves through the ambient plasma, two main regions form: a 
compression region in the ram, and a rarefaction or “wake” region behind the body. In general, 
the structure of the wake depends on a variety of factors. For example, the spacecraft’s velocity 
(both the magnitude and angle of attack), the (applied) potential on the back surface of the 
structure, and the ambient (or induced) magnetic field may all play a determining factor in the 
wake’s formation. Under certain simplifying assumptions an analytical solution can be obtained. 
For example, assuming quasi-neutral flow over a biased plate for which the sheath can be 
ignored, the solution is identical to that of a supersonic flow over a convex corner (which leads 
to an expansion fan) and may therefore be obtained using a standard Prandtl-Meyer fonnulation. 
In most practical problems, however, such as highly-biased spacecraft in low Earth orbit, the 
sheath may not be ignored and the wake structure must be found numerically. 

A spacecraft in low Earth orbit moves at a speed of about 7800 km/s. This speed is about seven 
times the local thermal speed of 0 + ions, but less than the electron thermal speed. To investigate 
high-voltage current collection within the spacecraft wake in low Earth orbit, the Air Force (then 
Philips Laboratory, now the Air Force Research Laboratory) sponsored the Charge Hazards and 
Wake Studies 4 (CHAWS) experiment. CHAWS flew on the Wake Shield Facility (WSF). The 
following example uses a model object of the WSF and Nascap-2k to compute space potentials 
and current collection in wake-type problems such as CHAWS. To illustrate some main features 
in this kind of problem, space potentials and ion current collected results are shown for 


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(1) stationary spacecraft, (2) plasma density calculated in the neutral approximation and space- 
charge density calculated using an analytic model, (3) space charge density calculated using the 
self-consistent with ion trajectories approach, and (4) same as (3), for a 10% hydrogen plasma. 

20.2 Object and Grid Definition 

First, make a new project (CHAWS 1, for example) and import the CHAWS object, which is in 
the Nascap2k_4/Manual/Example Problems/CHAWS folder. The WSF object is depicted in Figure 
95. It consists mainly of a disk of radius 1.83 m and thickness of 9.54 cm and a cylindrical probe. 
The probe has a diameter of 10.8 cm and is 45.7 cm long, separated by 1.3 cm from the disk. The 
large yellow object was part of the epitaxy experiment, which was the main WSF objective and 
contained an oven and ion gun, and shot ions toward another part of the experiment located on 
the back of the shield. The other object appearing in Figure 95 is one of the mounting struts for 
the epitaxy experiment. Other portions of the structure were sufficiently removed from the ion 
stream that they had no effect on the probe measurements. 

Click “Edit Grid” and import the CHAWS object and the grid which is also in the 
Nascap2k_4/Manual/Example Problems/CHAWS folder. The mesh is shown in Figure 96. It 
incorporates a total of 15 grids. The specifications of the largest grid (#1), and the grid in the 
immediate vicinity of the probe (#8) are also shown in Figure 96. 


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Figure 95. WSF Object. Top: Materials; Bottom: Conductors 


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Figure 96. Grid Used to Calculate Electric Potentials around WSF. Top: All Nested 15 Grids 
Highlighting Grid #1. Bottom: Grid #8 (Surrounding the Cylindrical Probe) 


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20.3 Calculating Space Potentials and Current Collection in the Wake 
20.3.1 Case 1: Current Collection by a Stationary Spacecraft. 

We begin the example by assuming a motionless spacecraft, and compute space potentials and 
current collection in an “LEO or Plume” environment using an “Analytic Space Charge” 
formulation for “Potentials in Space or Detector Analysis” and requesting “Surface Currents.” 
Thus the Problem tab is as shown in Figure 97. Figure 98 shows the Environment tab 
illustrating use of a moderately dense low Earth-orbit plasma, 10 in' at 0.1 eV. No spacecraft 
velocity is imposed and only oxygen ions are considered in this case. 

Figure 99 shows the Applied Potentials tab. The WSF (disk) is held at ground and the probe is 
biased to -2 kV relative to the disk. 

Figure 100 shows the Space Potentials tab with the “Non-Linear” charge density checked. 



Figure 97. Problem Tab for Case 1 of the “CHAWS” Example 


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EMM 


Nascap2k - C:\MyCalculations\ManualsYChaws\NoVelocity\ChawsProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials ^Charging \ Space Potentials Particles Script Results Results 3 dH 


LEO or Plume Environment 


_ LEO Environment Plasma- 

Density (m' 3 ): h -0Q0E11 
Temperature (eV):| o.10Q [ 

Debye Length (m):| 7.434E-3 
Electron Current (Am’ 2 ): 8.477E-4 
Ion Current (Am' 2 ): 4.964E-6 

- Magnetic Field (T)- 

Bxj o.o i Bipl o.o j Bz:l o n 

r Spacecraft Velocity (m/s)- 

Vk:| o.O j wl o.Q j Vz:| o.Q 


- Sun- 

r Direction to Sun- 

xj l.000 ~| Yil o.Q ~| Z:[cL0~ 


Relative* Sun lntensity:[ T.OOO ~| 

*|'value si Spacecraft) f (value at Earth Orbit) 


Particle Species 


Type 

Mass (amu) 

Charge (C) 

% 

Electron 

5.486E-4 

-1.602E-19 

100.0 

Oxygen 

16.00 

1.602E-19 

100.0 



Add Species 


Delete Species 


Figure 98. Environment Tab for Case 1 of the “CHAWS” Example 



Figure 99. Applied Potentials Tab for the “CHAWS” Example 


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File Edit View Materials Help 

Problem Environment Applied Potentials^| Charging \ Space Potentials j Particles [ Script j Results | Results 3D 


Charge Density Model- 

O Lapiace O Full Trajectory Ions 

O Linear (Debye Shielding) O Plume Ion Density 
(§) Non-linear □ Self-Consistent CEX 

C Frozen ion 

O Barometric O Full PIC 


— □ Geometric Wake Initialization 



Target Average (RMS) Error (V):1 q.0100 



Figure 100. Space Potentials Tab for Case 1 of the “CHAWS” Example 


To compute ion current collection we select the “Sheath” option for the initial particle 
distribution on the Surface Currents subtab of the Particles tab. As in the “Bipolar” example, 
we must supply an appropriate value of the sheath edge potential. Figure 101 shows that the 
sheath edge lies in a number of grids (1, 11, 15, 5, 4), but mostly in Grid #5. (See also Figure 
96.) We therefore choose 0.238 V as given in the Potentials in Space output file. As an accuracy 
check, the user can always perform a sensitivity analysis by comparing results using a sheath 
edge potential that corresponds to a different grid, e.g., #4. Figure 102 shows the Surface 
Currents subtab of the Particles tab. The potential profile, after running the script (Figure 103), 
is shown in Figure 104. To display (or hide) the cut plane, click on the “Show (Hide) Cut Plane” 
button. The Track Particles output file gives the collected oxygen ion current to the probe as 91 
p,A. 


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EMU 


Nascap2k - C:\MyCalculations\ManualsVChaws\NoVelocity\ChawsProject.xml 


File Edit View Materials Help 


Problem Environment Applied Potentials Charging Space Potentials Particles Script Results Results 3D 


BESff hEdCJU USD BEIGE) 


Cursor Tools 


Direct Movement & Rotation 




“T rajectories- 

Specify Trajectories... 

| Show Trajectories | 


“Color Scale 


d> Linear Q Log 

Min: |-1.000 ~ 
Max: |l .000 

Replot 




Figure 101. Location of Sheath Edge Potential for Case 1 of the “CHAWS” Example 


| File Edit View Materials Help 

Problem \ Environment | Applied Potentials | Charging j Space Potentials Particles [ Script [ Results I Results 3D 


Surface Currents ~\ Ion Densities f^me-Dependent 


Charged particles used for surface current calculation 


Initial Particle Distribution- 

<D Sheath 

Potential Value (V)^0.238 

O B Field 

Number per zoweqO 

O Boundary * 


O Charge Exchange 


O Surface* 


O None of above 


□ External File Filename: 

Browse 


’Additional parameters on advanced screen. 

- Particle Species- 


Electron 

Oxygen 


Figure 102. Surface Currents Subtab for Case 1 of the “CHAWS” Example 


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File Edit View Materials Help 

Problem ~f' Environment | Ap plied Potentials Charging | Space Potentials [ Particles | Script j Results [ Results 3D | 


Run Script [ Edit Script | 


Value 

9 C Read Object 

A FileName 

ChawsObject.xml 

? C Embed_Object_in_Grid 


A InputFileName 

Chaws_n2kdyn_in.txt 

A OutputFileName 

Ch aws_n2 kdyn_o ut.txt 

9 Q Potentials_in_Space 


A InputFileName 

Chaws_potent_OJn.txt 

A OutputFileName 

Chaws_potent_0_out.txt 

A Iteration 

0 

9 0 Create_Partides 


A InputFileName 

Chaws_partgen_Oxygen_OJn.txt 

A OutputFileName 

Ch aws_p a rtg e n_Oxy g e n_0_o uttxt 

A Track mode 

Surface Currents 

A Creation_mode 

Regular 

A Species 

Oxygen 

A ExecuteEvery 

1 

9 0 Track_Particles 


A InputFileName 

Chaws_tracker_traj_OJn.txt 

A OutputFileName 

Ch aws_tra eke r_traj_0_o uttxt 

A Iteration 

0 

A Track mode 

Surface Currents 

A Update_Time 

No 

A ElectronsOnly 

No 

A ExecuteEvery 

1 


Build Script Save Files 0 Automatically overwrite files Run Script 


Figure 103. Script for Case 1 of the “CHAWS” Example 



Figure 104. Potential Profile for Case 1 of the “CHAWS” Example 


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20.3.2 Case 2: Current Collection in the Wake using Analytic Space Charge Formulation. 


For this case, create a new project by either making a copy of the existing CHAWS folder with a 
new name or beginning one from scratch. In this second case we apply the non-zero spacecraft 
velocity by changing the Z-component on the Environment tab from zero to 7800 (Vz = 7800 
under the “Spacecraft Velocity” section). Notice that the Z-direction is nonnal to the WSF disk. 
The other two velocity components remain zero. The specifications on the Applied Potentials 
tab remain the same as in Case 1. 

The Space Potentials tab is shown in Figure 105. Note that “Geometric Wake Initialization,” 
which computes the wake of the (uncharged) spacecraft (i.e., wake is filled due to the thennal 
motion of ions), is checked. Because oxygen is the only ion species specified on the 
Environment tab, it is the only option under “Geometric Wake Initialization” (and therefore the 
mass used in this calculation is the mass of oxygen ions). All parameters on the Advanced 
Potential Solver Parameters dialog box remain unchanged from Case 1 except the value of 
“Maxitc,” which has to be increased from 50 to 75 in order to achieve adequate convergence 
(Figure 106). The usage of “Maxitc” is described in Section 14.1. 

Figure 107 shows the Surface Currents subtab of the Particles tab. The “Boundary” option is 
used for the initial particle distribution, which generates a thermal distribution of 0 + ions at the 
problem boundaries. The sequence representing how the undisplaced Maxwellian distribution is 
divided in this example is shown on the Advanced Particle Parameters dialog box (Figure 108) 
under “Fraction of Distribution.” (See Section 15.3.) Make sure all parameters match those 
shown in this figure. 

Once all of the values have been set, go to the Script tab and build and run the script. 


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133 



File Edit View Materials Help 

Problem j Environment j Applied Potentials [ Charging [ Space Potentials Particles { Script [ Results J Results 3D | 


Charge Density Model- 

0 Laplace O Full Trajectory Ions 

Linear (Debye Shielding) O Plume Ion Density 
(•) Non-linear □ Self-Consistent CEX 

G Frozen ion O Hybrid PIC 

O Barometric O Full PIC 

— 0 Geometric Wake Initialization - 

Species: [oxygen ▼ 

Target Average (RMS) Error(V)J l.000E-2| 


Figure 105. Space Potentials Tab for Case 2 of the “CHAWS” Example 




Figure 106. Advanced Potential Solver Parameters Dialog Box for Case 2 of the “CHAWS” 

Example 


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Figure 107. Surface Currents Subtab for Case 2 of the “CHAWS” Example 



Figure 108. Advanced Particle Parameters Dialog Box for Case 2 of the “CHAWS” Example 

Figure 109 depicts the potential distribution in the wake of the WSF. To display (or hide) the cut 
plane click on the “Show (Hide) Cut Plane” button. As the probe is in the wake for this 


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calculation, the plasma density behind WSF is lower and provides less shielding of the probe 
potential. The probe-induced potential extends far enough beyond the edge of the WSF, into the 
flow of ions, to deflect some of these ions into the wake where they can be collected by the 
probe. Figure 110 shows the specified distribution of particles around the boundary (ram region) 
and the manner by which they are collected by the probe in the wake region. To see the 
trajectories, click the “Specify Trajectories” button. The Particle Visualization dialog box 
appears. Select “Boundary” as the “Initial Particle Distribution for Trajectories” as shown in 
Figure 111. The distribution of initial directions is set on the Advanced Particles Parameters 
dialog box, which is accessed by clicking the “Advanced” button. Set the values shown in Figure 
112 and then return to the Particle Visualization dialog box after applying the changes. Finally, 
click the “OK” button to start the calculation. (After trajectories have been specified, it is only 
necessary to click on the “Show Trajectories” button to view trajectories.) The collected ions are 
attracted toward the probe tip, with a large portion of them striking the tip at an oblique angle. 
Those that miss the tip strike the inboard side of the probe while still moving toward the WSF. 
Very few ions hit the outboard side of the probe. The current (see CHAWS_tracker_traj_O.out.txt) to 
the probe (material: Kapton, conductor: 2) is 330 pA, considerably greater than the 91 pA 
calculated for the stationary case. 



Figure 109. Potential Distribution for Case 2 of the “CHAWS” Example 


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File Edit View Materials Help 
Problem Environment Applied Potentials 



\ Charging [ Space Potentials | Particles [ Script | Results Results 3D 

EtEllBI M9BII 


Cursor Tools Direct Movement & Rotation 



Hide Spacecraft 


Contours 


j Specify Trajectories... [ 


Hide Trajectories 


O Linear (•) Log 


Replot 


Spacecraft- 

Display:: P otential 


View:! Standard 


Display: Potentials 


View: Standard 


Show Cutplane 


Trajectories- 


Potentials 

Volts 
3.0.- 

1.0 - 

0.3- 

0.1 - 



Figure 110. Ion Trajectories for Case 2 of the “CHAWS” Example 



Figure 111. Particle Parameters Dialog Box for Graphical Display of Trajectories for “CHAWS” 

Example 


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Figure 112. Advanced Particle Parameters Dialog Box for Graphical Display of Trajectories for 

“CHAWS” Example 


20.3.3 Case 3: Current Collection in the Wake using “Self-Consistent with Ion 
Trajectories.” 

Here we repeat Case 2 but this time we will derive ion charge densities from ion trajectory 
calculations rather than from the analytic fonnulation. This requires iteratively calculating the 
space potentials and ion trajectories until self-consistency is attained. Recall that only positively 
charged species are modeled with this approach. On the Problem tab (Figure 113), “Self- 
consistent with Ion Trajectories” is checked instead of “Analytic Space Charge” model. This 
choice disables all charge density models on the Space Potentials tab except “Full Trajectory 
Ions.” The appropriate value for the minimum density is 100 times smaller than the ambient 
plasma density, 10 9 in '. The calculation of the plasma density variation due to the spacecraft 
motion is only done in a “NEW” potential run, i.e., the zeroth iteration. As shown in Figure 114, 
we first perform 10 iterations, using 30% of the previously calculated potential for each iteration, 
and 70% of the previously calculated plasma density for each iteration except the first. The first 
step (zeroth iteration) is the same as Case 2. 

Particles are generated using “Boundary” (Section 15.1) on the Ion Densities subtab of the 
Particles tab as shown in Figure 115. Notice the PVX, PVY, and PVZ divisions on the 
Advanced Particle Parameters dialog box in Figure 116. 

Potential profiles and particle trajectories are shown in Figure 117 and Figure 118, respectively. 
The tracking boundaries and other parameters for the Particle Parameters dialog box are the 
same as Case 2 (Figure 111). A comparison between Figure 109 and Figure 117 shows 


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differences in the potential distribution between Cases 2 and 3. The value of current collected by 
the probe is 120 pA, a factor of three less than in Case 2. The reason for this current reduction is 
additional screening of the probe potential by the space charge of the collected ions. Ten 
additional iterations change the current collected by the probe by less than 2%. 



Figure 113. Problem Tab for Case 3 of the “CHAWS” Example 


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Figure 114. Space Potentials Tab for Case 3 of the “CHAWS” Example 



Figure 115. Ion Densities Subtab for Case 3 of the “CHAWS” Example 


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Figure 116. Advanced Particle Parameters Dialog Box for Particle Generation and Tracking for 

Case 3 of the “CHAWS” Example 



Figure 117. Potential in the Wake of WSF for Case 3 of the “CHAWS” Example 


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Figure 118. Trajectories for Case 3 of the “CHAWS” Example 


20.3.4 Case 4: Current Collection in the Wake using “Self-Consistent with Ion 
Trajectories” and 10% H + . 

All previous cases assumed the ion population consists only of 0 + ions. However, even a small 
concentration of faster-moving, lighter ions such as H + can be a significant wake-filling 
mechanism that can lead to enhanced current collection. In this case we repeat Case 3 by 
including 10% H + ions, as shown in Figure 119, and perform five iterations (Figure 120) 
beginning from the solution of Case 3. Note on Figure 120, the number of iterations refers to the 
total number (the initial 10 for Case 3 and 5 additional for Case 4 for a total of 15 iterations). The 
boundary particle parameters on the Advanced Particle Parameters dialog box of the Ion 
Densities subtab remain as in Case 3. Notice in Figure 121 that both ion species are highlighted. 
Figure 122 depicts the script for this case. First delete all commands leading up to the Loop 
command. Then, edit the loop iterations to match what is seen in Figure 122, that is request five 
(5) iterations, starting with number 11 (since Case 3 did the first 10). 


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File Edit View Materials Help 

[ Problem Environment Applied Potentials [ Charging [ Space Potentials Particles I Script j Results j Results 3D | 


LEO or Plume Environment 


LEO Environment Plasma - 


Density (m~ 3 )j l 000E11 | 
Temperature (eV):| o.10Q 1 

Debye Length (m)j7 434E-3 


Direction to Sun - 

xj l.000 ] 


Y jo.Q 1 zj p.O | 


Relative* Sun Intensity^ l.OOO 


Electron Current (Am' 2 ): 8.477E-4 


'(value at Spacecraft) / (value at Earth Orbit) 


Ion Current (Am' 2 ): 6.453E-6 


Magnetic Field (T)- 

Bxj oQ | Byj P.O j BzJoiT 


Spacecraft Velocity with Respect to Plasma (m/s) 

VxJ o.Q j Vyj pQ j Vlj 7800. 


Particle Species 


Type 

Mass (amu) 

Charge (C) 

% 

Electron 

5.486E-4 

-1.602E-19 

100.0 

Oxygen 

16.00 

1.602E-19 

90.00 

Hydrogen 

1.000 

1.602E-19 

10.00 



Add Species | Delete Species 



Figure 119. Environment Tab for Case 4 of the “CHAWS” Example Showing Addition of 10% H + 

Species 


File Edit View Materials Help 

Problem j Environment J Applied Potentials j Charging Space Potentials Particles | Script j Results [ Results 3D j 


Target Average (RMS) Error (V):[ l.000E-2 
Minimum Density(m' 3 ): | l 000E9| | 


Advanced... 


O Laplace 

(§) Full Trajectory Ions 

O Linear (Debye Shielding) 

O Plume Ion Density 

O Non linear 

□ Self-Consistent CEX 

O Frozen ion 

O Hybrid PIC 

O Barometric 

O Full PIC 


— 0 Geometric Wake Initialization 


Species: Oxygen 


Number of iterationsjl5~ 


Iterations 

Frac. old potential 

Frac. old density 

1 tolls 

0.300 

0.700 


On Thruster 


Figure 120. Space Potentials Tab for Case 4 of the “CHAWS” Example 


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File Edit View Materials Help 

| Problem | Environ ment Applied Potentials | Charging | Space Potentials Particles j Scrip t ( Results i Results 3D 

f Surface Currents [ ion Densities Time-Dependent | _ 


Ions used to self-consistently compute ion density and potentials 

Initial Particle Distribution- 

O B Field Number per zone: 

@> Boundary (Additional parameters on advanced screen.) 

O Charge Exchange Cross Section(10' 20 M 2 )J Ll _ 

C None of above 

□ External File Filename: Browse 





Figure 121. Ion Densities Subtab for Case 4 of the “CHAWS” Example 


File Edit View Materials Help 

Problem | Environment j Applied Potentials j' Charging [ Space Potentials [ Particles Script Results [ Results 3D 


j Run Script Edit Script | 


■ Commands- 

Loop 

Read_0bject 
Append_Object 
lnitialize_Potentials 
Charge_Surfaces 
DoOneTimeStep 
DoTime Steps 
DoTrackTimeStep 
EmitCurrent 
FixGroundPotential 
Read Photoemission 
SetBField 
SetConductorBias 
SetCustomCurrentDLL 
SetEnvironment 
Setlllumination 
SetlnitialConductorPotential 
SetParameters 
SetVelocity 
SetVXBPotentials 
UseTrackedCurrent 
UseTrackedlons 
E m bed_Object_in_G rid 
Potentials_in_Space 
Static_A_Field 
Create_Particles 
Track_Particles 
Save_Files 


Script - 

Value 

? C Loop 


A Iterations 

5 

A StartAt 

11 

? Q Potentials_in_Space 


A InputFileMame 

CHAWS3_potent_7_in.txt 

A OutputFileName 

CHAWS3_potent_?_out.txt 

A Iteration 

? 

9 0 Create_Partides 


A InputFileName 

CHAWS3_partgen_Oxygen_?... 

A OutputFileName 

CHAWS3 partqen Oxygen ?... 

A Track_mode 

lon_Density 

A Creation_mode 

Regular 

A Species 

Oxygen 

A ExecuteEvery 

1 

9 C Create_Partides 


A InputFileName 

CHAWS3_partgen_Hydrogen... 

A OutputFileName 

CHAWS3 partqen Hydrogen... 

A Track_mode 

lon_Density 

A Creation_mode 

Regular 

A Species 

Hydrogen 

A ExecuteEvery 

1 

? Q Track Partides 


A InputFileName 

CHAWS3 tracker ? in.txt 

A OutputFileName 

CHAWS3 tracker ? outlxt 

A Iteration 

? 

A Track_mode 

lon_Density 

A Update_Time 

Yes 

A Spedes 

Ions 

A ExecuteEvery 

1 

? C Save Files 

A Directory 

Afterlter? 

A ExecuteEvery 

10 


Build Script 



0 Automatically overwrite files Run Script 


Figure 122. Script Used in Case 4 of the “CHAWS” Example 


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Figure 123 shows the potential distribution for Case 4. The potentials don’t extend as far in the Z 
direction as the lighter weight H + fills in the wake. As H + is four times faster than 0 + , the current 
would be expected to be about 30% higher, consistent with the computed 150 pA, about 25% 
more current than for a plasma of just 0 + ions. This value can be found in the tracker output file 
for the 15 th iteration. 



Figure 123. Potential Distribution in the WSF Wake for Case 4 of the “CHAWS” Example 


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21 Time Dependent Plasma (example name: “Dynamic”) 

21.1 Background 

In this example we address the different time regimes of the electron and ion motion and 
compute transient sheath dynamics about a simple object. As we are interested in time dependent 
space potentials and surface currents resulting from an impulsively changed surface potential, the 
“Problem Type” is “Time Dependent Plasma” with “Fixed Surface Potentials” as shown in 
Figure 124. 



Figure 124. Problem Tab Showing “Time Dependent Plasma” Checked for the “Dynamic” Example 


21.2 Object and Grid Definition 

The object is a gold-plated cube, 20 cm in size (Figure 125). The surrounding mesh consists of a 
cubic parent grid 0.96 m on a side with 4 cm mesh spacing, and one child grid 0.48 m on a side 
with 2 cm mesh spacing (Figure 126). 


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EHM 


Nascap2k - C:\MyCalculations\Manuals\Dynamic\Shortest\HybridPICProject.xml 


File Edit View Materials Help 

Problem Environment Applied Potentials ''Charging Space Potentials Particles Script Results Results 3D 


• Spacecraft- 

Display: Material 


View: Standard 


Hide Spacecraft 


[“Contours - 
Display. 


f Z ^New 


Show Cutplane 


'Trajectories - 


Specify Trajectories... 

Show Trajectories 


<§ Linear Log 

Min:[od3 


Replot 


UiLci QJ EIHEOEE) 


Direct Movement & Rotation 


A 



Figure 125. Gold-plated Cube Used in the “Dynamic” Example 


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Figure 126. Grid Definition for the “Dynamic” Example. Top: Primary Grid Definition. Bottom 

Child Grid Definition 


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21.3 Dynamic Calculations 

The calculations in this example are made assuming a moderately dense low Earth orbit plasma 

113 

(10 m' , 0.2 eV) and no magnetic field (Figure 127). Under these conditions the Debye length is 
approximately 1 cm. The electric potential of the current-collecting conductor is impulsively 
changed from 0 V to -100 V at time zero (Figure 128). 


File Edit View Materials Help 

Problem Environment Applied Potentials If Charging [ Space Potentials \ Particles j Script j Results [ Results 3D 


LEO or Plume Environment 


LEO Environment Plasma- 

Density (m~ 3 ): H 000E11 1 

Temperature (eV): 0 2 
Debye Length (m)j l.051E-2 j 
Electron Current (Am' 2 ):1-199E-3 
Ion Current (Am’ 2 ): 7 020E-6 



Spacecraft Velocity with Respect to Plasma (m/s) 

Vxj o.Q j Vyj O-O j Vzj o.Q 



Particle Species 


Type 

Mass (amu) 

Charge (C) 

% 

Electron 

5.486E-4 

-1.602E-19 

100.0 

Oxygen 

16.00 

1.602E-19 

100.0 



Add Species | Delete Species 



Figure 127. Environment Tab for the “Dynamic” Example 


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EMM 


Nascap2k - C:\MyCalculations\Manuals\Dynamic\Shortest\HybridPICProject.xml 


File Edit View Materials Help 


Problem Environment Applied Potentials ^ Charging | Space Potentials Particles Script | Results Results 3D 


[“Conductor Potentials & Electrical Connectivit 



y 



Conductor 

im? 

Initial Potential (V) 


1 

Fixed Potential 

-100.01 








Material Conductor I Sunlit/Dark | Surfaces I Type Initial Potential (V) 



Add Row 11 Delete Row 





Figure 128. Applied Potentials Tab for the “Dynamic” Example 


21.3.1 Case 1: Short Time-scales for Both Species. 

Create a folder for this example and copy in the object and grid files found in the 
Example Problems/Dynamic folder. You can examine the object and grid and check the 
Environment and Applied Potentials tabs to see that they correspond to those shown in Figure 
127 and Figure 128. 

For time scales in the order of nanoseconds, both electrons and ions move distances that are 
much less than a Debye length and may therefore be assumed to be motionless. In this time 
regime the plasma remains quasi-neutral, and we can therefore assume that space potentials are 
“Laplacian,” which is specified on the Space Potentials tab (Figure 129). Make sure the number 
of iterations is zero (0). The potential distribution around the object is shown in Figure 130. Note 
the monopole boundary conditions. 


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File Edit 


Materials Help 


Problem Environment Applied Potentials [ Charging Space Potentials Particles Script Results Results 3D 


Charge Density Model- 

(?) Laplace G Full Trajectory Ions 

G Linear (Debye Shielding) O Plume Ion Density 
O Non-linear □ Self-Consistent CEX 

G Frozen ion G Hybrid PIC 

G Barometric G Full PIC 


- O Geometric Wake Initialization 
Species: [o 


Target Average (RMS) Error (V) Jt000E-4 


Number of iterations: o| 


Frac. old potential | Frac. old density 


0"T 


Figure 129. Space Potentials Tab for Case 1 of the “Dynamic” Problem 



Figure 130. Results 3D Tab Showing Laplacian Space Potential Distribution 


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21.3.2 Case 2: Short Time-scale for Ions, Equilibrium (Barometric) Electrons. 

On a microsecond time-scale, electrons travel a distance corresponding to many Debye lengths, 
thereby reaching barometric equilibrium with the local potential. On this same timescale the ions 
remain stationary. We model this time regime by specifying the “Frozen Ion” analytic space 
charge fonnulation (sometimes called “ion matrix”) on the Space Potentials tab. (See Section 
14.1.) This is based on the assumption that electrons are in barometric equilibrium with the 
plasma potential but ion density remains uniform at the ambient value. 



Figure 131. Space Potentials Tab for Case 2 of the “Dynamic” Example 


The results (after clicking the “Run Script” button) are shown in Figure 132. The potentials 
extend to much smaller distances from the object because the negative potential is screened by 
the positive ion space charge. For example, the -5 V contour in the “Frozen Ion” solution is about 
the same distance from the object as the -45 V contour in the laplace solution, implying that the 
ion charge within the -5 V contour cancels about 90% of the negative charge on the -100 V cube. 


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Figure 132. Results from Case 2 of the “Dynamic” Example Compared with Laplacian Solution 

(Upper Left) 


21.3.3 Case 3: Time-dependent Ions, Equilibrium (Barometric) Electrons. 

After tens to hundreds of microseconds, ions can traverse many Debye lengths as well. We 
model this time regime using a “Hybrid PIC” formulation for the charge density (Section 14.1) in 
which the ion density is computed using particle tracking, while electrons are assumed to be in 
barometric equilibrium. 

Figure 124 shows the Problem tab for this calculation. Notice that “Time Dependent Plasma” is 
checked, which in turn enables the “Hybrid PIC” option on the Space Potentials tab (Figure 
133). We choose four iterations. On the Time-Dependent Particles subtab of the Particles tab, 
we choose a unifonn initial particle distribution for the first iteration only (Figure 134). We track 
particles for 1 jus per time step. Figure 135 shows the script for this problem, illustrating the 
number of iterations to be performed as specified on the user interface. The “0” potential 
iteration automatically uses “Frozen Ion” analytic space charge instead of “Hybrid PIC.” 


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File Edit View Materials Help 


Problem Environment Applied Potentials Charging Space Potentials Particles Script Results Results 3D 


Charge Density Model- 

O [Laplace) O Full Trajectory Ions 

G Linear (Debye Shielding) O Plume Ion Density 
G Non-linear 
G Frozen ion 
G Barometric 


□ Self-Consistent CEX 

(D Hybrid PIC 
O Full PIC 


— □ Geometric Wake Initializatic 
Species: loxygen 


Target Average (RMS) Error (V) Jl.000E-4 ~~j 
Minimum Density(m' 3 ): | l.000E9 j 




Number of iterations^ - 


Frac. old potential Frac. old density 


oj; 


Figure 133. Space Potentials Tab Depicting “Hybrid PIC” Choice for Case 3 of the “Dynamic’' 

Example 


File Edit Viev. Materials Help 

Problem j Environment | Appli ed Potentials ]' Charging""! - Space Potentials [ Particles Script j Results [ Results 3D 

f Surface Currents f Ion Densities \ Time-Dependent ; 


Particles used to compute charge density in a time-dependent calculation 


Particle creation- 

0 Initial Uniform Distribution □ Split particles 

□ Boundary Injection □ Split particles 


□ External File Filename: 

Browse 

□ Split particles 


Particle Species for Initial Uniform Distribution - 



Tracking time per timestep (s): l l.OOOE-6 Advanced 


Figure 134. Time-Dependent Subtab for Case 3 of the “Dynamic” Example 


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File Edit View Materials Help [N, 

Problem ] Environment Applied Potentials ^ Charging \ Space Potentials Particles | Script j Results Result s 3D~| 


j Run Script j Edit Script~| 


Value 

o- G Read_Object 


©- C Embed_Object_in_Grid 


o- C Potentials_in_Space 


9 C Create_Particles 


A InputFileName 

HybridPIC_partgen_Oxygen_OJn.txt 

A OutputFileName 

HybridPIC_partgen_Oxygen_0_out.txt 

A Track_mode 

TimeDependent 

A Creation mode 

Uniform 

A Species 

Oxygen 

A ExecuteEvery 

1 

9 C Track_Particles 


A InputFileName 

HybridPIC_tracker_0_in.txt 

A OutputFileName 

Hy b ri d P1 C_tra eke r_0_o ut.txt 

A Iteration 

0 

A Track_mode 

TimeDependent 

A Update_Time 

Yes 

A ElectronsOnly 

No 

A ExecuteEvery 

1 

9 C Lo °P 


A Iterations 

13 

A StartAt 

1 

9 G Potentials_in_Space 


A InputFileName 

HybridPIC_potent_7Jn.txt 

A OutputFileName 

HybridPIC_potent_7_out.txt 

A Iteration 

? 

9 C Track Particles 


A InputFileName 

HybridPIC_tracker_1_in.txt 

A OutputFileName 

HybridPIC_tracker_?_out.txt 

A Iteration 

? 

A Track_mode 

TimeDependent 

A Update_Time 

Yes 

A ElectronsOnly 

No 

A ExecuteEvery 

1 

©- C Save Files 


o- G Potentials_in_Space 


©- C Track_Particles 



Build Script 


Save Files 

□ Automatically overwrite files 

Run Script 


Figure 135. Script for the “Dynamic” Example Showing Four Iterations 


Figure 137 shows the Results 3D tab depicting oxygen particles on the Z=0 cut plane at the end 
of the fourth iteration. To plot the particles’ locations, choose “Present Particle Positions” in the 
drop-down list under “Plot” on the Particle Visualization dialog box and limit the Z value 
tracking limits to between 0 and 0.01 m as shown in Figure 138. 

Notice that eight particles are created for each (real) grid cube. Also notice the potential profile 
and the distribution of particles around the object. There is a slight outward extension of the 
potential by comparison with the “Frozen Ion” solution as ions begin to stream toward the probe, 
leaving lower densities behind. Current collection also increases over time as ions accelerate 
towards the negatively biased conductor. From the end of the file HybridPlC_tracker_4_out.txt, 
shown in Figure 139, it can be seen that the current has increased from 46.5 p,A at 1 ps to 170 pA 
at 5 ps. 

We can follow the evolution of particles for longer periods of time by restarting the calculation 
for another, say, six iterations. To avoid redoing the first four iterations again, we simply delete 
all commands leading up to the Loop command (note that this includes Create Particles 
because we have already created them) and then change the Loop “Iterations” from “3” to “6” 
and the Loop “StartAt” from “1” to “5.” The procedure may be repeated several times but not 
indefinitely because the solution is at some point in time affected by failure to supply new ion 
particles at the problem boundaries. Figure 140 shows results after ten iterations. Notice how the 


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potential profile extends farther away from the object as more ions enter the sheath. Figure 141 
shows current collected by the cube as a function of time over 20 iterations. 

To see how far the solution is from steady state, we can compute the steady-state current value. 
On the Problem tab check the “Potentials in Space or Detector Analysis” checkbox and select 
the Analytic Space Charge option, and check the “Surface Currents” checkbox (Figure 136). The 
“Non-Linear” Charge Density Model is chosen on the Space Potentials tab. In the Surface 
Currents subtab of the Particles tab, “Oxygen” should be selected as the “Particle Species” and 
the “Initial Particle Distribution” should be “Sheath.” Figure 142 shows the steady-state potential 
profile. The collected current is 25 juA for a sheath potential of 0.138 V. These values can be 
found in the tracker output and potent output files, respectively. 



Figure 136. Problem Tab for Case 3 of the “Dynamic” Example 


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Figure 137. Particle Distribution for Case 3 of the “Dynamic” Example at t=4 ps 



Figure 138. Particle Visualization Dialog Box Selections to Display Particle Locations 


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HybridPIC_tracker_4_out.txt - Notepad 




File Edit 

Format View 

Help 







ITi me 

Dt 

Time 

collected 

LOSt 

Trapped 

other 

saved 

- 

1 

0.OOE+OO 

0.00E+00 

0.OOE+OO 

0.OOE+OO 

0.OOE+OO 

0.OOE+OO 

F 


2 

1.00E-06 

1.00E-06 

4.65E-05 

0.OOE+OO 

0.OOE+OO 

0.OOE+OO 

F 


3 

1.00E-06 

2.00E-06 

1.63E-04 

0.OOE+OO 

0.OOE+OO 

0.OOE+OO 

F 


4 

1.00E-06 

3.00E-06 

1. 63E-04 

0.OOE+OO 

0.OOE+OO 

0.OOE+OO 

F 


5 

1.00E-06 

4.00E-06 

1.71E-04 

0.OOE+OO 

0.OOE+OO 

0.OOE+OO 

F 


6 

1.00E-06 

5.00E-06 

1.70E-04 

0.OOE+OO 

0.OOE+OO 

0.OOE+OO 

F 

- 


^ 


Figure 139. Partial contents of the HybridPIC_tracker_4_out.txt file showing total current collected 

for first five timesteps 



Figure 140. Particle Distribution for Case 3 of the “Dynamic” Example at t=10 ps 


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Figure 141. Ion Collection (Current) by Gold-plated Cube as a Function of Time for Case 3 of the 

“Dynamic” Example 


File Edit View Materials Help 

Problem | Environment Applied Potentials \ Charging [ Space Potentials ] Particles j Script i Results 



bEdLL EUEJBBBE 


Cursor Tools Direct Movement & Rotation 


Results 3D 





Figure 142. Steady-state Potential Profile for Comparison with Transient Results for the “Dynamic” 

Example 


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22 Additional Examples 

The following are examples of some specialized capabilities. 

22.1 Detector 

This example illustrates how to use the detector capability by computing the current to a detector 
with a guard ring. 

22.1.1 Object and Grid 

The object and grid are found in the Example Problems/Detector folder. The object, which 
represents a detector with a rudimentary collimator, is shown in Figure 143. The object consists 
of a box (green surface elements) with the element in the center of the top defined as the detector 
(cyan surface element) and a hollowed out cone (yellow surface elements) representing the 
collimator. The detector and eight surrounding elements forming the guard ring (green surface 
elements) are defined as conductor 3, so that they can be biased +5 V relative to the plate 
(remaining green surface elements) and collimator. 



Figure 143. Object for “Detector” Example 


The detector was defined in Object Toolkit to have the properties shown in Figure 144. It 
specifies the emission of test particles from four locations on the detector in 144 directions and 
with 20 energies ranging from 5 eV (0 eV of total energy) to 7 eV (2 eV of total energy). 


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~1 


Cancel ) 


Figure 144. Definition of the Detector “PartDetect” of the “Detector” Example 

The outer grid is 56 x 56 x 56 elements with size 0.0167 m. One inner grid encompassing the 
region about the collimator is defined. It extends from 22 to 36 in the x and y directions and from 
16 to 30 in the z direction. 

22.1.2 Problem Specification 

On the Problem tab, specify the environment as “LEO or Plume” and the problem type as 
“Potentials in Space or Detector Analysis” with “Analytic Space Charge” and “Surface 
Currents”. 

On the Environment tab specify a plasma with density 10 m" , temperature 0.3 eV, and no 
motion or magnetic field. 

On the Applied Potentials tab, set conductor 1 as fixed at 0 V (ground), conductor 2 (collimator) 
biased to 0 V (grounded), and conductor 3 (detector and guard ring) biased to +5 V. 

On the Space Potentials tab, set the charge density formulation to be “Non-linear”. 

On the Particles tab (Figure 145), specify “Electron” emission from a “Surface” using the 
“Detector” treatment. The specifications for the “PartDetect” detector were defined during object 
definition using Object Toolkit and can be modified on the Advanced Particles Parameters 
dialog box shown in Figure 146. 

Once the above settings have been specified, the script can be created and executed. To build the 
script click “Build Script” on the Script tab. The script is the same as for the other current 
collection calculation examples with an analytic representation of the plasma environment 
(“Bipolar” Cases 1 and 2, “CHAWS” Cases 1 and 2, and “Dynamic” Cases 1 and 2). However, 
the input file for the Create Particles command specifies that the reverse trajectory technique is 
to be used to compute currents for the particles created. Then, run the script to obtain the results 
discussed in the following section. 


; Detector PartDetect Properties 


NumLocations |4_ 

NumPhis| l2 
NumThetas| l2 
MinTheta | o.Q 
MaxTheta[l 57 
NumEnergies 
MinEnergy 


20 

5.0 


MaxEnergy|7 0 


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File Edit View Materials Help 

Problem | Environment | Applied Potentials Charging f Space Potentials j Particles J Script I Results j Results 3D | 

Surface Currents ^on Densities \ Time-Dependent | _ 


Charged particles used for surface current calculation 


■ Initial Particle Distribution- 

O Sheath 

Potential Value (Vyjo.O | 

O B Field 

Number per zone^O 

O Boundary * 


O Charge Exchange 


d> Surface* Detector ▼ PartDetect ▼ 


O None of above 


□ External File Filename: 

Browse | 


’Additional parameters on advanced screen. 


Particle Species 
■ Electron 


Advanced 


Figure 145. Particles Tab for the “Detector” Example 



Figure 146. Advanced Particle Parameters Dialog Box for “Detector” Example 


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22.1.3 Results 


The current density to the detector can be obtained from the Results tab by displaying the 
“Tracked Electron Current” to all the surfaces of “Material” Aluminum (i.e., to the element 
corresponding to the detector) as shown in Figure 147. The current density is -3.228 mA m' , 
which for an area of 0.00132 m 2 gives a total current of 4.26 pA. The Surface Element 
Information Tool (see Section 17.2) can be used to obtain the surface area of the detector 
element. 


I File Edit View Materials Help 

K 

| Problem \ Environment | Applied Potentials \ Charging f Space Potentials | Particles f Script 

Results f Results'SD 


Surface Element Groups 

Plot 

Condu.. 

Material 

Norma.. 

X 

Y 

z 

Sunlit 

1 0 

Any 

Alumi... 

180.0 

0.0 

0.0 

0.0 

Any 


Tracked Electron Current ▼ 


TimeSteps 


Add Row Delete R 


, MaxO, AvgO, MinO 
0.0, -3.228E-3, -3.228E-3, -3.228E-3 


Individual Surface Elements 


Plot 

Element 

Conductor 

Material 

Tracked Ele... 

n 

0 





Add Row Delete Row 



Conductor 

Tracked Electron Curr 









2 





3 



Graph Settings jj Text 


Figure 147. Results Tab for “Detector” Example Following Execution 


The potentials can be seen on the Results3D tab, shown in Figure 148. The color scale is 
reversed from the default using the “Color Scale Direction” option on the View menu. The 
potential bows out significantly from the collimator aperture, suggesting that the current is 
somewhat greater than the aperture area times the electron thermal current. Since the aperture 
approximates a circle of 2.5 cm radius and the electron thermal current is 1.468 mA m' (shown 
on the Environment tab), the planar current through the aperture would be only 2.9 pA. (By 
comparison, a sheath calculation with the sheath potential set to 0.2 V gives 3.4 pA to the 
detector surface element.) 


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Figure 148. Results3D tab Showing Bowing Out of Potentials Through the Collimator 

Additional infonnation can be found in the Track Particles output file, 

Detector_tracker_trajE_0_out.txt, the relevant excerpt of which is shown in Figure 149. Of 11520 
test particles launched from the detector surface element, 1365 left the primary grid (meaning 
that they represent electrons from the environment), while 10155 struck object surfaces (meaning 
they represent phase space that does not connect to the environment). The code applies 
environmental factors to the “lost” current particle weights to yield the 4.3 pA noted above. This 
current is assigned to conductor 3 “Alum” surface elements (representing the detector). Applying 
environmental factors to the 10155 test particles that struck the object yields 5.14 pA; this is not 
necessarily a meaningful number as these particles do not represent electrons from the 
environment, but gives a better estimate than the raw particle numbers or weights of how much 
of the detector’s phase space is blocked. The question of which surfaces block which portion of 
phase space can be explored by defining the detector as an emitter and using the same particle 
definitions. As the particles are distributed evenly in the cosine of the polar angle, the test 
particles at near normal angles represent a larger fraction of phase space than those at glancing 
incidence. 


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Figure 149. Tracker Output from Detector Run. 


22.2 Current Balance in a System with an Electron Gun (Emitter) 

In this example, the floating potential of an object on which an electron gun is mounted is 
computed. The current balance is between the electron current from the electron gun and sheath 
electrons collected from a LEO plasma, including limiting by a magnetic field. This calculation 
illustrates how to specify a current balance simulation in which the sources of current are 
detennined differently. It also illustrates how Nascap-2k’s algorithms interact with user choices 
to determine the rate of charging. 

22.2.1 Object and Grid 

The object and grid are found in the Example Problems/Emitter folder. The object is a 1 m long, 
0.4 m diameter, aluminum cylinder with the long axis along z, as shown in Figure 150. One side 
surface is the emitter “EGun.” The properties of “EGun” were defined in Object Toolkit to be as 
shown in Figure 151. The electron gun emits 0.3 Am' 2 of 3 keV electrons from a surface of area 
of 0.03451 in' 2 , for a total current of 10.35 mA. The current is represented by a single 
macroparticle. 

The computational space is three nested grids with a 20 cm resolution outer grid and a 5 cm 
resolution inner grid. 


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File Edit View Component Mesh Wizards Materials Help 



h.gdLlEJ CJEJBBBU 


Cursor Tools Direct Movement & Rotation 



Emitter 


EGun 


Figure 150. Aluminum Cylinder Showing Emitter Surface Element 


Emitter EGun Properties 1^*' ! ® [*£|h| 



CurrentDensity|o.3 


NumLocations 1 

NumPhisI 

NumThetas|l 

MinThetaO.O 

MaxThetaO.1 

NumEnergies 1 

MinEnergy 2999.0 

MaxEnergy 3001.0 



OK Cancel 





Figure 151. Definition of the Emiter “EGun” of the “Emitter” Example 


22.2.2 Problem Specification 

On the Problem tab, specify the environment as “LEO or Plume” and the problem type as 
“Charging” with “Tracked Particle Currents”. 

On the Environment tab specify a plasma with density 10 m' , temperature 0.3 eV, and a 
magnetic field of 3 x 10' 5 tesla along z (parallel to the cylinder axis). Also, define an extra 
species to represent the emitted electrons. These settings are shown in Figure 152. 


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File Edit View Materials Help Ltf 

Problem Environment | Applied Potentials^ Charging f Space Potentials \ Particles ^ Script [ Results j Results 3D | 


LEO or Plume Environment 


LEO Environment Plasma- 

Density <m' 3 )j lQ0QE11 
Temperature (eV)j o.30Q | 

Debye Length (m)j l.288E-2 1 

Electron Current (Am 2 ): 1 468E-3 
Ion Current (Am’ 2 ): 8.597E-6 



Spacecraft Velocity with Respect to Plasma (m/s) 

Vxj o.o | Vyj o.o | Vzj o.o 




Figure 152. Environment Tab for “Emitter” Example. 


On the Applied Potentials tab, set the conductor to be floating with an initial potential of +5 V. 

On the Charging tab, set the calculation to proceed with 20 0. 1 ms timesteps for a total of 2 ms 
charging time. 

On the Space Potentials tab, specify that the “Non-linear” charge density model is to be used. 
Note that the 20 iterations also appears on this tab. 

On the Particles tab (Figure 153), specify that particles of type “ElectronsEmitted” are to be 
emitted from a “Surface” representing an “Emitter”. The properties of the “Emitter” “EGun” 
were specified during object definition and can be modified on the Advanced Particles 
Parameters dialog. 


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Charged particles used for surface current calculation 


Initial Particle Distribution- 



O Sheath 



1 Value (V): 

O B Field 


N 


O Boundary * 




O Charge Exchange 




(§> Surface* 

Emitter 

▼ 

EGun 

'w 

Current Density (Am* z ):|0.300 

O None of above 




□ External File 

Filename: 


Browse 



•Additional parameters on advanced screen. 



Figure 153. Particles Tab Specification for Emitter Electrons. 


22.2.3 Building and Modifying the Script 

The problem as specified so far only includes the emitter current, so the cylinder would continue 
to charge to the energy of the emitted electrons. In order to also include the collection of 
electrons from the sheath, separate input files for the two sources of electrons are needed. The 
approach we’ll use is to first create the input files to specify the creation of the macroparticles 
representing the emitter electrons and then specify a current balance problem between two 
tracked current sources. The calculation will then be performed using the previously written 
input file for the electrons from the emitter. 

Start on the Script tab by clicking the “Build Script” button to create the default script. Then 
delete all of the Embed Object in Grid, Potentials in Space, and Track Particles commands. 
To delete a command, highlight the command and then click the “Delete Item” button. The 
resulting script looks as shown in Figure 154. In the resulting script, the only commands left that 
take an input file are the CreateParticles commands. Click the “Save Files” button to save the 
input files. 


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File Edit View Materials Help 

Problem [ Environ ment Applied Potentials Charging | Space Potentials i Particles I Script [ Results [ Result s 3D | 

Run Script | Edit Script 

Commands- 

Loop 

Read_Object 
Append_Object 
lnitialize_Potentials 
Charge_Surfaces 
DoOneTimeStep 
DoTime Steps 
DoTrackTimeStep 
EmitCurrent 
FixGroundPotential 
ReadPhotoemission 
SetBField 
SetConductorBias 
SetCustomCurrentDLL 
SetEnvironment 
Setlllumination 
SetlnitialConductorPotential 
SetParameters 
SetVelocity 
SetVXBPotentials 
UseTrackedCurrent 
UseT racked Ions 
Embed_Object_in_Grid 
Potentials in Space 


Build Script Save Files □ Automatically overwrite files Run Script 


Figure 154. Edited Script Used to Write Input Files for Creating Macroparticles to Represent those 

Originating at the Emitter 

Now that we have the input files for the particles emitted by the emitter, return to the Particles 
tab and specify parameters for tracking particles from a sheath, as shown in Figure 155. As we 
want to generate a script and “Track Particles” input files for both species, select both 
“Electrons” and “ElectronsEmitted” here. While these settings alone would specify tracking both 
species from a sheath, the input files to create particles on the surface of an emitter of species 
“ElectronsEmitted” that have already been created will be used. 


»Add Command» 


Delete Item 


Duplicate Item 




Up 

Down 


Script 


Value 


►* G Read_Object 
►- C Create_Particles 
>- G Charge Surfaces 


C Loop 


Alterations 19 


A StartAt 1 

6- C Create_Particles 
C Save_Files 
o- G Charge_Surfaces 
C Create_Pafticles 


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Figure 155. Particles Tab Specification for Sheath Electrons 


Return to the Script tab and click the “Build Script” button to build the default script shown in 
Figure 156. This script iteratively performs the following computation: 

• Compute potentials throughout the computational space. 

• Create macroparticles with properties specified in the previously generated input files 
Emitter_partgen_ElectronsEmitted_7_in.txt . When performing the calculation, it is important 
to make sure that the previously computed input fdes are used. 

• Create macroparticles with properties specified in newly generated input files 
Emitter_partgen_Electron_7_in.txt. These files will be constructed based on the selections on 
the Particles tab when the “Run Script” button is clicked. 

• Track the species selected on the Particles tab, that is “ElectronsEmitted” from the 
emitter and “Electrons” from the sheath of the positive spacecraft. (The option “Yes” for 
the “ElectronsOnly” keyword in the script specifies that the tracked charge is to be stored 
in electron specific arrays. This distinction is needed for some calculations using the 
“Full PIC” charge density model.) 

• Compute new surface potentials using the surface currents just computed. 

In order to use the input files already created, make sure that the “Automatically overwrite files ” 
box is unchecked. 

Finally, click the “Run Script” button and click “No to All” in response to the “Do you want to 
overwrite the existing file?” question. 


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File Edit View Materials Help 

| Problem"] Environment | Applied Potentials | Charging | Space Potentials | Particles | Script | Results [ Results 3D | 

Run Script Edit Script | 


Commands - 


Loop 

Read_Object 
AppendObject 
lnitialize_Potentials 
Charge_Surfaces 
DoOneTimeStep 
DoTime Steps 
DoTrackTimeStep 
EmitCurrent 
FixGroundPotential 
ReadPhotoemission 
SetBField 
SetConductorBias 
SetCustomCurrentDLL 
SetEnvironment 
Setlllumination 
SetlnitialConductorPotential 
SetParameters 
SetVelocity 
SetVXBPotentials 
UseTrackedCurrent 
UseTrackedlons 
Em bed_Object_in_G rid 
Potentials_in_Space 
Static_A_Field 
Create_Particles 
Track_Particles 
Save_Files 


»Add Command^ 


Script- 



Value 


o- C Embed_Object_in_Grid 
o- 0 Potentials_in_Space 
o- C Create_Particles 
o- C Create_Paiticles 
o- 0 Track_Partides 
o- 0 Charge_Surfaces 
? C Loop 

A Iterations 
A StartAt 

«- C PotentialsJn_Space 

? Q Create_Particles 
A InputFileName 
A OutputFileName 
A Track_mode 
A Creation_mode 
A Species 
A ExecuteEvery 
? C Create_Particles 
A InputFileName 
A OutputFileName 
A Track_mode 
A Creation_mode 
A Species 
A ExecuteEvery 
? 0 Track_Particles 
A InputFileName 
A OutputFileName 
A Iteration 
A Track_mode 
A Update_Time 
A ElectronsOnly 
A ExecuteEvery 
o- 0 Save_Files 
•>- 0 Charge_Surfaces 
0 Potentials_in_Space 
0 Create_Particles 
0 Create_Particles 
o- 0 Track_Partides 


19 

1 


Emitter_partgen_Electron_9Jn.txt 

Emitter_paitgen_Electron_9_out.txt 

Surface_Currents 

Regular 

Eledron 

1 

Emitter_partgen_ElectronsEmitted_9_in.txt 

Emitter_partgen_EledronsEmilted_?_out.txt 

Surface_Currents 

Regular 

ElectronsEmitted 

1 

Emitter_tracker_trajE_?_in.1xt 

Emitter_tracker_trajE_9_out.txt 

? 

Surface_Currents 

No 

Yes 

1 


□ Automatically overwrite files 


Figure 156. Final Script for Current Balance Calculation 


22.2.4 Results 


The final potential shown on the Results tab is 840 V. The potential versus time is shown in 
Figure 157. Using the vacuum capacitance, one would expect the cylinder to charge at a rate on 
the order of 100s of volts per microsecond. For stability, Nascap-2k limits the change in potential 
in a single timestep by adding a dJ/dV term to the charging equation. For this calculation, early 
on, the charging rate is limited by the dJ/dV, which, for calculations with only tracked currents, is 
set to 0.75J/V. The potential increases until the sheath current balances the emitter current at 
about 840 V. The charging rate continues to be limited because the code sets 


dl y dJ 

-0.75 V 

j 

« -0.75 

I 

dV“eEmdV = 

elem 

V 


V 


i.e, dFdV is large and negative even though I is near 


zero due to cancellation of the emitted and sheath electrons. 


The net current versus potential is shown in Figure 158. At about 840 V the sheath electron 
current cancels the emitter current. The net current is obtained by taking the average “Tracked 
Electron Current” to all surface elements and multiplying by the total area of 1.4823 m . 

If the option is used to set the stabilizing current derivatives to zero, then the correct (using the 
vacuum capacitance) charging timescale (microseconds) is achieved, as shown in Figure 159. 


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Note that the floating potential depends on the electron plasma thermal current (which scales the 
sheath current), the magnetic field (which limits the sheath current), and the emitter current. If 
the floating potential were close to the emitter energy, then we would need to define the emitter 
to emit a spectrum of particle energies to simulate the fraction of emitted electrons that return to 
the spacecraft. 


Potential 



Figure 157. Potential versus Time for the Emitter Example. 



Figure 158. Net Current versus Potential for the Emitter Problem. 


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Figure 159. Charging Dynamics with the Stabilizing Current Derivatives Set to Zero. 


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COMMON GOTCHAS AND FREQUENTLY ASKED QUESTIONS 


Caveats 

Generally, a “Potentials in Space” “Self-consistent with Ion Densities” computation is only done 
with a sizeable velocity. A finite velocity is not required, but if the velocity is small the user 
should carefully consider the appropriateness of the approach. 

Computing space potentials self-consistently with ion densities requires ion densities throughout 
the computational space. Thus the ion should be tracked from the boundary of the problem and 
not from a sheath edge. 

The analytic model of ions in the auroral environment is only applicable at very low densities. 

The analytic model of plasma currents in a LEO environment is only applicable at very low 
densities. 

Frequently Asked Questions 

Question: Nascap-2k keeps dying before the end of the computation. I’ve run the same case 
three times to make sure it wasn’t a fluke. And it’s taking over four hours to run up to the point 
that it dies. 

Answer: The following questions can help you diagnose the problem. 

• Is there any message in the last output file? What is the code doing when it dies? 

• Is there an error message on the console? Or in the prefix.log file? 

• Are the results reasonable up until the point the code dies? (Do the space potentials look 
reasonable? Are the currents reasonable numbers? Is the chassis potential varying smoothly?) 
What is the first thing that looks strange? Once a solution goes bad, it generally won’t get 
better. 

• How does it behave when you restart with the existing files? 

• How does it behave when you use a very simple object, like a cube, to do the same problem? 

Question: How do I see messages on the console? The command prompt window disappears 
before I can read it. 

Answer: To run from a persistent window (so you can see the error messages), navigate to the 
Program Files (x86)\Leidos or Program Files\Leidos directory as appropriate, and with the shift key 
held down, right-click the Nascap2k_4 folder and select “Open Command Prompt Here”. Then 
type Nascap2k.bat at the command prompt. 

Question: Can I use my files from a previous version of Nascap-2kl 

Answer: The pref/xObject.xml and prefix .grd files are fully compatible. In general, 
pre/7xProject.xml files from previous versions can be used. Some new capabilities and name 
updates do not appear if an old project file is used. To gain the full capabilities, creation of a new 
project file is recommended. As two copies of Nascap-2k (using different files) can execute at 


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the same time, it is easy enough to bring up one copy of the code using the old project fde and 
another copy using a new bla nk project file and then transfer all the settings. 

Question: Until last week I had no problems using Nascap-2k. Last week my PC’s operating 
system was updated and now it crashes before it gets started. 

Answer: The problem may be that Java 3D is not installed in the version of Java that you are 
using. Uninstall and reinstall Java 3D as described in Section 4.3. 

Question: I get an error message that says, “Exception in thread ‘main’ 
java.lang.NoClassDefFoundError: java/vecmath/Tuple3f 
at com.maxwell.nascap.N2kMain.main(N2kMain.java).” 

Answer: Your Java 3D is not installed properly. Uninstall and reinstall Java 3D as described in 
Section 4.3. 

Question: When I start up, I get an error message that says, “No compatible device found.” 

Answer: Java 3D for OpenGL requires 32-bit color. To set the color quality, select “Display” on 
the “Control Panel” (on the Start menu) to bring up the Display Properties dialog box. Select 
the Settings tab to access the screen resolution and color quality. 

Question: When I start up, I get an error message that says, “wglCreateContext Failed: The pixel 
format is invalid” or “java.lang.NullPointerException: Canvas3D: null GraphicsConfiguration.” 

Answer: Java 3D for OpenGL requires 16-bit Z buffering. 

Question: When 1 clicked on the Run button on the Script tab, 1 get a dialog box labeled dgetfZ 
and a message about A( 18,18) = -l.#IND00. 

Answer: Something is wrong with the object; look for those red lines. A doubly defined surface 
element won’t generate a red line, but will cause this type of trouble. A badly distorted surface 
element can also. 

Question: 1 get a convergence failure in INE1MP message. What does this mean? 

Answer: Something is wrong with the secondary electron emission material properties. The SEE 
Interactive Spacecraft Charging Handbook provides a convenient testbed for testing property sets 
or developing sets that will work. 

If you cannot see what the problem is just by looking at the numbers, here is something you can 
try. 

First create a boring object with all the materials defined in the file. The easy way to do 
this is to open your object with Object Toolkit, specify new object (so your object 
disappears leaving the material definitions), create a 6 sided box, assign the various 
materials to surfaces of the box, and save out the box. 

Next run a one step charging calculation (new project), ft may only be necessary to 
execute the first step or two. The calculation should fail in the same way. 


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If it does fail, delete the materials one by one from the end of the object file and repeat. It 
is important to start a clean project each time. (Actually it might be okay to keep the 
project fde, but nothing else). 

If the calculation does not fail, diff the original object file with the simple object file and 
look for differences in the material definitions. 

Question: On the Problem tab, the “Potentials in Space” “Problem Type” is not available. 

What’s up? 

Answer: The Potentials in Space computation requires a grid. 

Question: On the Problem tab, nothing under the “Problem Type” is active. 

Answer: Nothing is available until the object is loaded. Select “Load Object” on the File menu. 

Question: How do I get the new object with a grid from GridTool to Nascap-2kl 

Answer: For a grid created by GridTool to be read by Nascap-2k, the fde needs to be where 
Nascap-2k expects it and to have the same prefix as the Nascap-2k project. Make sure to save the 
grid fde to Prefix, grd in the Nascap-2k problem folder. 

Question: Does Nascap-2k automatically see the grid once it’s been embedded, or does one need 
to input or do something else? 

Answer: Actually, the Nascap-2k user interface sees the prefix.g rd file. If the file is in the right 
place with the right name, the Nascap-2k Problem tab should give you a “Grid Status” of 
“Loaded.” However, the computational modules only see the results of having embedded the 
object in the grid. If you have not yet embedded the object in the grid, the code knows that it 
needs doing when you click the “Build Script” button on the Script tab to request a script to 
compute the potentials in space. 

Question: My GridTool TreeView seems incorrect after adding an outer grid. 

Answer: Save the grid. Exit and restart GridTool. Import your saved grid. 

Question: I’m trying to run Case 2 of the “CHAWS” example. I’ve entered all the infonnation, 
but when I click “Build Script” it says I have no species selected, but I really think I do. 

Answer: See the bluish highlight in Figure 90 in Section 19.5 for an example of how it should 
look if a species is selected. Multiple species may be selected. 

Species for each purpose are selected separately. The selections on the Problem tab detennine 
which subtabs on the Particle tab are available. Species need to be selected on all available 
subtabs. It’s easy to miss one. 

Question: I am running a LEO charging problem and my spacecraft doesn’t charge. 

Answer: Did you specify any applied potentials? An object at uniform potential in low Earth 
orbit rapidly reaches a slightly negative potential. 


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Question: I edited the script file and saved it. I unchecked the “automatically overwrite files” 
checkbox and then clicked the “Run Script” button. My script was overwritten. What’s up? 

Answer: The “automatically overwrite files” checkbox refers to the input files to the 
computational modules, not to the script itself. The script file may be saved out and read in using 
the “Save Script” and “Load Script” choices on the File menu. The pref/xDriver.xml file is saved 
every time the “Run Script” button is clicked even if the checkbox is unchecked. 

Question: I did a calculation and nothing appears on the Results tab. 

Answer: The checkboxes along the left side of the tab indicate which quantities are plotted and 
which values are displayed. The plotted and displayed values are updated when the “Plot” button 
is clicked. 

Alternatively, there may be nothing to plot. Nascap-2k keeps time histories of charging 
calculations and self-consistent iterations between space potentials and surface currents. The 
results of a single calculation of potentials in space and surface currents are not saved for display 
by the Results tab. 

Question: I changed one of the parameters on the Settings subtab of the Results tab, and the 
change does not appear in my plot. 

Answer: The change takes effect the next time the “Plot” button is clicked. 

Question: I’m not able to do cut planes. Is that only available if there’s a grid? 

Answer: Cut planes are only available if space potentials have been calculated, which requires a 
grid. 

Question: I tried to do a trajectory calculation and nothing happened. A monitor briefly 
appeared, but no lines appeared on the three-dimensional figure. 

Answer: The code can only handle a reasonable number of trajectory segments and just stops 
when there are too many. This can lead to trajectory segments at the outer edge of the grid that 
don’t get noticed. The same problem can occur when plotting particle locations. Use the 
“Tracking Limits” to constrain the region of space in which particles trajectories begin. 

Alternatively, the cut plane can hide the trajectories. 

Question: I am getting extra lines in the three-dimensional display on the Results 3D tab. 

Answer: Four items to check are the following: (1) Check if the Z buffering is turned on. (2) 
Check for updated video drivers. (3) Check the version of OpenGL. Can you use an older or 
newer one? (4) Try an older or more recent version of Java 3D. 


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REFERENCES 


I. J.R. Stevens, A.L. Vampola, Eds., Description of the Space Test Program P78-2 Spacecraft 
and Payloads, SAMSO TR-78-24, USAF Space Division, El Segundo, CA, 1978. 

2.1. Katz, G.A. Jongeward, V.A. Davis, M.J. Mandell, R.A. Kuharski, J.R. Lilley, Jr., W.J. Raitt, 
D.L. Cooke, R.B. Torbert, G. Larson, and D. Rau, Structure of the bipolar plasma sheath 
generated by SPEAR I, JGR, 94, A2, p. 1450, 1989. 

3. M.J. Mandell, G.A. Jongeward, D.L. Cooke, and W.J. Raitt, SPEAR 3 flight analysis: 
Grounding by neutral gas release and magnetic field effects on current distribution, JGR, 101, 
Al,p. 439, 1998. 

4. V.A. Davis, M.J. Mandell, D.L. Cooke, and C.L. Enloe, High-voltage interactions in plasma 
wakes: Simulation and flight measurements from the Charge Hazards and Wake Studies 
(CHAWS) experiment, JGR, 104, AO, p. 12445, 1999. 

5.1. G. Mikellides, et ah, Assessment of spacecraft systems integration using the Electric 
Propulsion Interactions Code (EPIC), AIAA Paper 02-3667, 38th Joint Propulsion Conference, 
Indianapolis, IN, July 2002. 

6. V. A. Davis, B.M. Gardner, and M.J. Mandell, Object Toolkit Version 4.2 User’s Manual, 
Leidos Inc., San Diego, CA, AFRL-RV-PS-TR-2015-0108, October 2014. 

7. S. A. Brebbia, Boundary Element Methods, Springer Verlag, New York, NY, 1981. 

8. M.J, Mandell, T. Luu, J.R. Lilley, G.A. Jongeward, and I. Katz, Analysis of Dynamical Plasma 
Interactions with High Voltage Spacecraft, (2 volumes), Rep. PL-TR-92-2258, Phillips Lab., 
Hanscom Air Force Base, MA, June 1992. 

9. C.K. Purvis, H.B. Garrett, A.C. Whittlesey, and N.J. Stevens, Design Guidelines for Assessing 
and Controlling Spacecraft Charging Effects, NASA TP 2361, 1984. 

10. E.G. Mullen, M.S. Gussenhoven, and H.B. Garrett, A Worst-Case Spacecraft Environment as 
Observed by SCATHA on 24 April, 1979, AFGL-TR-81-0231, Air Force Geophysics Laboratory, 
Hanscom Air Force Base, Massachusetts, 1979. 

II. E.G. Fontheim, K. Stasiewicz, M.O. Chandler, R.S.B. Ong, E. Gombosi, and R.A. Hoffman, 
Statistical study of precipitating electrons, JGR , 87, A5, p. 3469, 1982. 

12. T. Nakagawa, T. Ishii, K. Tsuruda, H. Hayakawa, and T. Mukai, Net current density of 
photoelectrons emitted from the surface of the GEOTAIL spacecraft, Earth Planets Space, 52, p. 
283, 2000. 

13. R.L. Guernsey and J.H.M. Fu, Potential Distribution Surrounding a Photo-Emitting Plate in a 
Dilute Plasma, J Geophys Res, 75, p. 3193, 1970. 


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14. R. E. Ergun, D.M. Malaspina, S.D. Bale, J.R McFadden, D.E. Larson, F.S. Mozer, N.Meyer- 
Vernet, M. Maksimovic, RJ. Kellogg, and J.R. Wygant, Spacecraft charging and ion wake 
fonnation in the near-Sun environment, Physics of Plasmas, 17, 072903, 2010. 

15. V.A. Davis and L.W. Duncan, Spacecraft Charging Handbook, PL-TR-92-2232, Nov 1992. 

16. H.B. Garrett, The charging of spacecraft surfaces, Rev. of Geophysics and Space Physics, 19, 
4, p. 577, 1981. 

17. E.C. Whipple, Potentials of surfaces in space, Reports on Progress in Physics, 44, p. 1197, 
1981. 

18. C. Feldman, Range of 1-10 keV electrons in solids, Phys. Rev., 117, p. 455, 1960. 

19. V.A. Davis, M.J. Mandell, F.J. Rich, and D.L. Cooke, Reverse trajectory approach to 
computing ionospheric currents to the Special Sensor Ultraviolet Limb Imager on DMSP, IEEE 
Trans Plasma Sci, 34, p. 2062, 2006. 


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APPENDICES 


A. Files 

Nascap-2k uses a large number of files for different purposes. This appendix describes the files 
associated with a project, the contents of the input and output text and XML files, and the files 
placed on the user’s disk during installation. 

Four of the computational modules, Embed Object in Grid, Potentials in Space, Create 
Particles, and Track Particles have input and output files. As the command executes, it first 
uses information on the various tabs to construct the text input file and write it to disk. Then it 
starts the computational module. The module reads the input file, executes using the parameters 
specified in the input file, and writes a text output file in addition to writing its results into the 
database. The contents of these files are described in Section A.2 of this appendix. 

A.l Files Associated with a Project 

A Nascap-2k project always has an associated “ prefix ” (i.e., name of project) that is used to 
identify the files associated with the project. Table 36 describes the files that may be found. To 
re-create a project (e.g., to make a copy or re-create a corrupted database) requires only the 
pref/xProject.xml and pref/xObject.xml files and (if present) the prefix. grd, prefix Photo.xml, and 
prefix.P\ume.xm\ files. 


Table 36. Files Created and Used by Nascap-2k 


FILE 

CONTENTS 

prefix. NBS 

Contains information about the bounding surface elements of the special elements and is needed to 
calculate electric fields in special elements and to display potentials in space. 

prefix. NDB 

Main data file containing time independent information about the calculation. 

prefix. NME 

Contains the potential solver finite-element matrices for special elements in grid nn. There is one 
such file for each grid containing special elements. 

prefix. NTM 

Contains stored histories of spatial and surface properties. 

prefix.NPTrm 

Contains present location, velocity, and other properties of macroparticles. 

prefix.g rd 

ASCII file generated by GridTool that contains the grid information 

prefix_n_\n.txt 

Automatically generated ASCII input file containing well-labeled project parameters whose values 
may be altered by the user. 

prefix_n_out.txt 

ASCII output file created by a Nascap-2k module. The file contains a large amount of diagnostic 
information. 

prefix Photo.xml 

Contains the description of the photoemission spectrum. 

prefix O bj ect.x m 1 

Contains the description of the object. 

pref/xPlume.xml 

Contains the plume map (ions and optionally neutral atoms) for any thrusters. 

prefix Project.xml 

The project (xml) file. Contains all the information specified on the interface. 

prefix, log 

Text file containing some of the information displayed in the console. Overwritten each time 
Nascap-2k is run. 

ProjectDir.txt 

Text file that points to the directory of the last project or object saved. Nascap-2k uses this as the 
starting directory for searching for an existing project or object or saving a new one. 


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A.2 Contents of Input Files 


Nascap-2k is designed to perfonn a standard set of computations with minimal guidance from 
the user. More complex computations can be perfonned by editing the script and by editing the 
input files. When using edited input files, the “Automatically overwrite files” checkbox should 
be unchecked. 

Each line of the input files consists of a keyword followed by a value. Keywords can be one or 
two words. The value can be one or more real numbers, an integer, or a text string, depending on 
the keyword. A comment can follow. The keywords “Comment” and “Remark” indicate lines 
that are to be ignored. The keyword “End” specifies the end of the file. Table 37 through Table 
40 list the keywords and the tabs from which the associated values are determined. In addition, 
the tables provide commentary for many of the keywords. The simplest way to generate a valid 
input file is to edit an automatically generated one. 


Table 37. Contents of Input File for Embed Object in Grid Module 


KEYWORD 

COMMENTS 

Prefix 

Define the file prefix for this run. (Required.) 

Diagnostics 

Generate a large amount of diagnostic output. 

Echo 

Echo the neutral file. 

Noecho 

Do not echo the neutral file. (Default.) 

Noprocess 

Stop before generating any matrix elements. 

OffDiag 

Suppress off-diagonal matrix elements between surface elements. 

Process ix jy kz Grid igrid 

Proceed as expeditiously as possible to process the requested special element 
(for diagnostic purposes). If any of ix, jy, or kz is zero, process all of grid igrid. 


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Table 38. Contents of Input File for Potentials in Space Module 


KEYWORD 


TAB 


COMMENTS 


Run 


None 


Solution Mix 


Potential 


Temperature 

Debye 

Density 

Objvel 

Problem 


Environment 

Environment 

Environment 

Environment 

Potential 


Default value is “New” for “Iteration” attribute “0” and “Continue” for 
other iteration values. 

The value is labeled fraction old potential and varies for different input 

files. The “Iteration” attribute provides the correspondence with the table 

on the tab. If the “Iteration” attribute is “0,” a value of 0.0 is generated. 

Temperature of the plasma 

Debye length of the plama 

Number density of the plasma 

Three values for the x, y, and z velocity components. 

Charge density model. The correspondence between the values on the tab 
and the keyword argument are as follows: 


Value on tab 

Keyword in file 

Laplace 

Laplace 

Linear 

Linear 

Non-linear 

Non Linear 

Frozen ion 

Frozen Ion 

Barometric 

Barometric 

Full trajectory ions 

Traj Ion 

Plume ion density 

Plume 

Hybrid PIC 

Track Ion 

Full PIC 

Explicit 

Not on tab 

Special 

Not on tab 

Sheath Wake 

Not on tab 

OldTracklon 


Rmass 

RmsMin 


Wake 


Potential 

Potential 


Potential 


Mass used for geometric wake calculations. 

Root mean square error below which the potential is considered 
converged. 

If “Wake” is “On” and “Run” is “New,” do a geometric wake calculation. 


TIon Environment 

Conv Effect Advanced 


DebLim 

DebyeScale 

BField 

MinDensity 

Boundary 


Advanced 

Advanced 

Environment 

Potential 

None 


Save Interval 


Advanced 


Diag Final 
Diag Init 


Advanced 

Advanced 


Otherwise, don’t. 

Temperature used for wake calculation. 

Only relevant for “Non-linear” space charge density formula. If “On,” 
include the convergence factor in the formula. If “Off,” don’t. 

The number of Debye screening lengths allowed per volume element. 
Allowed values are “Local” and “Primary.” 

Three values specifying the three components. 

Minimum density. 

Sets boundary condition on grid boundary. Allowed values are “Zero,” 
“Monopole,” and “Debye.” Module assumes “Monopole” for “Laplace 
charge density model, “Debye” for “Linear” and “Non-linear” charge 
density models, and “Zero” otherwise. To change the default behavior, 
“Boundary” keyword must follow “Problem” keyword. 

Keyword is followed by two integer values giving the frequency of 
saving and at which iteration saving should start. 

Print final potential values. 

Print initial potential values. 




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Table 38. Contents of Input File for Potentials in Space Module (continued) 


KEYWORD 

TAB 

COMMENTS 

Diag Interface 

Advanced 

Integer value that indicates level of diagnostics information output 
regarding grid interface details. 

Diag Matrix 

Advanced 


Diag Scg 

Advanced 

Integer value that indicates level of diagnostics information output 
regarding scaled conjugate gradient calculations. 

Diag Screen 

Advanced 

Integer value that indicates level of diagnostics information output 
regarding space charge screening. 

Diag Wake 

Advanced 

Integer value that indicates level of diagnostics information output 
regarding geometric wake calculations. 

GridHigh 

Advanced 

Maximum grid number defining the range of grids in which potentials 
are to be computed. 

GridLow 

Advanced 

Minimum grid number defining the range of grids in which potentials are 
to be computed. 

Maxltc 

Advanced 

The maximum number of minor iterations within each conjugate gradient 
solution. 

Maxlts 

Advanced 

The maximum number of major or “space charge” potential iterations to 
be performed. 

NAdd 

Advanced 

Number of extra vertices to add to compute object shadow for geometric 
wake calculation. 

NPhi 

Advanced 

Number of polar angle divisions in geometric wake calculation. 

NTheta 

Advanced 

Number of azimuthal angle divisions in geometric wake calculation. 

PotCon 

Advanced 

The number of orders of magnitude that the RDotR parameter drops 
within each conjugate gradient solution before it is considered 
converged. 

RdrMin 

Advanced 

The value of the “RDotR” parameter below which the potential is 
considered converged. 

Time Start 

None 

Multiply the conductor potential by a factor of 

( ( t-t Yi ( t-t ^ 

1 - exp- ex p -starp where t is the time in 

V V tfise J J v tfall , 

seconds before computing space potentials. 

Time Rise 

None 

Time Fall 

None 

Timer 

Advanced 

Integer value that indicates the frequency at which the time since the 
computer was last rebooted is given in output file. 

Algorithm 

None 

Not used. 


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Table 39. Contents of Input File for Create Particles Module 


KEYWORD 

TAB 

COMMENTS 

Part Type 

Particles 

Allowed values are “Default,” “Sheath,” “Contour,” “B field,” “Boundary,” 

“CEX,” “Inject,” “Detector”, “Emitter”, “External.” “Default” specifies a uniform 
distribution. “Inject” macroparticles require the timestep as an additional 
argument. 

Sheath Pot 

Particles 

Sheath potential. 

N Zone 

Particles 

Number per boundary surface element. 

Cut Plane 

Particles 

The keyword is followed by “X,” “Y,” or “Z” specifying the cut plane direction 
and a real number specifying the cut plane location in grid coordinates. (1,1,1) is 
the lowest comer of the grid. 

External File 

Particles 

Filename. 

External Type 

Particles 

Allowed values are “Formatted” and “Unformatted.” 

BField 

Environment 

Three components of ambient magnetic field. 

TIon 

Environment 

Initial thermal energy of particles. Also plasma temperature used for thermal 
distribution. 

Rholon 

Environment 

Plasma density used to generate particles. 

VRam 

Environment 

Three components of spacecraft velocity. 

Species 

Environment 

Keyword followed by a string specifying the species name and two real numbers 
specifying the species charge in coulombs and mass in either AUM or kilograms. 
This keyword must follow “Part Type” keyword. 

Delete 

None 

Delete the species whose name follows the keyword. To delete all species, specify 
“All.” 

Pvx 

Advanced 

Fraction of distribution in each orientation that each particle represents. 

Pvy 

Advanced 

Fraction of distribution in each orientation that each particle represents. 

Pvz 

Advanced 

Fraction of distribution in each orientation that each particle represents. 

Random 

None 

No argument. Create seed for random number generator from date and time. 

Diag Partgen 

Advanced 

Integer giving level of diagnostics information output during particle generation. 

Diag Dynalib 

Advanced 

Integer giving level of diagnostics information output. 

Timer 

Advanced 

Frequency at which cpu time is given in output file. 

Subdivision 

Advanced 

A single integer and the string “ALL” specify the default ratio. Additional 
subdivision lines can be used to specify finer (or coarser) resolution. A line with 
the keyword “Subdivision” and four integers is understood to give (1) the ratio by 
which to subdivide boundary elements before generating particles at centers and 
(2) the low index comer of the boundary element. Only for Boundary type. 

Emitter Name or 
Detector Name 

Particles 

Name of emitter or detector. 

Speed_Values 

Advanced 

Integer giving the number of speed values and two real numbers giving the 
minimum and maximum speeds in meters/sec. 

Theta Values 

Advanced 

Integer giving the number of polar angle values and two real numbers giving the 
minimum and maximum polar angles in radians. 

Phi Values 

Advanced 

Number of azimuthal values. 

Num Locations 

Advanced 

Number of locations on each surface element of the emitter or detector at which 
to create particles. 

Current Density 

Particles 

Emitted current density. 

Grid 

None 

Generate particles in specified grid. If no “Grid” keyword appears, particles are 
generated in all grids. Multiple lines are needed to specify multiple grids. 

Split 

Particles 

Split particles unless followed by keyword “Off,” “No,” or “False.” If followed 
by the keyword “Skip” and integers follow that, particles in the grids specified by 
the integers are not split. 


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Table 40. Contents of Input File for Track Particles Module 


KEYWORD 

TAB 

COMMENTS 

Process 

Problem or 

Results 3D 

Available value are “Traj Charge” for self-consistent with ion 
trajectories, “Space Charge” for time-dependent problems, “Implicit” 
for time-dependent problems in which the charge is to be saved at every 
substep, “Plot Particles” for viewing particle locations, and 
“Trajectories” to view trajectories or compute surface currents. 

BField 

Environment 

Three components of the ambient magnetic field. 

TrackTime 

Particles 

Tracking time per timestep. 

Species 

Particles 

Name of species to be tracked. Multiple “Species” keywords can be 
present. 

MaxStep 

Particles 

Maximum number of substeps. 

Mix 

Potentials 

Fraction old density. 

DxMax 

Advanced 

Distance a particle can go in one substep (in local mesh units). 

Save Interval 

Advanced 

Keyword is followed by two integer values giving the frequency of 
saving and at which iteration saving should start. 

X Limit, 

Y Limit, 

Z Limit 

Advanced 

Only track particles whose initial location begins within the specified 
region. Location given in grid units where (1,1,1) is the lowest corner of 
the grid. 

X Plot Limit, 
YPlotLimit, 

Z Plot Limit 

Particles & 
Advanced 

Limit particle tracking to specified region. Location given in grid units 
where (1,1,1) is the lowest corner of the grid. 

Save Interval 

Advanced 

Keyword is followed by two integer values giving the frequency of 
saving and at which iteration saving should start. 

Diag Tracker 

Advanced 

Integer giving level of diagnostics information output during particle 
generation. 

Diag Dynalib 

Advanced 

Integer giving level of diagnostics information output. 

Timer 

Advanced 

Frequency at which cpu time is given in output file. 

UpdateTime 


Change the time by the tracking time at the end of execution. 

Split 

Advanced 

Split particles on entering subgrid unless first argument is “Off,” “No,” 
or “False.” If the first argument is “Skip” and integers follow, particles 
entering the grids specified by the integers are not split. If the first 
argument is “MinTemp,” particles with temperatures below the value 
given in the second argument are not split. 

Track Electrons 

None 

Save volume charge and current to database using electron keywords. 

Random 

None 

No argument. Create seed for random number generator from date and 
time. 

PrintTrack 

None 

Include position, potential, and volume charge density at each timestep 
in the output file. Can be used with particles defined in an external file 
to generate potentials along a line. 


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A.3 Contents of Output Files 
A.3.1 Embed Object in Grid 

The Embed Object in Grid module produces voluminous output. Normally, this output is of no 
concern to the user. However, if an error occurs during processing (such as a limit being 
exceeded) or potential solutions look strange or fail to converge, the n2kdyn_out.txt file may hold 
the key to the problem. The following sections describe this output file in a way that guides an 
ordinary user to find error indicators that may be meaningful. 

A.3.1.1 Input Echo 

The file begins with echo of the input file. Nascap-2k creates an input file with the project prefix 
followed by an end line. It is possible to limit processing to a specific volume element and 
request an increased level of diagnostic output. This is not likely to be helpful to most users. 

A.3.1.2 Grid Echo 

Following the input echo, the output echoes the grid file. This should correspond to the grid as 
defined in GridTool, and reflect the correct object dimensions and centering. 

A.3.1.3 Grid Analysis and Special Element Determination 

Next, the code cycles through the grids to classify each node as interior or exterior, and to 
classify each volume element of the volume as filled, empty, or “Special.” A volume element is 
filled if (a) it is interior to the object; (b) it belongs to a child (subdivided) grid; or (c) all eight of 
its nodes are interior. A volume element is “Special” if it (a) contains a surface centroid; (b) 
contains a surface node; or (c) contains at least one interior node and at least one exterior node. 
The limit on the number of “Special” elements is 8191, which is roughly double the 4095 limit 
on the number of object surfaces. The output shows the accumulation of special elements grid by 
grid, so the user can determine which grid is contributing an excess number. 

The first part of this process for each grid is the node interior/exterior determination. To do this, 
intersections of grid lines and surfaces are found. Usually, a grid line passes through a surface 
from exterior to interior, and then through another surface from interior to exterior. Ambiguities 
may occur, for example when a grid line is nearly coplanar with an object surface. However, as 
each node is traversed by grid lines in three directions, an unambiguous detennination can 
virtually always be made. The user may see diagnostic messages reflecting this process. Usually 
no action is required unless more serious errors occur later, in which case moving the object so 
that surfaces are not coplanar with grid lines may help. 

In this process we fill an array with a dimension (2 Ni- 1)(2N2-1) < 9000, where (Ni,N 2 ) are a pair 
of Fortran grid dimensions (Nx,Ny), (Ny,Nz), or (Nz,Nx). (The Fortran dimensions are one unit 
greater than the values entered in GridTool .) This places a limit on products of pairs of grid 
dimensions of about 2250. So, for example, a grid of (41, 51, 7) is allowed, but a grid of (47, 51, 
5) is not. If a grid does not satisfy this requirement, the “Too many grid lines” message appears, 
and the code exits. 


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187 



A.3.1.4 Special Element Matrix Construction 

Having identified the special elements, the code proceeds grid by grid and volume element by 
volume element to analyze the special elements and to construct their bounding surfaces and 
finite-element matrices. That is, the code must find the pieces of surface elements that lie within 
the volume element, relate the potentials on those surface elements to the unique potential 
iteration scheme for the object surface, and construct a volume potential interpolation scheme 
based on those surfaces and on the free surfaces of the surface element. Some output is written 
for each special element. For example: 

EltMat = XYZO = 3.0 1.0 27.0 Grid 8 

CCLTR3 successfully formed 3 triangles. 

CCLTR3 successfully formed 3 triangles. 

Boundary Surface Structure for special cell 2816 has 1309 words. 

Dimension reduced from 62 to 62 

is a typical error-free output. The “3.0 1.0 27.0” indicates the location of the volume element 
within grid 8. The lowest indexed corner of the grid is “1.0 1.0 1.0.” CCLTR3 is one of several 
routines that provides harmless diagnostic output. Other such routines include CRNSUB and 
ADLNOD. The size of the “Boundary Surface Structure” may range from a few hundred to a few 
thousand words, and indicates the complexity of the special element. If volume elements appear 
with the size of this structure larger than about 3000, additional subdivision should be considered 
to reduce complexity in that region. Other types of usually benign output include: 

EltMat = XYZO = 31.0 19.0 5.0 Grid 9 

SrfBpl - no surfaces and all corners filled 
Error encountered at index= 6817, grid 9 XYZ0= 31.0 19.0 5.0 

Zone will be marked as filled. 

EltMat = XYZO = 2.0 1.0 3.0 Grid 11 

EmptMt called: Index= 52 KeyNo= 5838 Fi11ed=FFFFFFFF 
Revising Ltbl to show empty cube element. 

These indicate volume elements that, for some reason, have been incorrectly identified as 
special. In the first case the volume element was reclassified as filled and in the second as empty. 
Such reclassification may be the result of the code moving nodes by small amounts in order to 
simplify the local matrix structure. Other types of benign errors may appear as well. Nonetheless, 
if the potential solution shows errors in these regions, these error messages may be indicative of 
a problem that can be resolved through minor modifications of object definition, grid structure 
(or additional subdivision), or object placement in grid. 

Other errors strongly indicate that the code was unable to correctly analyze the volume element. 
While fatal errors are rare, incorrectly analyzed volume elements may be hannless or may cause 
local errors in the potential solution. Such local errors may cause poor convergence (or non¬ 
convergence) of the entire potential solution. Additional subdivision is the usual remedy. Some 
examples are: 

EltMat = XYZO = 11.0 15.0 8.0 Grid 3 

GetCen - unable to find centroid 

Error - Path with undetermined sense. Assume Counter-Clockwise. 

Boundary Surface Structure for special cell 507 has 2943 words. 

Dimension reduced from 90 to 90 


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188 



This volume element has two problems, as well as a fairly large boundary surface structure. 
Possibly an object comer pierces an edge leaving both nodes free, or pierces a face leaving its 
four nodes free. 

EltMat = XYZO = 18.0 17.0 9.0 Grid B 

DogNut Warning - Non-monotonicity in counter-clockwise path point thetas. 

DogNut Warning - Non-monotonicity in counter-clockwise path point thetas. 

DogNut Warning - Non-monotonicity in counter-clockwise path point thetas. 

DogNut Warning - Non-monotonicity in counter-clockwise path point thetas. 

DogNut Warning - Non-monotonicity in counter-clockwise path point thetas. 

Warning - DogTri - got stuck at dead-end 
Warning - Error in CCLTr3 - NTri= 5 

Boundary Surface Structure for special cell 597 has 1526 words. 

This type of error is usually associated with a boom or stmt piercing one or more faces of a 
volume element. Try making the stmt thicker or have it lie along a grid line. 

EltMat = XYZO = 7.0 10.0 7.0 Grid 9 

Warning - Error in CCLTrB - NTri= 0 
Error - AddSeg could not add triangle for 1 2 

Error - AddSeg could not add triangle for 2 3 

Error - AddSeg could not add triangle for 3 4 

Error - AddSeg could not add triangle for 4 1 

Boundary Surface Structure for special cell 2373 has 807 words. 

This error indicates serious failure of the analysis. The volume element appears to have had 
multiple surfaces cutting through volume element comers at slant angles. There were four 
volume elements with similar errors. In this case, subdivision cured the errors for all four volume 
elements. 

A.3.2 Potentials in Space 

The output file from the Potentials in Space module is used mainly to determine whether the 
potential solution has adequately converged and, if not, to help determine the region of space that 
is causing the problem. It also can be used to verify that the input to the module is correct and/or 
has been correctly interpreted. 

A.3.2.1 Input Echo 

The first section echoes the input and should be virtually identical to the input file. Following the 
input echo, the plasma density, temperature, and Debye length are listed, followed by parameters 
relating to spacecraft motion, such as the ram energy, ion thermal velocity, and Mach number. 

A.3.2.2 Grid Pairs 

The section headed “Final grid pairs list ...” is an analysis of the grid stmcture showing pairs of 
grid having common faces that must be interfaced. For example, the following list 

Final grid pairs list ... 

# Pairs IFaces 

1 1:2 111110 

2 1:3 111100 

3 1:4 111101 

4 1:9 010100 

5 2: 3 0 0 0 0 1 0 

6 2: 5 111110 


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189 




7 

2 

6 

1 

1 

1 

1 

1 

0 

8 

2 

7 

1 

1 

1 

1 

1 

0 

9 

2 

8 

1 

1 

1 

1 

1 

0 

10 

2 

9 

0 

0 

0 

0 

1 

0 

11 

2 

10 

1 

1 

1 

1 

1 

0 

12 

2 

11 

1 

1 

1 

1 

1 

0 

13 

2 

12 

1 

1 

1 

1 

1 

0 

14 

2 

13 

1 

1 

1 

1 

1 

0 

15 

3 

4 

0 

0 

0 

0 

1 

0 

16 

3 

9 

1 

0 

1 

0 

0 

1 

17 

5 

9 

0 

0 

0 

0 

1 

0 

18 

6 

9 

0 

0 

0 

0 

1 

0 

19 

7 

9 

0 

0 

0 

0 

1 

0 

20 

8 

9 

0 

0 

0 

0 

1 

0 

21 

9 

10 

0 

0 

0 

0 

0 

1 

22 

9 

11 

0 

0 

0 

0 

0 

1 

23 

9 

12 

0 

0 

0 

0 

0 

1 


shows that grid 2 interfaces with grid 1 on all its faces but +Z, grid 4 interfaces with grid 1 on all 
its faces but -Z, and grid 3 interfaces with grid 1 on its ±X and ±Y faces, with grid 2 on its -Z 
face (the +Z face of grid 2), and with grid 4 on its +Z face (the -Z face of grid 4). 

A.3.2.3 Wake Calculation 

If a wake calculation is taking place, it is described by the section containing words such as 
“A2Driv” and “GiComp.” 

A.3.2.4 Preparatory Section 

Preparation for the potential calculation takes place in the “PSprep” section, which repeats many 
of the parameters extracted from the input and the database. It includes the grid spacing for the 
various grids, recommended sheath potentials in those grids, conductor potentials, and 
magnetically induced electric field. 

Of particular note are the sheath boundary potentials for non-linear charge density calculations 
and the barometric potentials for frozen ion charge density calculations. Lines similar to the 
following appear in the output file for these types of problems. 

Sheath boundary potentials: 

Grid # 1 Ymesh= 1.000000 meters. SthPot= 1.485810 volts. 

Grid # 2 Ymesh= 0.500000 meters. SthPot= 0.589644 volts. 

Grid # B Ymesh= 0.250000 meters. SthPot= 0.2B4000 volts. 

Grid # 4 Ymesh= 0.125000 meters. SthPot= 0.092863 volts. 

Frozen ions - for YMesh= 1.000 Phil= -45.1773 

Frozen ions - for YMesh= 0.500 Phil= -11.2943 

Frozen ions - for YMesh= 0.250 Phil= -2.8236 

Frozen ions - for YMesh= 0.125 Phil= -0.7053 

The use of the sheath boundary potential and the way in which it is calculated is described in 
Section 15.1. The barometric potential used in computing the charge density for frozen ion 
calculations is defined in Section 14.1. 


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190 




A.3.2.5 Potential Solution 

The potential solution solves for the potential, electric field, and space charge in the volume 
surrounding the spacecraft. It consists of a sequence of steps in which the space charge is 
linearized about the current trial solution, and the resulting linear problem is solved (to a limited 
degree of convergence) by a conjugate gradient technique. Surface element potentials, electric 
fields, and areas are output for each linearization. 

In the linear (conjugate gradient) portion of the potential solution, the default convergence 
requirement is that the error parameter rdotr decrease (by default) by two orders of magnitude. 
The following lines containing “rdotr” are selected out from three space-charge iterations. 

PSscg - after initializing U() and R(), initial rdotr= 7.618D+02 
rdotrO, rdrlas, rdotr = 7.618D+02 7.618E+02 5.346D+02 

rdotrO, rdrlas, rdotr = 7.618D+02 5.B46E+02 7.265D+01 

rdotrO, rdrlas, rdotr = 7.618D+02 7.265E+01 9.247D+01 

rdotrO, rdrlas, rdotr = 7.618D+02 9.247E+01 5.176D+01 

rdotrO, rdrlas, rdotr = 7.618D+02 5.176E+01 B.084D+01 

rdotrO, rdrlas, rdotr = 7.618D+02 3.084E+01 2.126D+01 

rdotrO, rdrlas, rdotr = 7.618D+02 2.126E+01 1.341D+01 

rdotrO, rdrlas, rdotr = 7.618D+02 1.341E+01 1.010D+01 

rdotrO, rdrlas, rdotr = 7.618D+02 1.010E+01 6.615D+00 

PSscg -- converged after 9 iterations. rdotr= 6.615D+00 
PSscg - after initializing UO and R(), initial rdotr= 6.886D+00 
rdotrO, rdrlas, rdotr = 6.886D+00 6.886E+00 3.478D+00 

rdotrO, rdrlas, rdotr = 6.886D+00 3.478E+00 2.604D+00 

rdotrO, rdrlas, rdotr = 6.886D+00 2.604E+00 1.865D+00 

rdotrO, rdrlas, rdotr = 6.886D+00 1.865E+00 1.764D+00 

rdotrO, rdrlas, rdotr = 6.886D+00 1.764E+00 1.002D+00 

rdotrO, rdrlas, rdotr = 6.886D+00 1.002E+00 7.740D-01 

rdotrO, rdrlas, rdotr = 6.886D+00 7.740E-01 4.800D-01 

rdotrO, rdrlas, rdotr = 6.886D+00 4.800E-01 5.004D-01 

rdotrO, rdrlas, rdotr = 6.886D+00 5.004E-01 2.056D-01 

rdotrO, rdrlas, rdotr = 6.886D+00 2.056E-01 1.321D-01 

rdotrO, rdrlas, rdotr = 6.886D+00 1.321E-01 7.751D-02 

rdotrO, rdrlas, rdotr = 6.886D+00 7.751E-02 3.251D-02 

PSscg -- converged after 12 iterations. rdotr= 3.251D-02 
PSscg - after initializing U() and R(), initial rdotr= 1.837D-01 
rdotrO, rdrlas, rdotr = 1.837D-01 1.837E-01 9.941D-02 

rdotrO, rdrlas, rdotr = 1.837D-01 9.941E-02 2.142D-02 

rdotrO, rdrlas, rdotr = 1.837D-01 2.142E-02 1.407D-02 

rdotrO, rdrlas, rdotr = 1.837D-01 1.407E-02 1.295D-02 

rdotrO, rdrlas, rdotr = 1.837D-01 1.295E-02 1.185D-02 

rdotrO, rdrlas, rdotr = 1.837D-01 1.185E-02 1.173D-02 

rdotrO, rdrlas, rdotr = 1.837D-01 1.173E-02 8.420D-03 

rdotrO, rdrlas, rdotr = 1.837D-01 8.420E-03 4.378D-03 

rdotrO, rdrlas, rdotr = 1.837D-01 4.378E-03 2.904D-03 

rdotrO, rdrlas, rdotr = 1.837D-01 2.904E-03 2.105D-03 

rdotrO, rdrlas, rdotr = 1.837D-01 2.105E-03 1.096D-03 

PSscg -- converged after 11 iterations. rdotr= 1.096D-03 

The above lines illustrate the convergence from rdotrO through the final rdotr through three 
space-charge iterations. In this well-behaved problem, the parameter rdotr decreases 
monotonically within each space-charge iteration, and the parameter rdotrO (or initial rdotr) 
decreases monotonically from each space-charge iteration to the next. However, there is no 
mathematical requirement for this monotonic behaviour, and highly non-monotonic behavior is 
commonly observed. 


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191 



Another measure of convergence from one space-charge iteration to the next is the “rms error,” 
which measures the difference in potentials and electric fields from the previous linear solution to the 
current one. The following lines containing “rms” are selected from three space-charge iterations: 

RMS Error for Grid # 1 = 8.6822E-02 

RMS Error for Grid # 2 = 2.8675E-01 

RMS Error for Grid # 3 = 2.1929E-01 

RMS Error for Grid # 4 = 1.6132E-01 

RMS Error for Grid # 5 = 1.3876E-01 

RMS Error for Grid # 6 = 1.8677E-01 

RMS Error for Grid # 7 = 1.2993E-01 

RMS Error for Grid # 8 = 1.3343E-01 

RMS Error for Grid # 9 = 1.2599E-01 

RMS Error for Grid # 10 = 1.2674E-01 

RMS Error for Grid # 11 = 1.5381E-01 

RMS Error for Grid # 12 = 1.1919E-01 

RMS Error for Grid # 13 = 1.7715E-01 

PSMAIN -- space charge iter= 1 rmserr= 1.8358E-01 

RMS Error for Grid # 1 = 6.5594E-03 

RMS Error for Grid # 2 = 5.1048E-02 

RMS Error for Grid # 3 = 3.4787E-02 

RMS Error for Grid # 4 = 1.4695E-02 

RMS Error for Grid # 5 = 3.6307E-02 

RMS Error for Grid # 6 = 2.7121E-02 

RMS Error for Grid # 7 = 3.3636E-02 

RMS Error for Grid # 8 = 1.7829E-02 

RMS Error for Grid # 9 = 4.5233E-02 

RMS Error for Grid # 10 = 2.6144E-02 

RMS Error for Grid # 11 = 3.6491E-02 

RMS Error for Grid # 12 = 1.8405E-02 

RMS Error for Grid # 13 = 2.9253E-02 

PSMAIN -- space charge iter= 2 rmserr= 3.4853E-02 

RMS Error for Grid # 1 = 2.2271E-03 

RMS Error for Grid # 2 = 5.1493E-03 

RMS Error for Grid # 3 = 4.3516E-03 

RMS Error for Grid # 4 = 3.7434E-03 

RMS Error for Grid # 5 = 3.0820E-03 

RMS Error for Grid # 6 = 7.0575E-03 

RMS Error for Grid # 7 = 2.5721E-03 

RMS Error for Grid # 8 = 2.4259E-03 

RMS Error for Grid # 9 = 7.1831E-03 

RMS Error for Grid # 10 = 2.1519E-03 

RMS Error for Grid # 11 = 2.9523E-03 

RMS Error for Grid # 12 = 2.3842E-03 

RMS Error for Grid # 13 = 8.1659E-03 

PSMAIN -- space charge iter= 3 rmserr= 4.8034E-03 

PSMAIN -- converged, rmserr= 4.8034E-03 

Again, in this well-behaved problem the rmserr parameter decreases monotonically, although there 
is no mathematical requirement that it do so. The reason for including the “ RMS Error for Grid ...” 
values is so that, in case of non-convergence, it may be possible to identify the grid that is failing to 
converge and to resolve the problem by further subdivision of some portion of that grid. 

A.3.2.6 Potential Text Output File 

If the potential solution has converged (or completed the allotted effort without diverging), the 
output concludes with a lengthy listing of the potential and field values for the central XY planes 
of each grid. A sample output for a 5x5x37 grid is as follows: 


Approved for public release; distribution is unlimited. 

192 



POT_Grid DATA FOR GRID 8 SLICE Z = 19 


-->X IS HORIZONTAL, Y IS VERTICAL<-- 



l.E 

1 * 

-0.27 


0.00 


0.90 


0.46 


0.01 


5 

l.E 

1 * 

-0.09 

-0.23 

0.00 

0.00 

-0.06 

1.25 

-0.03 

0.70 

-0.01 

0.21 


l.E 

1 * 

-0.16 


-0.25 


0.00 


0.55 


0.16 


4 

l.E 

1 * 

-0.09 

-0.24 

-0.10 

-0.25 

0.00 

0.00 

-0.05 

1.93 

-0.01 

0.33 


l.E 

1 * 

-0.15 


-0.11 


-0.39 


-0.26 


0.11 


3 

l.E 

1 * 

-0.08 

-0.25 

-0.09 

-0.23 

-0.10 

-0.20 

-0.05 

1.96 

-0.02 

0.45 


l.E 

1 * 

-0.03 


-0.01 


0.04 


-0.18 


0.16 


2 

l.E 

1 * 

-0.08 

-0.27 

-0.09 

-0.25 

-0.09 

0.00 

-0.06 

1.58 

-0.02 

0.66 


l.E 

1 * 

0.02 


0.04 


0.05 


0.10 


0.41 


1 

l.E 

1 * 

-0.08 

-0.29 

-0.09 

-0.26 

-0.10 

-0.32 

-0.10 

1.12 

-0.03 

0.87 




1 


2 


3 


4 


5 



The numbers 1 through 5 at the bottom and left are the x and y node indices, respectively. The 
value preceding the asterisk (here all values of l.E 1) is a power-of-ten multiplier to be applied to 
the line. On the lines having y indices, each x-index is represented by a pair of numbers giving 
the node’s potential and x-component of potential gradient. The y-components of potential 
gradient appear on the line above. For example, the node (1,1) has V=-0.8 V, E x =+2.9 V/m and 
E y =-0.2 V/m. (Note that potential gradient is the negative of electric field.) Interior nodes have 
all values zero, so, in this example, node (3,4) may be an interior node. 

A.3.2.7 Conclusion 

An example of a nonnal conclusion of the potential solver output file follows: 

CPV Data , NCond = 1 

1 -1.6220E+00 

About to close input - unit 5 

End Potential Solver. 

About to return from PSMAIN 

If the file ends in any other way, the calculation did not conclude properly. 

A.3.3 Create Particles 

Output from the Create Particles module generator varies somewhat depending on the type of 
particle distribution being generated and the particle’s intended purpose. The example being 
followed here generates electron macroparticles for space charge (Full PIC). We show 
differences for particles generated for visualization under control of an external file. Differences 
between these and other types of particle generation should be fairly apparent. 

Note that each run generates only one species of particle. If multiple species are requested, there 
are multiple input and output files. 

A.3.3.1 Initialization and Input 

The output file begins with a welcome followed by a list of recognized keywords with syntaxes 
and meanings. When the “PREFIX” input line is found, the database is opened and the grid 
structure is enumerated. Remaining input lines are then processed. When the “END” line is 
encountered, a summary of the environment and available species is given. This summary 
appears as follows: 


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193 



PCInpu: Particle type is SHEATH 

PGInpu: DebLim= 2.00 Debye,Temp,Dens = 1.0520E-02 1.0000E-01 4.9938E+10 

PGInpu: TIon,RhoIon= 1.0000E-01 5.0000E+10 VRam= 0.0000E+00 0.0000E+00 0.0000E+00 

PGInpu: sheath boundary potential= 4.3440 volts. 

Cut plane: Z= 9.00 
B Field: 0.00E+00 4.00E-05 0.00E+00 
Energy: 1.00E+00 NZone= 1 

PGInpu: Object velocity (m/s) = 0.00 0.00 0.00 

PGInpu: lunout, idiag, itimer= 611 

PGInpu: total of 4 species defined. 

ISpeci Name Charge(coul) Mass(Kg) 

1 OXYGENPL 1.6020E-19 2.6569E-26 

2 ELECTRON -1.6020E-19 9.1097E-31 

3 OXYGEN 1.6020E-19 2.6569E-26 

4 ELECTRPL -1.6020E-19 9.1097E-31 

For some choices of particle type, some lines do not appear. All the species defined in the 
database are listed. Execution of Create Particles is how species specified in the user interface 
are added to the database. Note the “PL” suffix on two of the species. The suffix indicates that 
this is an added version of the species to be used only for plotting. The “PL” suffix is generated 
automatically by the Nascap-2k user interface. 

A.3.3.2 Particle Generation 

The line 

PGInpu: loop over grids 1 to 8 

signifies the beginning of particle generation. It is followed by lines similar to the following: 

GenPa2: end of grid # 1 found 3878 OXYGEN particles. 1 pages written to disk. 

***TIMER*** Total Elapsed User Time =257977.156 Seconds. 

GenPa2: end of grid # 2 found 6020 OXYGEN particles. 1 pages written to disk. 

***TIMER*** Total Elapsed User Time =257977.188 Seconds. 

GenPa2: end of grid # 3 found 8072 OXYGEN particles. 1 pages written to disk. 

Particles are grouped into batches of 10,000, referred to as pages. When a page of particles has 
been created, it is written to disk. 

In the case that particles are read from an external file, the file is read and echoed as the particles 
are created: 


LOCATION 1.59 1.1 0.0 
DIRECTION -100 
ENERGY 4.5 

LOCATION 1.59 1.0 0.0 
DIRECTION -100 
ENERGY 4.5 

LOCATION 1.59 0.9 0.0 
DIRECTION -100 
ENERGY 4.5 


END 

GenPar: end of input. Found 35 OXYGENPL particles. 0 pages written to disk. 
GenPar: found 35 OXYGENPL particles spanning 1 pages. 


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194 



After looping through the grids, the following is written. 

CenPar: there are 3454B4 ELECTRON particles. The new ones are distributed as follows 

Grid # 12345678 

Page # 1 10000 0 0 0 0 0 0 0 

Page # 2 10000 0 0 0 0 0 0 0 

Page # 3 10000 0 0 0 0 0 0 0 

Page # 4 10000 0 0 0 0 0 0 0 

Page # 33 0000000 10000 

Page # 34 0000000 10000 

Page # 35 0000000 5434 

Summary data is written into the database and a table is written that shows how many particles 
from each grid are contained in each page. Note that the total of 345,434 electron particles is 
consistent with 35 pages of 10,000 particles each and a final page of 5434 particles. 

A.3.3.3 Conclusion 

An example of normal exit from the particle generator is: 

PGExit: closing files ... 

Close Prefix=Antenna 
Close Prefix=Antenna 

Exiting Particle Generator. 

If the file ends in any other way, the calculation did not conclude properly. 

A.3.4 Track Particles 

Output from the particle tracker varies depending on the intended use of the particles. 

Unlike the particle generator, the particle tracker tracks all existing particles within a single run, 
with the outennost loop being over particle species. 

A.3.4.1 Initialization and Input 

The output file begins with a welcome followed by a list of recognized keywords with syntaxes 
and meanings. When the “PREFIX” input line is found, the database is opened and the grid 
structure is enumerated. The particle summary information, as well as the object information, is 
read from the database. This includes all species defined in the database, including species 
automatically created for visualization. 

RedObj: Nsurfs= 155 Nnodes= 153 

The remaining input lines are then processed. When the “END” line is encountered, a summary 
of the parameters and current status is listed. A list of all species is written out. If any of the 
particle species are intended for visualization only, a “PL” suffix appears at the end of the species 
name. 

The limits for particle tracking and for trajectory recording for plotting are given in grid units, 
with the lowest indexed comer defined by (1, 1, 1). 


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195 



A.3.4.2 Particle Tracking 

No output is generated during particle tracking. 

Species 1 0 new particles. Weight: 0.0000E+00 

S85621 were partially tracked. Weight: -1.4357E+06 
0 were dead. Weight: 0.0000E+00 
683 went off primary grid. Weight: -1.1261E+04 
0 were trapped. Weight: 0.0000E+00 
0 with unknown status. Weight: 0.0000E+00 

The initial pass through each species (as in 387 pages of species 1, above) is for the purpose of 
initializing and categorizing each particle prior to tracking. In this case, all the particles had been 
tracked previously, 683 had left the computational space, and none had hit the object (which 
would put them in the “dead” category). As these lines were taken from an example in which 
particles are being used to compute space charge, the “Weight” of the particles is the sum of all 
the macroparticle charges divided by So (8.854x 10' ). If the macroparticles are used to compute 
steady-state space charge from trajectories or to calculate current-to-object surfaces, then each 
macroparticle represents a current. The weight of each macroparticle is the macroparticle current 
divided by so. When macroparticles are being tracked to a detector, the weight reflects only the 
part of the current known at the detector. The actual current is computed when it leaves the 
computational space. When tracked for visualization only, the weight is not used and often has a 
value of “1” for each macroparticle. 

For each species, particle tracking consists of a loop through the grids, and for each grid reading 
the pages containing particles that start in that grid. Particle tracking stops when the timestep 
time or number of timesteps is reached or when the particle strikes the object or exits the 
computational space. Particle status summaries are for each grid. 

A.3.4.3 Conclusion 

Several snippets of potentially useful information are included at the conclusion of the particle 
tracker. First is a summary of the total current: 

Proces: current to object: -5.4743E-04 amps, 

lost current(off grid): 0.0000E+00 amps, 
trapped current : 0.0000E+00 amps, 
other current : 0.0000E+00 amps. 

Next is a matrix of currents split by material name and conductor number: 

Cond. ALUM COLD Total 

1 -5.5E-04 0.0E+00 -5.474E-04 

2 0.0E+00 0.0E+00 0.000E+00 
Total -5.5E-04 0.0E+00 -5.474E-04 

And finally a summary of currents measured timestep by timestep: 


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Summary of current collected after 34 steps: 

ITime time step # 

Dt tracking time step (seconds) 

Time total tracking time (seconds) 

Collected current collected at surfaces (amperes) 
Lost current went off primary grid (amperes) 
Trapped current in trapped orbit (amperes) 
Other current with unknown status (amperes) 
Saved true if potentials is saved 


ITime Dt 

Time Collected Lost Trapped Other Saved 


1 

1.00E-07 

1.00E-07 -9.46E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

2 

1.00E-07 

2.00E-07 0.00E+00 

0.00E+00 

0.00E+00 

0.00E+00 

F 

3 

1.00E-07 

3.00E-07 -2.75E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

4 

1.00E-07 

4.00E-07 -8.65E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

5 

1.00E-07 

5.00E-07 -1.97E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

6 

1.00E-07 

6.00E-07 -4.68E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

7 

1.00E-07 

7.00E-07 -8.26E-03 

0.00E+00 

0.00E+00 

0.00E+00 

T 

8 

1.00E-07 

8.00E-07 -9.14E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

9 

1.00E-07 

9.00E-07 -1.07E-02 

0.00E+00 

0.00E+00 

0.00E+00 

F 

10 

1.00E-07 

1.00E-06 -1.02E-02 

0.00E+00 

0.00E+00 

0.00E+00 

T 

11 

1.00E-07 

1.10E-06 -7.70E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

12 

1.00E-07 

1.20E-06 -6.79E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

13 

1.00E-07 

1.30E-06 -5.38E-03 

0.00E+00 

0.00E+00 

0.00E+00 

T 

14 

1.00E-07 

1.40E-06 -4.13E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

15 

1.00E-07 

1.50E-06 -2.45E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

16 

1.00E-07 

1.60E-06 -1.87E-03 

0.00E+00 

0.00E+00 

0.00E+00 

T 

17 

1.00E-07 

1.70E-06 -1.36E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

18 

1.00E-07 

1.80E-06 -5.33E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

19 

1.00E-07 

1.90E-06 -3.49E-04 

0.00E+00 

0.00E+00 

0.00E+00 

T 

20 

1.00E-07 

2.00E-06 -2.81E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

21 

1.00E-07 

2.10E-06 -1.63E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 

22 

1.00E-07 

2.20E-06 -1.23E-03 

0.00E+00 

0.00E+00 

0.00E+00 

T 

23 

1.00E-07 

2.30E-06 -7.54E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

24 

1.00E-07 

2.40E-06 -1.77E-02 

-1.58E-01 

0.00E+00 

0.00E+00 

F 

25 

1.00E-07 

2.50E-06 -1.96E-02 

-2.01E-01 

0.00E+00 

0.00E+00 

T 

26 

1.00E-07 

2.60E-06 -1.85E-02 

-1.66E-01 

0.00E+00 

0.00E+00 

F 

27 

1.00E-07 

2.70E-06 -1.50E-02 

-3.56E-01 

0.00E+00 

0.00E+00 

F 

28 

1.00E-07 

2.80E-06 -9.42E-03 

-1.15E-01 

0.00E+00 

0.00E+00 

T 

29 

1.00E-07 

2.90E-06 -5.43E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

30 

1.00E-07 

3.00E-06 -3.67E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

31 

1.00E-07 

3.10E-06 -2.20E-03 

0.00E+00 

0.00E+00 

0.00E+00 

T 

32 

1.00E-07 

3.20E-06 -1.10E-03 

0.00E+00 

0.00E+00 

0.00E+00 

F 

33 

1.00E-07 

3.30E-06 -5.47E-04 

0.00E+00 

0.00E+00 

0.00E+00 

F 


The currents in this table are the sum of all ion and electron currents computed for the indicated 
timestep. 

An example of normal tennination of the particle tracker is: 

Q_Conductors: 

1 -6.1829E+00 

2 0.0000E+00 

Exiting Particle Tracker. 

If the file ends in any other way, the calculation did not conclude properly. 


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197 



A.4 Installed Files 


The files installed by the Nascap-2k installer and their uses are listed in Table 41. 


Table 41. Installed Files of Nascap-2k 


FILE 

DIRECTORY 

USE 

N2KReadMe.rtf 

Nascap2k 4 

Read Me file for Nascap-2k. 

ObjectToolkit.jar 

Nascap2k_4 

Executable for Object Toolkit used to create finite- 
element representations of spacecraft surfaces. It 
also has materials editing capability. Object 

Toolkit output (in XML) contains the recipe for 
recreating/reassembling the object, object 
definition by nodes and surface elements, and 
material definitions. 

GridTool.jar 

Nascap2k_4 

Executable for GridTool used to interactively 
define an arbitrarily nested cubic grid system for 
the space surrounding the object. 

Nascap2k.jar 

Nascap2k_4 

Executable for Nascap-2k user interface. It is 
based on an index-tab metaphor, and contains tabs 
for problem selection, initial conditions, parameter 
specification, script writing, time-dependent 
results analysis, and two- and three-dimensional 
display of surface potentials and fields. 

ObjectToolKitHelp.htm 

Nascap2k 4 

Online help for Object Toolkit. 

GridToolHelp.html 

Nascap2k 4 

Online help for GridTool. 

Nascap2kDocumentation.htm 

Nascap2k 4 

Online help for Nascap-2k user interface. 

ObjectToolKit.bat 

Nascap2k_4 

Used to start Object Toolkit to create an object 
description for Nascap-2k. Will have a 64 in the 
title if the 64-bit version is installed. 

GridTool.bat 

Nascap2k_4 

Used to start GridTool. Will have a 64 in the title 
if the 64-bit version is installed. 

Nascap2k.bat 

Nascap2k 4 

Used to start Nascap-2k. 

Nascap2k OTkSpecs.xml 

Nascap2k 4 

File tailoring Object Toolkit for Nascap-2k. 

N2kDB.dll 

Nascap2k 4 

C++ callable gateway to the database. 

N2kDBTool.dll 

Nascap2k_4 

C++ callable gateway to N2kDBTool utility, a 
utility to examine the contents of an N2kDB 
database. 

N2kDBTool.jar 

Nascap2k_4 

Executable for N2kDBTool, a utility to examine 
the contents of an N2kDB database. 

N2kDBToolConsole.exe 

Nascap2k_4 

Console executable version of N2kDBTool, a 
utility to examine the contents of an N2kDB 
database. 

N2kDLL.dll 

Nascap2k 4 

Computational modules. 

NoradOrbitCalc.dll 

Nascap2k 4 

Needed by Object Toolkit for other applications. 

libifcoremd.dll 

Nascap2k 4 

Intel Fortran file 

libmmd.dll 

Nascap2k 4 

Windows system file 

N2kScriptRunner.exe 

Nascap2k_4 

Executable to optionally use for long running 
calculations when no user interface is desired. 

ObjectToolkitManual.pdf 

Manuals 

Object Toolkit manual in PDF format. 

Nascap2k Users Manual.pdf 

Manuals 

This manual in PDF format. 

Nascap2k_ScientificDocumentation.pdf 

Manuals 

Documentation of physical and numeric models 
embedded in Nascap-2k. 

Example Problems 

Manuals 

Folder containing all the files needed to exactly 


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Table 41. Installed Files of Nascap-2k (continued) 


FILE 

DIRECTORY 

USE 



reproduce the examples of Part III of this manual. 

MaterialsReadMe.txt 

Materials 

Read Me file that explains how to use XML 
material files in directory. 

*.xml 

Materials 

Files containing material properties as measured 
by Utah State University in SEE Interactive 
Spacecraft Charging Handbook format. See 

Section 7. 

image.jpg, image*.jpg, props037.xml 

Nascap2k 

Documentation 

files 

Files needed for Nascap-2k user interface online 
documentation. 

*Orbits.xml 

Orbits 

Files used by Object Toolkit for other applications. 

CombineCrids 

Utilities 

Folder containing CombineGrids.jar, used for 
combining two disjoint grids 

CustomCurrentDLLTemplate 

Utilities 

Folder containing files needed to build a custom 
current DLL. 


A.5 File Formats 

The fonnats for the object definition, material definition, grid, and external plume files are listed 
below. The object definition and external plume files are in XML file format. 

A.5.1 XML 

Microsoft defines XML as “Extensible Markup Language (XML) is the universal format for data 
on the Web ... XML allows developers to easily describe and deliver rich, structured data from 
any application in a standard, consistent way.” 

Using XML, it is easy to structure data in a way that is both logical and flexible, and easily 
interpreted by both human and artificial intelligence. Java and C# contain integrated, standard, 
World Wide Web Consortium (W3C)-compliant software to read, interpret, construct, modify, 
and write XML-structured data. XML parsers are also available for other languages and 
platforms. 

Microsoft Internet Explorer is a convenient tool for displaying XML data files, allowing parts of 
the data tree to be expanded and collapsed. While XML files can be edited using an ordinary text 
editor, it is usually more convenient to use commercial software designed for that purpose. 
XMLShell (http://www.softgauge.com/xmlshell/index.htm) is an excellent aide for working with 
XML files. 

A.5.2 Object Definition File Format 

Nascap-2k uses object definition files created by Object Toolkit. The Object Toolkit output file 
provides the “Nodes” (points) and “Elements” (elemental surfaces) that define the geometry of 
the object, attributes of those surfaces, and the properties associated with the attributes. Figure 
160 shows a nearly collapsed version of an Object Toolkit output file. 


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199 














<?xml version="1.0" encoding-'UTF-8” ?> 

- <Assembly Name="Project" xmlns="x-schema:assembly_schema.xml"> 

+ <Assembly Name="Consolidated" xmlns="x-schema:assembly_schema.xml"> 
transformation >1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0</Transformation> 

- <Mesh xmlns="x-schema:mesh_schema.xml" IMNodes="284" l\IEIt="296"> 

+ <Nodes> 

+ <Elements> 

<Commands xmlns="" /> 

</Mesh> 

+ <MaterialProperties Name="Kapton" Color=”32896" xmlns="material_schema"> 

+ <MaterialProperties Name-Teflon" Color="255" xmlns="material_schema"> 

+ <MaterialProperties Name="Aluminum" Color="16776960" xmlns="material_schema"> 

+ <MaterialProperties Name-'Gold" Color=”65535" xmlns="material_schema"> 

+ <MaterialProperties Name="OSR" Color=”65280" xmlns="material_schema"> 

+ <MaterialProperties Name="Black Kapton" Color="32768" xmlns="material_schema"> 

+ <MaterialProperties Name="Solar Cells" Color- 16711680" xmlns=”material_schema"> 

+ <MaterialProperties Name-'Graphite" Color="8421504" xmlns="material_schema“> 

+ <AttributeProperties Attribute="Subsystem" Value="SA" xmlns=""> 

+ <SpecialObjectProperties ObjectType-'Thruster" 0bjectName="SPT100" xmlns=""> 

</'Assembly> 

Figure 160. Example of an Object Toolkit XML Output File 

The enclosing tag (“Document Element”) of the file is an “Assembly,” with the name of 
“Project” whose mesh represents the full model that has been defined. Constituent components 
of this assembly (in this case, a single “Primitive”) are included as child elements of “Project.” 
The XML element for a constituent component (excepting primitive components) does not 
contain the component’s full mesh, but rather contains the directions used by Object Toolkit to 
rebuild the mesh, so that Object Toolkit can be used to edit the model at the component level. 

The tags of interest to applications that read the file are “Mesh” (defining the Nodes and 
Elements of the model), “AttributeProperties” (defining the pointing properties of portions of a 
spacecraft), “MaterialProperties” (defining material properties for use in Nascap-2k ), and 
“SpecialObjectProperties” (used to define position and direction of thrusters and the properties of 
any other special components). Other tags describe the components that are combined to make 
the assembly; these are ignored by Nascap-2k, but are important to Object Toolkit for editing the 
object. 

The “Mesh” tag (whose attributes include the numbers of Nodes and Elements) encloses the 
Nodes and Elements that define the object geometry, as well as Commands that specify 
additional operations to be performed when assembling the component meshes. Each Node 
(Figure 161) has attributes of “index” (by which it can be referenced) and “x,” “y,” and “z” 
(specifying its absolute position in space in meters). Figure 162 shows a series of Element tags. 
Each Element has attributes that include the indices of the three or four Nodes that define its 
geometry, and the name of its surface material. The “Subsystem” parameter (“SolarArrayl” for 
the elements shown) is a special attribute included as a “Param” child element. 


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200 


- <Nodes> 

<Node index="0" x="0.40815289726477266" y=”-0.4933721350833382" 
z ="0.37499676406649896" /> 

<Node index="l" x="0.40487264290363767" y="-0. 29339903706431464" 

Z="0. 3749967629466572" /> 

<Node index="2" x="0.24489416451861146" y=”-0. 29602324055271007” 
z ="0.3749998715249687" /> 

<Node index="3" x="0.24817441887974662" y="-0. 4959963385717336" 
z="0.3749998726448105" /> 

<Node index="4" x="0.08491568613358555" y="-0. 2986474440411052” 

Z="0.37500298010328037" /> 

Figure 161. Series of Node Tags 

- <Element index="163" Material-'Graphite" InitialPotential-'O.O" Conductor="l" 

Node_0="155" Node_l="163" Node_2="164" Node_3="156" EFieldCondition="false"> 

<Param ParamName="Subsystem" ParamValue-'SA" /> 

</Element> 

- <Element index="164" Material="Graphite" InitialPotential="0.0" Conductor="l" 

Node_0="156" Node_l="164" Node_2="165" Node_3="157" EFieldCondition="false”> 

<Param ParamName="Subsystem" ParamValue="SA" /> 

</Element> 

- <Element index="165" Material="Solar Cells" InitialPotential="0.0" Conductor="2" 

Node_0="166" Node_l="167" Node_2="168" Node_3="169" EFieldCondition="false”> 

<Param ParamName-'Subsystem" ParamValue="SA" /> 

</Element> 

- <Element index="166" Material="Solar Cells" InitialPotential-'O.O" Conductor=”2" 

Node_0="169" Node_l="168" Node_2="170" Node_3="171" EFieldCondition="false”> 

<Param ParamName="Subsystem" ParamValue-'SA" /> 

</Element> 

- <Element index="167" Material="Solar Cells" InitialPotential="0.0" Conductor=”2" 

Node_0="171" Node_l="170" Node_2="172" Node_3="173" EFieldCondition="false”> 

<Param ParamName="Subsystem" ParamValue-'SA" /> 

Figure 162. Series of Element Tags 

Figure 163 shows the properties to be associated with a particular value of the emitter attribute. 
The properties describe the current density emitted, the solid angle into which charged particles 
are emitted, and how many macroparticles are to be used to characterize the emission. 


- <AttributeProperties Attribute="Emitter" Value="E2"> 

<Property name="CurrentDensity" value="2.0" /> 

<Property name="NumLocations" value="l" /> 

<Property name="NumPhis" value="l" /> 

<Property name-'NumThetas" value="l" /> 

<Property name="MinTheta" value="0.0" /> 

<Property name="MaxTheta” value="3. 14159" /> 

<Property name="NumEnergies" value="l" /> 

<Property name="MinEnergy" value="0.0" /> 

<Property name="MaxEnergy" value="10.0" /> 

</AttributeProperties> 

Figure 163. Attribute Properties for a Specified Value of “Subsystem” 

Figure 164 shows the properties to be associated with a particular instance of a “SpecialObject” 
of type “Thruster.” The properties include the location and pointing direction, as well as the 
display color (in Object Toolkit). 


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201 


- <SpecialObjectProperties ObjectType='Thruster" ObjectName="SPT100" xmlns=""> 

<Property name-'Name" value-SPTlOO'' /> 

<Property name-'Type" value-'Hall Thruster" /> 

<Property name="x" value="0.0" /> 

<Property name="y" value="0.4" /> 

<Property name="z" value="-0.2875" /> 

<Property name="r" value="255” /> 

<Property name="g" value="192" /> 

<Property name="b" value="0" /> 

<Property name="dirX" value="0" /> 

<Property name="dirY" value="l" /> 

<Property name="dirZ" value="0" /> 

</SpecialObjectProperties> 

Figure 164. Special Component Properties for an Instance of “Thruster” 

Each material is defined by a separate “MaterialProperties” element. Each “MaterialProperties” 
element has three attributes. The “Name” attribute specifies the name for the material. If the 
“App” attribute is not present, Object Toolkit assumes the material is for the current application. 
The material color is used when displaying the object in Object Toolkit and Nascap-2k. If the 
“Color” attribute is not present Object Toolkit assigns a random color to the material. The 
allowed values are strings representing the defined colors (Blue, Green, Red, Yellow, Magenta, 
Cyan, Grey, Dark Green, Dark Red, Dark Blue, Dark Yellow, Dark Magenta, Dark Cyan, Black) 
and numbers specifying the RGB color definitions. 

The properties of the material are specified as child elements of the “MaterialProperties” 
element. A property element has three attributes “Name,” “Index,” and “Value.” The “Name” 
attribute is the value displayed in the Edit dialog box for the material. The “Index” attribute 
contains an integer index for the property. A specific application may use either the name or the 
index to identify a property. Nascap-2k uses the “Index” to identify each property. The “Value” 
attribute, specifies the value for the property and must be a number. 


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202 


+ <MaterialProperties xmlns="material_schema" App="Nascap2K“ Color="32768" Name- Black Kapton"> 

+ <MaterialProperties xmlns="material_schema" App="Nascap2K" Color="32896" Name="Kapton"> 

+ <MaterialProperties xmlns-'material_schema" App="Nascap2K" Color="255” Name="Teflon"> 

+ <MaterialProperties xmlns="material_schema" App="Nascap2K” Color="16776960" Name-Aluminum'^ 

+ <MaterialProperties xmlns="material_schema'' App="Nascap2K" Color="65535” Name="Gold"> 

+ <MaterlalProperties xmlns="material_schema" App=”Nascap2K" Color=”65280" Name="OSR"> 

- <MaterialProperties xmlns="material_schema" App="Nascap2K” Color=”16711680" Name- Solar Cells"> 

<Property lndex="0” Name="Dielectric Constant" Value="3.8'' /> 

<Property Index=”l" Name="Thickness(m)" Value="1.25E-4" /> 

<Property Index="2" Name- Bulk Conductivity(ohms<sup>-l</sup>m<sup>-l</sup>)” Value="1.0E-13" /> 

<Property Index="3" Name="Atomic Number" Value=”10.0" /> 

<Property Index="4" Name="Delta-Max” Value="5.8" /> 

<Property Index="5" Name="E-Max(keV)" Value="1.0" /> 

<Property Index="6” Name="Range 1(&#197)" Value=''77.5” /> 

<Property Index="7" Name-Exponent 1” Value="0.45" /> 

<Property Index="8" Name="Range 2(&#197)" Value="156.1” /> 

<Property Index="9" Name="Exponent 2" Value="1.73" /> 

<Property Index="10" Name-Proton Yield" Value="0.244" /> 

<Property Index="ll" Name-Proton Max(eV)" Value=”230.0" /> 

<Property Index=”12" Name="Photoemission” Value="2.0E-5" /> 

<Property Index=”13" Name-'Surface Resistivity(ohms/square)" Value="1.0E19" /> 

<Property Index="14" Name =" Atomic Weight(amu)" Value="20.0" /> 

<Property Index=”15" Name="Density(g cm<sup>-3</sup>)" Value="2660.0'' /> 

<Property Index=”16" Name="Not Used 1" Value="17.0" /> 

<Property Index="17" Name="Not Used 2" Value="18.0" /> 

<Property Index=''18" Name="Rad. Cond." Value="1.0E-l8" /> 

<Property Index=”19" Name="Not Used 3" Value="20.0" /> 

</'MaterialProperties> 

+ <MaterialProperties xmlns="material_schema" App="Nascap2K" Color="8421504'' Name="Graphite"> 


Figure 165. Material Properties Specification in Object Definition File 

A. 5.3 SEE Interactive Spacecraft Charging Handbook Material Definition File 

Material definitions in the XML format shown in Figure 166 can be read into Object Toolkit by 
choosing “Import SEE Handbook Materials File” on the File menu. The name is unrestricted, 
although some software has constraints. ( Nascap-2k treats material names as four-character 
significant and case insensitive.) Table 42 shows the correspondence between the labels used in 
the file and the property names. 


<ROOTSTUBxMaterials>Material Nodes<Mkapton name="Kapton" type="lnsulator" pO="3.5" 
pi ="0.0001 27" p2="le-16" p3="5" p4="2.1" p5="0.15" p6="71.48" p7="0.6" p8="312.1" p9="1.77" 
pi 0="0.455" pi 1 ="140" pi 2="0.00002" pi 3="10000000000000000" pl4="12.01" pl5="1600" 
pi 6="1 7" pi 7="18" pi 8="1 e-18" pi 9="20">Kapton</Mkapton></Materialsx/ROOTSTUB> 

Figure 166. SEE Handbook Material Definition File for Material Kapton with Default Properties 


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203 



Table 42. Correspondence Between Material Property Numbers and Names 


pO 

Dielectric Constant 

pi 

Thickness 

p2 

Bulk Conductivity 

p3 

Atomic Number 

p4 

Delta-Max (Secondary yield) 

p5 

E-Max (Secondary yield) 

p6 

Range 1 (Electron range) 

p7 

Exponent 1 (Electron range) 

p8 

Range 2 (Electron range) 

p9 

Exponent 2 (Electron range) 

plO 

Proton Yield (Ion induced secondary emission) 

pll 

Proton Max (Ion induced secondary emission) 

pl2 

Photoemission 

p 13 

Surface Resistively 

pl4 

Atomic Weight 

p 15 

Density 

pl6 

Not used 1 

pl? 

Not used 2 

p 18 

Radiation-Induced Conductivity 

pl9 

Not used 3 


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A.5.4 Grid File Format 


GridTool saves the grid description in a file with the name p refix.gr d, using the fonnat shown in 
Table 43. 


Table 43. Format of Grid Definition File 


LINE(S) 

FIELD(S) 

CONTENTS 

1 


Total number of grids defined 

2-5 


Grid 1 parameters 

2 

1 

Grid number 

2 

2-4 

Number of grid lines in each of the three directions 

2 

5 

Parent grid number 

2 

6-11 

Limits in parent grid coordinates 

3 

1-6 

Limits in primary grid coordinates 

3 

7 

Mesh size (m) 

4 

1 

Mesh ratio with respect to parent grid 

4 

2 

Mesh ratio with respect to primary grid 

5 


Reserved for future use (20 zeros) 

6-9 


Grid 2 parameters (as 2-5) 

10-13 


Grid 3 parameters (as 2-5) 

14 on 


Parameters for further grids 

Last 

1-3 

Object size in meters 

Last 

4-6 

Object center relative to primary grid center (m) 

Last 

7 

Unit conversion factor 


A.5.5 Plume Map File Format 

The ion thruster plume map and the parameters used to specify the neutral density for charge 
exchange ion generation are specified in a file of the format generated by PlumeTool. Figure 167 
shows the top level view of this XML file. The parameters used to specify the neutral density 
appear as text nodes or attributes within the “EngineSpecs,” “NeutralGas,” and 
“Neutrallonlnteractions” elements. The plume map is specified within the “PlumeData” element. 


<?xml version ="1.0" encoding ="UTF-8" ?> 

- <PlumeToolCalculation> 

<Directory>C:\Program Files\PlumeTool\Plumel<v'Directory> 
<ProblemDescription>Plume for description of Tile format </ProblemDescription> 
<DateCreated>8/30/05 11:03 AM</DateCreated> 

+ <EngineSpecs> 

+ <NeutralGas> 

+ <MainBeam> 

+ <NeutralIonInteractions> 

+ <CalculationGrid> 

+ <PlumeData> 

<?/PlumeToolCalculation> 


Figure 167. Contents of Plume Map File Shown Nearly Fully Contracted 


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Figure 168 and Figure 169 show the beginning part of the plume map file, fully expanded. The 
elements understood by Nascap-2k are shown in blue. All other are ignored. The tags for the 
elements used by Nascap-2k are listed and described in Table 44. The alterative units provided as 
attributes for four of the tags are only understood by Nascap-2k and are neither written nor read 
by PlumeTool. They can only be added to the file by explicitly editing the file in a text or XML 
editor. When both the text node and the alternative unit attribute are present within a given 
element, the value given in the alternative unit attribute takes precedence. All text strings are 
case sensitive. 


<?xml version="l .0" encoding="UTF-8" ?> 

<PlumeToolCalculation> 

<Directory>C:\Program Files\PlumeTool\Plumel </Directory> 
<ProblemDescription>Plume for description of file format </ProblemDescription> 
<DateCreated>8/30/05 11:03 AM</DateCreated> 

<EngineSpecs> 

<Geometry> 

<OuterRadius>20.0</OuterRadius> 

<lnnerRadius>0.0</lnnerRadius> 

<NeutralizerDistanceFromCL>29.0</NeutralizerDistanceFromCL> 

<NeutralizerHeight>9.0</NeutralizerHeight> 

<EngineRadius>20.0</EngineRadius> 

</Geometry> 

<OperatingConditions> 

<PropellantMass>l 31.3</PropellantMass> 

<AnodeMassFlowRate sccm="54">5.27</AnodeMassFlowRate> 

<MeanSpeed Kelvin="400">225</MeanSpeed> 

<NeutralizerMassFlowRate sccm="5.16"> 0.504 
</NeutralizerMassFlowRate> 

</OperatingConditions> 

<Performance> 

<Thrust>263.0</Thrust> 

<PropellantUtilization>0.9</PropellantUtilization> 

<AnodeSpecificlmpulse>4763.</AnodeSpecificlmpulse> 

</Performance> 

</EngineSpecs> 

<NeutralGas> 

<Thruster> 

<Type>Holes</Type> 

<EffectiveHoleDensity>l .14E18</EffectiveHoleDensity> 
<HoleDiameter>0.00114</HoleDiameter> 
<HoleLength>7.6E-4</HoleLength> 

</Thruster> 

<Neutralizer> 

<EffectiveTemperature>810.0</EffectiveTemperature> 

<MeanSpeed>l 81 .</MeanSpeed> 

</Neutralizer> 

<BackGround> 

<Type>Lab</Type> 

<BackgroundDensity torr="l .e-6">3.54E+16</BackgroundDensity> 
</BackGround> 

</NeutralGas> 


Figure 168. Problem Specification Portion of Plume Map XML File, Part 1 (Tags Shown in Blue 

are Understood by Nascap-2k) 


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206 



<MainBeam> 

<PlumeReferenceConditions> 

<PlumeTemperature>8.0</PlumeTemperature> 
<ReferenceElectronDensity>l .El 2</ReferenceElectronDensity> 
</PlumeReferenceConditions> 

<LagrangianAlgorithm> 

<lonFluxFractions> 

<SinglelonFraction>0.978</SinglelonFraction> 

<DoublelonFraction>0.022</DoublelonFraction> 

<TriplelonFraction>0.0</TriplelonFraction> 

</lonFluxFractions> 

<MeanBeamSpeed>51904.</MeanBeamSpeed> 
<EffectiveBeamSpeed>51436.</EffectiveBeamSpeed> 
<EffectiveBeamEnergy>l 803.</EffectiveBeamEnergy> 
<BeamlonCurrent>3.8</BeamlonCurrent> 
<EffectiveBeamlonCurrent>3.75</EffectiveBeamlonCurrent> 
<NumericalViscosity>l .0</NumericalViscosity> 
</LagrangianAlgorithm> 

<ExitPlaneConditions> 

<ExitPlaneType>File</ExitPlaneType> 

<lntialConditions>Particles</lntialConditions> 

</ExitPlaneConditions> 

</MainBeam> 

<Neutrallonlnteractions> 

<ChargeExchange> 

<SingleCrossSectionArea>55.0</SingleCrossSectionArea> 
<DoubleCrossSectionArea>25.0</DoubleCrossSectionArea> 
<TripleCrossSectionArea>l 0.0</TripleCrossSectionArea> 
<EffectiveCrossSectionArea>54.1 </EffectiveCrossSectionArea> 
<NumberOflterations>l 5</NumberOflterations> 
<CXCeneratedlonCurrent>0.045381 </CXCeneratedlonCurrent> 
<ConvergenceRate>0.31 </ConvergenceRate> 
</ChargeExchange> 

<ElasticScattering> 

<ExitDensity>3.81 El 5</ExitDensity> 
<BackgroundDensity>0.0</BackgroundDensity> 
<EffectiveBeamSpeed>51436.</EffectiveBeamSpeed> 
<EffectiveBeamlonCurrent>3.75238</EffectiveBeamlonCurrent> 
<MaxRadialVelocity>8000.0</MaxRadialVelocity> 
<MinScatteringEnergy>50.0</MinScatteringEnergy> 
</ElasticScattering> 

</Neutrallonlnteractions> 


Figure 169. Problem Specification Portion of Plume Map XML File, Part 2 (Tags Shown in Blue 

are Understood by Nascap-2k) 


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207 



Table 44. Problem Specification Tags in Plume Map File Understood by Nascap-2k 


ELEMENT TAGNAME 

USE 

UNITS 

ALTERNATIVE 

UNITS 

EngineRadius 

Radius of originating region of thruster un-ionized 
propellant. 

cm 


PropellantMass 

Atomic mass of neutral atoms from all thrusters 
and neutralizers 

amu 


AnodeMassFlowRate 

Total flow rate of propellant, both ionized and un¬ 
ionized, through thruster 

mg/s 

standard cubic 
centimeters per 
minute (ssm) 

MeanSpeed 

Temperature of un-ionized propellant. Nascap-2k 
and Plumetool use the mean speed differently in 
their computations of neutral density. In Nascap- 
2k , the use of the Kelvin attribute to specify the 
temperature is recommended over the use of the 
text node. 

m/s 

Kelvin 

NeutralizerMassFlowRate 

Flow rate of neutral atoms from neutralizer (The 
ions are ignored) 

mg/s 

standard cubic 
centimeters per 
minute (seem) 

PropellantUtilization 

Fraction of propellant ionized. Used with 
AnodeMassFlowRate to determine flow rate of 
neutral atoms from thruster. 



EffectiveTemperature 

Temperature of gas from neutralizer 

Kelvin 


BackgroundDensity 

Density (or pressure) of background gas. Use zero 
for space cases. The density is computed from the 
pressure assuming standard temperature (273 
Kelvin). 

m- 3 

torr 

EffectiveCrossSectionArea 

Charge exchange cross section. The value from the 
plume map fde is only read if no value appears on 
the Particles tab. 




The plume map is specified within the “PlumeData” element. Figure 170 shows the first level 
nodes within the “PlumeData” element. The density values are specified on an R-0 grid in the 
thruster’s coordinate system. Nascap-2k ignores any azimuth values. The radial values are 
specified in meters and the angles in radians. The densities and velocities at the points specified 
are given within the “MainBeam,” “Scattered,” and “ChargeExchange” elements. Each of these 
elements encloses four text nodes: “Densities,” “Velocities,” “Description,” and “Abbreviation.” 
The “MainBeam” may have an optional “Neutrals” text node listing the neutral density. The 
density for each radius-angle pair is listed successively, with all the densities for a given radius 
listed before the value for the next angle. The densities are given in ions per cubic meter. 

Nascap-2k reads only the “MainBeam” elements, ignoring the “Scattered” contribution as it is 
typically orders of magnitude smaller. Charge exchange ions are generated and tracked self- 
consistently within Nascap-2k. 


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<?xml version="1.0" encoding="UTF-8" ?> 

- <PlumeToolCalculation> 

<Directory>C:\Program Files\PlumeTool\Plumel</Directory> 
<ProblemDescription>Plume for description of file format </ProblemDescription> 
<DateCreated>8/30/05 11:03 AM</DateCreated> 

+ <EngineSpecs> 

+ <NeutralGas> 

+ <MainBeam> 

+ <NeutralIonInteractions> 

+ <CalculationGrid> 

- <PlumeData> 

<RadiiValues>0. 050005 0.07591264 0.107215755 0.14390935 0.18599342 
0.23346795 0.28633296 0.3445885 0.40823445 0.4772709 0.55169785 
0.6315152 0.7167231 0.8073215 0.9033103 1.0046896 1.1114594 
1.2236197 1.3411704 1.4641116 1.5924433 1.7261655 1.8652781 
2.0097814 2.159675 2.3149588 2.4756334 2.6416986 2.813154 
2.989701</RadiiValues> 

<ThetaValues>0.0 0.10689655 0.2137931 0.32068965 0.4275862 0.5344828 
0.6413793 0.7482759 0.8551724 0.962069 1.0689656 1.1758621 1.2827586 
1.3896551 1.4965518 1.6034483 1.7103448 1.8172414 1.924138 2.0310345 
2.137931 2.2448275 2.3517241 2.4586208 2.5655172 2.6724138 2.7793102 
2.8862069 2.9931035 3.09969</ThetaValues> 

<PhiValues>0.0</PhiValues> 

+ <SputteringMultiplier> 

+ <MainBeam> 

+ <Scattered> 

+ <ChargeExchange> 

+ <ScatteredBinned> 

</PlumeData> 

</PlumeToolCalculation> 


Figure 170. Contents of Plume Map File with the First Level Under “PlumeData” Node Expanded 


B. Using the Nascap-2k Script Runner 

Nascap-2k includes a script runner that can be used for long running calculations. The 
executable, N2kScriptRunner.exe, is installed with the rest of the code in C:\Program 
Files\Leidos\Nascap2k_4. 

Create the desired script on the Nascap-2k user interface Script tab as usual. Click the “Save 
Files” button at the bottom of the screen. At this point all the files need for N2kScriptRunner are 
generated and saved to the project directory. Among others, these include a file/ur/zxDriver.xml, 
which contains the script commands, and several prefix* in.txt files. After creating the files, exit 
the Nascap-2k user interface. 


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209 




Figure 171. Edit Script Subtab of Script Tab Showing “Save Files” Button at the Bottom of the 

Screen 

N2kScriptRunner is most conveniently executed using a batch file. The content of the “bat” file 
should be the following single line: 

C:\Program Files\Leidos\Nascap2k_4\N2kScriptRunner.exe prefix Driver.xml prefix > outputfile.txt 

where prefix is your project prefix, outputfile.txt is the desired location for the text output, and 
“C:\Program Files\Leidos\Nascap2k_4” is the directory in which Nascap-2k is installed. The 
name of the script file and the project prefix are supplied to the N2kScriptRunner as command 
line arguments. 

Alternatively, the content of the “bat” file can include the following two lines: 

PATH %Program Files%\Leidos\Nascap2k_4;%PATH% 

N2kScriptRunner.exe pref/xDriver.xml prefix > outputfile.txt 

where prefix is your project prefix, outputfile.txt is the desired location for the text output, and 
“%Program Files%\Leidos\Nascap2k_4” is the directory in which Nascap-2k is installed. 


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Figure 172. Output File Showing Beginning of Execution of N2kScriptRunner 

Once N2kScriptRunner has completed the calculation, the Nascap-2k user interface can be used 
to view the results. 

C. Template for Nascap-2k Custom Current DLL 
C.l Purpose 

The purpose of a “Custom Current” DLL is to calculate currents to surface elements in a manner 
the analyst considers more appropriate to his or her problem than the fonnulations built in to 
Nascap-2k , s surface charging module, N2KDLL. For example, the template contains the “EWB 
Plate” formulation, which is appropriate to a low Earth-orbiting spacecraft with no highly biased 
surface elements, and takes into account ram ions and wake effects. 

C.2 Mechanics of Use 

The custom current DLL is loaded dynamically by N2kDLL, which expects to find the two entry 
points described below. The analyst assigns the DLL an appropriate filename and specifies the 
name of the file, complete with its entire path, in Nascap-2k. The filename, with its path, is 
specified to N2kDLL in the SetCustomCurrentDLL script item. 

C.3 Template 

The template contains the C++ and project files needed to create a custom current DLL. The 
supported programming environment is Microsoft Visual Studio 8. 

C.4 Entry Points 

The DLL contains two entry points, which are called by N2kDLL. 

CALLBACK setEnvironmentParams(double* den, double* te, double* ti, Vector3* objvel, 
double* ionamu) 


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211 








is called once each timestep to set the calculation parameters, which are: 

■ den - The first electron density of a GEO environment 

■ te - The first electron temperature of a GEO environment 

■ ti - The first ion temperature of a GEO environment 

■ objvel - The spacecraft velocity 

■ ionamu - The ion atomic mass, presently hardwired to be 16. 

The analyst may hardwire additional parameters into the DLL, read parameters from a file, or 
otherwise obtain additional parameters. 

CALLBACK getCustomCurrent(element* elem, double* 10, double* II) 

is called for every surface element at each timestep. The element structure’s public member 
variables (listed below) are accessible to the analyst. Element public methods are NOT 
accessible, as the source code is not provided. (The header file element.h must be identical to the 
file used in building N2kDLL.) The analyst is responsible for calculating and returning 10 - the 
surface element current divided by so (=JA/ so, units of Vms' 1 ), and II - the derivative of 10 with 
respect to surface potential. (Note that II must be non-positive.) 

C.5 The Vector3 Class 

The Vector3 class, implemented in Vector3.cpp, is used to encapsulate three-vectors and 
numerous useful methods. The analyst can easily discover these methods through inspection of 
the code (provided). Note that many of the Vector3 methods return pointers to new Vector3 
objects; it is the responsibility of the custom DLL programmer to delete these objects. 

C.6 Other Files 

The Nascap-2k/src/CustomCurrentDLLTemplate/lnclude folder contains several include files, the 
most noteworthy of which is element.h, whose properties are described below. The file derf.cpp 
is used in the “EWB Plate” fonnulation and is not generally required. 

C.7 Surface Element Properties 

The surface element properties listed in Table 45 are accessible to the analyst via the 
elem ->propertyname construct: 


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212 



Table 45. Surface Element Properties 


Type 

Variable Name 

Description 

double 

area 

Surface element area (m 2 ) 

double 

capacitance 

Surface element Capacitance/£ 0 (meters) 

Vector3* 

center 

Location of surface element center (meters) 

conductor* 

conduc 

Structure with info about associated conductor 

int 

conductorlndex 

Index of the associated conductor 

boolean 

eFieldCondition 

True if EFieldCondition for surface is “true” in the object definition file. 

double 

field 

Normal component of electric field (V m" 1 ) 

boolean 

fixedlnsulator 

True if FixedPotential for surface is “true” in the object definition file. Value is 
set using the “Insulator Surface Potentials” region on the Applied Potentials 
tab. 

int 

index 

Fortran-style index of the surface element 

double 

initialcurrent 

Current at the beginning of the timestep 

double 

initialPotential 

Cell potential to be used in SetlnitialPotentials (V) 

char 

materialN ame(3 2) 

Name of the surface element’s material 

material* 

matl 

Pointer to the associated material structure 

double 

maxpotential 

Maximum potential on the object (V) 

double 

minpotential 

Minimum potential on the object (V) 

element* 

next 

Pointer to the next surface element to be iterated over 

node* 

nodes(4) 

An array of pointers to the four nodes in counterclockwise order 

Vector3* 

normal 

Unit outward normal to the surface element 

double 

normalfield 

Normal component of electric field (V m" 1 ) 

double 

potential 

Surface element potential (V) 

element* 

prev 

Pointer to the previous surface element iterated over 

Projection 

proj 

Structure describing the projection of the surface element onto a plane normal 
to the velocity vector 

Vector3* 

ram 

Unit vector in the velocity direction 

double 

speed 

Magnitude of the spacecraft velocity (m s" 1 ) 

Vector3* 

sundir 

Unit vector from the spacecraft toward the sun 

double 

sunlntensity 

Ratio of sun intensity to the usual sun intensity at 1 AU 

BOOL 

sunlit 

True if the surface normal has a positive scalar product with the sun direction 


For the node object, the only potentially useful public variable is the index. For the material 
object the name and the arrays of input property values (plnput) and processed values (pProps) 
are publicly available. (Note that the property array indices in C++ are one less than their Fortran 
indices.) The properties of the conductor object are all publicly accessible. 

D. Disjoint Grids in Nascap-2k 

D.l Overview 

Objects can be defined in disjoint grids and used for Nascap-2k calculations. The idea is that, 
while the grid and object models are disjoint, the objects are electrically connected, so that 
meaningful calculations may be perfonned. In the course of this description, we illustrate a 
simple example of such a calculation. 


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D.2 Defining the Objects and Grids 


We start by defining each of the disjoint objects together with its grid structure in the usual way. 
At present, it is necessary for both outer grids to have the same mesh spacing. Using different 
primary grid spacings causes potentials to be both wrongly calculated and displayed. Each object 
should be centered in its own computational grid before starting. 

For this example, we define a “Lower” object as a three-meter 6x6x6 gold cube, and an “Upper” 
object as a one-meter 4x4x4 aluminum cube. Both use a 0.8 meter primary grid, with a three- 
grid structure for the “Lower” object and a four-grid structure for the “Upper” object. Figure 173 
and Figure 174 show GridTool pictures of these two object and grid structures. 



Figure 173. The “Lower” Object and Grid 


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Figure 174. The “Upper” Object and Grid 


D.3 Combining the Grids 

The two grid files must be combined using the CombineGrids Java application. The jar for this 
application is included in the Utilities folder in the Nascap-2k installation. Figure 175 shows the 
CombineGrids user interface. The full pathnames to the primary, secondary, and combined grid 
structures are entered. In the “Offset Vector” field, enter the vector distance from the center of 
the primary grid structure to the center of the secondary grid structure. In this case, we place the 
“Upper” object 20 meters above (+Z) the “Lower” object. (This relatively modest distance is 
chosen so that the results can be easily seen in the Nascap-2k user interface. If more realistic 
multikilometer distances are used, displaying the secondary grid is difficult, and displaying both 
grids is impossible.) 



Figure 175. The CombineGrids User Interface 

Clicking the “Combine” button writes out the combined grid (.grd) file. In this case, grids 1-3 
are the grids of the “Lower” object, grid 4 is the primary grid of the “Upper” object, and grids 
5-7 (descended from 4) are the refined grids of the “Upper” object. 


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D.4 Creating the Combined Project and Database 

The new project and database should be created in a directory containing the new grid file 
(Combined.grd), possibly the two component objects, and no other “Combined” files. (Note that 
we use the prefix “Combined” in this appendix, but, of course, the actual project name is at the 
user’s discretion.) 

Create a new project 

Launch the Nascap-2k user interface and click the “Create New Project” button. Uncheck 
“Create New Folder” and click “Set Location” to place the project in the folder containing 
Combined.grd. Assign a prefix (in our case, “Combined”) to the project. Click “OK.” 

Load the primary object 

On the File menu select “Load Object..Navigate to the primary object definition file (in our 
case LowerObject.xml), select it, and click “Open.” The second object (UpperObject.xml) is added 
later through the script. The “Grid Status” should show the grid already loaded. 

Select “Problem Type” and parameters 

For this example, we select a “LEO” “Environment” and the “Analytic Space Charge” option 
under “Potentials in Space or Detector Analysis” as the “Problem Type.” On the Environment 
tab, set Density=10 n m' 3 , Temperature=0.3 eV, B=(0., 2.5e-5, 0.) tesla (northward), 

V=(7500, 0, 0) (eastward). (Correspondingly, VxB is in the Z direction, which we consider 
upward.) Add the Oxygen species. On the Space Potentials tab the “Non-linear” “Charge 
Density Model” is selected. 

Build the script 

The script used to create the combined object (as it appears in the Script window) is shown 
in Figure 176. This can be built by adding commands to the script within the interface. 
Alternatively, it may be written to a file (shown in Figure 177) and loaded by selecting “Load 
Script” on the File menu. Note that the (x,y,z) coordinates in the AppendObject command 
correspond to the “Object Center Offset” displayed by CombineGrids and are not necessarily the 
same as the grid offset. The argument of the AppendObject command is the filename of the 
second object, UpperObject.xml. 


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216 




Figure 176. Script Used to Append “Upper” Object 


<?xml version="1.0" encoding="UTF-8" standalone="no"?> 

<SCRIPT> 

<COMMAND Fi1eName="CombinedObject.xml" cmd="Read_Object"/> 

<COMMAND Fi1eName="C:\Nascap\Combined\UpperObject.xml" cmd="Append_Object" x="0.0" 
y="0.0" z="20.0"/> 

<C0MMAND InputFi1eName="Combined_n2kdyn_in.txt" 

OutputFi1eName="Combined_n2kdyn_out.txt" cmd="Embed_Object_in_Grid"/> 

<C0MMAND InputFi1eName="Combined_potent_0_in.txt" Iteration="0" 

OutputFi1eName="Combined_potent_0_out.txt" cmd="Potentials_in_Space"/> 

</SCRIPT> 


Figure 177. XML Version of Script Used to Append “Upper” Object (CombinedDriver.xml) 


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217 
































After running the script, the combined object can be viewed on the Results 3D tab, as shown in 
Figure 178. 



Figure 178. View of Combined Object 


D.5 Calculating Potentials 

The script used for calculating potentials is shown in Figure 179. The potential solver input file 
is shown in Figure 180. 


Materials Help 


Problem | Envir onment Applied Potentials Charging | Sp ace Potential s - ] Particles [ Script [ Results [ "Results 3D j 
| Run Script | Edit Script [ 


Commands- 



Script- 

Loop 



Value 

Read_Object 



? Q Charge Surfaces 

Append_Object 



? 0 SetVelocity 

lnitialize_Potentials 



A « 7500. 

Charge_Surfaces 



Ay o.o 

DoOneTimeStep 



A z o.o 

DoTime Steps 



9 Q SetEnvironment 

DoTrackTimeStep 



? CJ Environment 

EmitCurrent 



A type LEO 

A nel 1.000E11 

FixGroundPotential 



1 A tel 0.300 

ReadPhotoemission 


1-.—_-1 

A massl 2.657E-26 

SetBField 


»Add Command» 

[■ A faction 1 1.000 

SetConductorBias 



A numSpecies 1 

SetCustomCurrentDLL 


Delete Item 

*- A begintime 0.0 

SetEnvironment 



f C SetBField 



Duplicate Item 

A« o.o 




A y 2.500E-5 

SetParameters 



A 2 o.o 



? c SetVXBPotentials 

SetVelocity 



A Value 3.000 

SetVXBPotentials 



? C Potentials in Space 

U seT rackedCu rrent 



A InputFileName Combined_potent_0Jn.txt 

UseTrackedlons 



A OutputFileName Combined_potent_0_out.txt 

E mbed_Object_i n_G rid 



A Iteration 0 

Potentials_in_Space 







Create Particles 

- 

1 up II Down 


Figure 179. Script for Calculating Potentials 


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1 Comment -- Potential Solver Input 

: Fi 1 e 

Comment 



Comment -- File 

Prefix . . . 


PREFIX 

Combined 


Comment 



Comment — New or Continue run . 


RUN 

NEW 


Comment 



Comment -- Time 

parameters (NEW 

run only) . . . 

TIME START 

0.0000E00 

seconds 

TIME RISE 

0.0000E00 

seconds 

TIME FALL 

1.0000E30 

seconds 

Comment 



Comment — Convergence criteria 


MAXITS 

20 

max space charge iterations 

RMSMIN 

1.0000E-04 

min RMS error 

MAXITC 

50 

max potential iterations 

POTCON 

2.0000E00 

SCG Convergence - orders of magn. 

RDRMIN 

1.0000E-04 

min rdotr 

DEBLIM 

2.0000E00 

debye per zone limit 

Comment 



Comment — environment ... 


DEBYE 

1.2877E-02 

debye length (meters) 

TEMP 

3.0000E-01 

plasma temperature (eV) 

TION 

3.0000E-01 

ion temperature (eV) 

DENSITY 

1.0000E11 

plasma density (l/m**3) 

MIN_DENSITY 

1.0000E09 

minimum density (l/m**3) 

Comment 



Comment — algorithm ... 


ALGORITHM 

32_NODE 

32-node algorithm 

Comment 



Comment — problem type ... 


PROBLEM 

NON_LINEAR 

Nonlinear screening 

BOUNDARY 

ZERO 


EPIC_Name 

NoChange 


Comment 



Comment -- other 

options . . . 


DEBYE_SCALE 

LOCAL 

Scaled by local xmesh 

CONV_EFFECT 

ON 

analytic convergence 

Comment 



Comment — range 

of loop over grids ... 

GRIDLOW 

0 

lower limit 

GRIDHIGH 

0 

upper limit 

Comment 



Comment — mixing old and new solutions ... 

S0LUTI0N_MIX 

0.0000E00 

old solution fraction 

SAVE_INTERVAL 

1 

STARTING 1 

Comment 



Comment -- Wake 

parameters (NEW 

run only) . . . 

WAKE 

ON 


OBIVEL 

7.5000E03 0. 

0000E00 0.0000E00 

BFIELD 

0.0000E00 2. 

5000E-05 0.0000E00 

RMASS 

16 

AMU 

NADD 

1 


NPHI 

36 


NTHETA 

180 


Comment 



Comment — diagnostics ... 


DIAG INIT 

1 

PSinit 

DIAG FINAL 

1 

PSfinal 

DIAG SCG 

1 

PSscg 

DIAG SCREEN 

0 

PSscrn 

DIAG MATRIX 

0 

PSmtrx 

DIAG INTERFACE 

1 

PSgrds 

DIAG WAKE 

1 

Wake Diags 

Comment 



Comment — miscellaneous ... 


TIMER 

1 

Timer Level 

END 




Figure 180. Potential Solver Input File (Combined_potent_0_in.txt) 


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The “Value” in the “SetVXBPotentials” command is the maximum (most positive or least 
negative) potential to appear on the object. If timesteps are run, object potentials are adjusted 
from this initial condition based on the charging currents. 

Figure 181 shows a display of the resulting object and space potentials. Note the magnetically 
induced potential variation on the object surface elements, and the fact that the potentials are 
split between the two disjoint grid structures. Figure 182 is a blow-up of the “lower” part of 
Figure 181, showing that potentials have been correctly calculated and plotted in this region. 



Figure 181. Results 3D Picture after Running Potential Script. Note Magnetically Induced Potential 

Variations on Object. 


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Figure 182. Expanded View of “Lower” part of Figure 181, Showing that the Potentials Have Been 

Correctly Calculated and Plotted 


D.6 Displaying Trajectories 

Particle calculations can be done, but care must be taken to ensure that the particle generation 
and particle tracking input files are as intended. Make sure that the particle tracking and plotting 
limits are large enough to include the secondary grid (note that the tracker visualization input file 
specifies x, y, and z limits in grid units). Because the second object was offset in the +Z 
direction, this is the limit that must be adjusted for both the tracking and plotting limits. Note that 
the default of “Track particles throughout grid” will not work because the second object is 
outside the limits of the first grid. Make sure that the magnetic field is included correctly in the 
particle tracking input file. Check the output files to make sure the charge and mass of the 
tracked species is correctly specified. If, after specifying trajectories, the “Show Trajectories” 
button is not enabling, it is most likely that the particles tracked are outside the visualization 
limits. Double check the output files to ensure that particles are generated and then adjust the 
particle tracking and plotting limits. 

Figure 183 shows trajectories for electrons generated at the intersection of the 0.5 V contour with 
the Y = 0 plane in the secondary grid with “Contour” selected as the “Initial Particle Distribution 
for Trajectories.” To get extended potentials the density (in the potential solver input file) was 
reduced to 10 6 m 3 and the potentials recomputed. The potentials in Figure 183 are on the X = 0 
plane. As expected, the particles ExB drift along the potential contour, and none hit the object. 
Figure 184 and Figure 185 show trajectories for electrons generated at the intersection of the 0.5 
V contour with the X = 0 plane in the secondary grid. The potentials in these figures are on the Y 
= 0 plane. In this case, the electrons whose Y-values pass through the object are rapidly 
collected, while the remainder bounce parallel to the Y-axis while ExB drifting. 


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Figure 183. Trajectories of Particles Generated at the Intersection of the 0.5 V Contour and the 
Y = 0 Plane, which ExB Drift Along the Potential Contour 



Figure 184. Trajectories of Electrons Generated at the intersection of the 0.5 V Contour and the 
Plane X = 0, Superimposed on Potential Contours on Y = 0 Plane Showing that Electrons Follow 
Magnetic Field Lines (Parallel to Y) to Hit or Miss the Object 


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Figure 185. Trajectories of Electrons Generated at the Intersection of the 0.5 V Contour and the 
Plane X = 0, Superimposed on Potential Contours on Y = 0 Plane (Magnetic Field Direction 
Normal to Paper) Showing that Electrons that Miss the Object ExB Drift Along the Potential 


Contour in a Clockwise Direction until the Calculation Runs Out of Time 
E. Using Plume Densities in Nascap-2k 

Nascap-2k can use ion thruster plume densities read from an imported plume map file in a 
“Potentials in Space” calculation. The overall steps to perform the calculation are as follows: 

1. In Object Toolkit, create or open an object. Make sure that one or more thrusters are 
defined at the correct location(s). Add any neutralizers. Save the object file. 

2. If reading a two-dimensional plume map file directly into Nascap-2k, use either 
PlumeTool or any other tool to create a plume map with the correct format. Import the 
plume map into Nascap-2k using “Import Plume” on the File menu. 

3. lnNascap-2k: 

a. Import the saved object file and define an appropriate computational grid. 

b. On the Problem tab, select “Potentials in Space/Consistent with Plume Ion 
Densities.” 

c. On the Environment tab, define the appropriate ambient environment. 

d. On the Applied Potentials tab, specify potentials for all the surfaces. 

e. On the Space Potentials tab, choose “Plume Ion Density” charge density model. Set 
the appropriate “Target average error.” Optionally check “Self-consistent CEX” and 
specify appropriate iteration sharing parameters. 

f. On the Script tab, generate and run the script. 

g. On the Results 3D tab, view the potentials. 


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Further details are given in the following paragraphs. 

E.l Problem Tab 

The computation of “Potentials in Space” that are “Consistent with Plume Ion Densities” is only 
available for the “LEO or Plume” environment. If no plume map has been imported, the option is 
disabled. 

E.2 Space Potentials Tab 

The charge density model that uses ion thruster plume infonnation is “Plume Ion Density.” If no 
plume map has been imported, the “Plume Ion Density” option is disabled. The charge density 
model used for this case is the same as the one for “Full Trajectory Ions” with the plume map ion 
density replacing the tracked ion density. 

If “Plume Ion Density” is selected, the option to self-consistently compute the charge exchange 
ion density is available. If “Self-consistent CEX” is not selected, the ion density is the sum of the 
Main Beam and Charge Exchange components of the plume map. If the charge exchange is self- 
consistently computed, the ion density is the sum of the Main Beam component of the plume 
map and the tracked ion density. The zeroth iteration of the potential solution uses the charge 
exchange ion density in the plume map. The sharing of the charge density with the previous 
charge density for the first iteration should be zero. 

E.3 Particles Tab 

If “Self-consistent CEX” is selected, the Particles tab is enabled. On the Particles tab, the 
particles are specified to be charge exchange, the charge exchange cross section is set, and the 
species of particles created is set. The charge exchange current is proportional to the product of 
the cross section, the ion beam density, and the neutral density. The neutral density is the sum of 
three components: un-ionized propellant from thruster, un-ionized gas flow through neutralizers, 
and the background density. The parameters used to compute these tenns appear in the plume 
map file. Additional attributes are used to specify the parameters in units appropriate to Nascap- 
2k. (See Appendix A for file fonnat.) 

E.4 Results 3D Tab 

The option “Ion Charge Density” on the “Cut plane” “Display” drop-down list displays the ion 
charge density, computed from the plume map, or computed by particle tracking. After execution 
of the zeroth Potential in Space iteration, the “Ion Charge Density” is the sum of the Main 
Beam and Charge Exchange densities in the plume map. After the first Track Particles iteration, 
the “Ion Charge Density” is the tracked charge density. 

E.5 Files 

The text input file for “Potentials in Space” has a value of “Plume” for the “Problem Type.” 


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GLOSSARY 


ATS-6: Applications Technology Satellite 6. Geosynchronous, three-axis stabilized, 
communications satellite launched by NASA in 1974 for research. 

Attribute: Property associated with an element or XML tag. For example, Nascap-2k surface 
elements have attributes of material name, conductor number, and four pointers to nodes. 

Aurora: The precipitation of charged particles in the auroral region, causing the beautiful visible 
displays of the Northern and Southern Lights (Aurora Borealis and Aurora Australis) that are 
often connected with geomagnetic substorm activity. 

Auroral region: A narrow oval band around each geomagnetic pole, at about 75 degrees 
magnetic latitude at local noon to about 67 degrees magnetic latitude at midnight, in which 
auroral activity is generally most intense. It widens to both higher and lower latitudes during the 
expansion phase of a magnetic substorm. 

Backscattered electrons: Electrons with energy (50 eV < E < primary electron energy) reflected 
due to coulomb scattering by the nuclei of the target material. 

BEM: Boundary Element Method. A mathematical technique for solving elliptic equations (such 
as Laplace's equation or the Helmholtz equation) in bounded regions of two or three dimensional 
space. The method requires that the boundary be gridded (into line segments for two dimensional 
space or surface elements for three dimensional space), but does not require gridding of the area 
or volume. In Nascap-2k, it is used to establish a relationship between surface potentials and 
surface electric fields. (See Section 13.2 and Reference 7.) 

Charge exchange: Collision between a fast ion and a slow neutral atom in which an electron 
transfers from the atom to the ion. Of relevance to ion plumes when the atom is low energy and 
the ion is high energy, such as from an ion thruster. 

Charging calculation: Calculation in which surface potentials are computed from surface 
currents. 

Charging current: Current to a surface element used in a charging calculation. Current can have 
both analytic and tracked components. 

CHAWS: Charge Hazards and Wake Studies, an Air Force (Philips Laboratory)-sponsored 
experiment, which flew on the Wake Shield Facility (WSF) for the purpose of investigating high- 
voltage current collection within the spacecraft wake. 

Child grid: A grid contained within a larger grid (its “parent” grid) for the purpose of enhanced 
spatial resolution. In Nascap-2k a child grid usually has one-half the mesh spacing of its parent. 

Compatible elements: Set of surface elements such that each edge has exactly one element on 
its right and exactly one element on its left. Nascap-2k prohibits incompatible elements. 


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Conductor number: Number used by Nascap-2k to define electrical connectivity. Conductor 1 
is always chassis ground. All conducting surface elements with the same conductor number have 
the same surface potential. Each element must have a conductor number as an attribute. 

Conjugate gradient: Conjugate gradient methods are (popular) iterative methods for solving 
large systems of linear equations, Ax=b, where x is the unknown vector, b is the known vector, 
and A is a known square, symmetric, positive-definite matrix. Conjugate gradient methods are 
best suited for systems with sparse matrices. 

DataBase manager: Nascap-2k 's library for storing and retrieving grid, element, particle, and 
miscellaneous infonnation. 

Debye length: Most commonly denoted as A, D , the characteristic length for falloff of electrostatic 
potential in a plasma in the linear regime (originally defined in the Debye-Htickel theory for 

strong electrolytes). It is given by ^s o 0/en where s Q is the permittivity in vacuum, 0 is the 
plasma temperature, n is the plasma density, and e is the electron charge. 

Differential charging: The difference in the potential of one part of the spacecraft with respect 
to another part of the spacecraft. 

Direct-X: A Windows technology that enables higher perfonnance in graphics and sound when 
playing games or watching video on computers with the Windows operating system. 

See http://www.microsoft.com/windows/directx/default.aspx. 

DLL: Dynamic Link Library. 

DMSP: Defense Meteorological Satellite Program. Series of Earth observing satellites with 101 
minute, sun-synchronous, near-polar orbits at an altitude of 830 km. Some of the DMSP 
spacecraft have carried particle detectors that are able to measure charging events. 

Double Maxwellian distribution function: An approximation representing the plasma energy 
distribution as the sum of two Maxwellian distributions of differing density and temperature. 

DynaPAC : Dynamic Plasma Analysis Code. Computer program to model dynamic behavior in 
plasmas developed under Air force contract 1989-1999. Most of Nascap-2k2 s computational 
abilities were originally developed for DynaPAC. 

Electron thermal current density: Electron current density incident on one side of an 
imaginary surface in a thennal plasma: en e yjcQ c /2nm c ,where e is the electron charge, n e is the 
density, 0 e is the temperature, and m e is the mass. 

Element: An elemental surface defined by three (a triangle) or four (a quadrilateral) nodes. The 
nodes are ordered counterclockwise as viewed from an exterior point. 

EPIC : Electric Propulsion Interactions Code. Engineering tool to model interactions between 
electric propulsion effluents and spacecraft systems developed by Leidos and distributed by the 
SEE Program at NASA/MSFC. EPIC uses Object Toolkit to define spacecraft geometry and 
materials. Available from see.msfc.nasa.gov. 


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Finite element method: Technique for solving elliptical equations (such as Poisson’s equation) 
in which the computational domain is divided into small elements within each of which the 
spatial variation of a trial function is defined by interpolation of a small number of nodal values. 
The solution to the discretized elliptical equation is detennined by finding the set of nodal values 
that minimizes an integral functional of the trial function. 

Floating potential: The potential of an object in a plasma at which the incident electron current, 
the emitted electron currents, and the ion current to the object exactly balance, so that no net 
current flows to the object. 

Geosynchronous altitude: The altitude at which a spacecraft orbiting Earth has an orbital period 
of 23 hours and 56 minutes, thereby maintaining a constant latitudinal position with respect to 
Earth . This is approximately 6.6 Earth radii from Earth’s center. Substorms, which generate kilo- 
electron-volt charged particles, can occur near this altitude. 

GridTool : Interactive program for building an arbitrarily nested grid structure about an object. 
(See Section 10.) 

Hybrid: In the context of computer modeling, refers to algorithms that employ a combination of 
particle and fluid methods to model the physics of the problem. 

Ion thermal current density: Ion current density incident on one side of an imaginary surface in 
a thermal plasma: enj ^/e0j /2jxni j , where e is the electron charge, n, is the ion density, 9; is the 
temperature, and m; the mass. 

JNI: Java Native Interface, which is used in Nascap-2k to program the interface between 
interactive Java modules and computational modules written in C++ or Fortran. 

Laplace’s equation: The equation satisfied by electrostatic potential in vacuum: V § = 0. (See 
Poisson’s equation.) 

Macroparticle: An object representing a large number of ions or electrons that is tracked (as a 
single particle of the appropriate species) in an electromagnetic field for the purpose of 
calculating charge density or surface current. 

Material: A name and a set of associated properties. Each surface element must have a material 
name as an attribute. 

Mesh: A set of elements together with their defining nodes. A mesh describes the surface(s) of a 
spacecraft. 

MESSENGER: MErcury Surface, Space ENvironment, Geochemistry, and Ranging. A NASA 
scientific spacecraft to Mercury launched August 2004. 

MIRIAD: Module Integrator and Rule-based Intelligent Analytic Database. ALeidos proprietary 
model integrating technology that provides a framework for integrating a variety of physical 
models and their constituent data into a single executable application. The resulting application 
lets the user define systems of interest and perform parametric analyses on those systems. The 


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MIRIAD architecture manages the flow of data between the user, the database(s), and the 
models, enabling the user to study phenomenological relationships. 

NASCAP/GEO : NASA Charging Analyzer Program for geosynchronous orbit environments is a 
set of computer codes that models the charging of spacecraft surfaces in a geosynchronous 
plasma in three dimensions. The codes allow for a three-dimensional, finite-element 
representation of a spacecraft within a 16x 16x32 grid. They use orbit-limited current 
collection algorithms to compute the current incident to surfaces, including secondary electron 
emission, backscatter, and photoemission. NASCAP/GEO calculates the three-dimensional 
electric fields around the object and includes their role in limiting the emission of low energy 
secondary and photo electrons. NASCAP/GEO was developed under NASA and Air Force 
support, 1976-1984. 

NASCAP/LEO: NASA Charging Analyzer Program for Low Earth Orbit. Computer program to 
study electrostatic interaction between a spacecraft with surfaces at high potential and a cold 
(0.1-1 eV), dense (10 -10 m' ) plasma (Debye length much shorter than spacecraft 
dimensions). 

Node: An entity representing a point in space. 

Object Toolkit : Nascap-2k’s object definition tool. (See also Section 9.) 

OpenGL: Widely used and supported two-dimensional and three-dimensional graphics 
application programming interface introduced in 1992. See http://www.opengl.org. 

Orbit-limited current collection: Collection of current by a biased probe from surrounding 
plasma when the plasma density is such that the potential has a range larger than the largest 
impact parameter and is sufficiently well behaved so that no angular momentum barriers exist. 
For a sphere, this means the potential drops off no faster than r" . 

OSR: Optical Solar Reflector. 

Particle type: A set of species parameters (label, mass, and charge). Each macroparticle has a 
type. In the database, a separate particle type is created for each species used in a calculation and 
for each species tracked for visualization. 

PATRAN: Popular, general purpose, three-dimensional, finite-element modeling software 
package distributed by MSC Software Corporation. 

Photoemission: Emission of electrons by surfaces under the influence of electromagnetic 
radiation. In Nascap-2k the “electromagnetic radiation” in question is always sunlight. 

Plasma: An ionized gas that is quasi-neutral, exhibits collective behavior (A, D much less than the 
characteristic dimension of the plasma), and has enough particles in a Debye sphere to be a 
statistically valid concept (i.e., N D =4/3 n7tA, D »1). 

PlumeTool: A program for modeling axisymmetric thruster plumes that is distributed with EPIC. 
The output is a map of ion densities and velocities. PlumeTool was developed by Leidos. 


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2 

Poisson’s equation: The general equation for electrostatic potential: -s 0 V“c))=p, where p is the 
space charge density. 

POLAR : Potentials of Large Objects in the Auroral Region. A set of computer codes that model 
spacecraft charging, taking account of wake effects and precipitation of high-energy electrons. 
The codes allow for a three-dimensional, finite-element representation of a spacecraft and can 
use either space-charge-limited or orbit-limited current collection algorithms to compute the 
current incident to surfaces. It includes secondary electron emission, backscatter, and 
photoemission. Developed under Air Force support, 1978-1988. 

Primary grid: The outermost (largest) grid in Nascap-2E s arbitrarily nested grid structure. 
Contains the object and all subgrids. 

Primitive (object): An object defined by its mesh. (See also Section 9.) 

RdotR: A measure of the current solution’s failure to satisfy the linearized Poisson’s equation. 
See Sections 14.1 and 14.4. 

RGB color definition: An integer that specifies a color as a mixture of red, green, and blue. The 
RGB integer is given by the fonnula R + 256(G + 256B), where R, G, and B are integers 
between 0 and 255 inclusive. 

SCATHA: Spacecraft Charging AT High Altitude. NASA spacecraft that flew a spacecraft 
charging experiment in the 1980s. 

SCG: Scaled conjugate gradient. A simply preconditioned version of the conjugate gradient 
method. 

Secondary electrons: Electrons with energy <50 eV emitted from surfaces under the influence 
of charged particle bombardment. 

SEE Interactive Spacecraft Charging Handbook: Interactive handbook used to assess material 
models, environment models, and their interactions. Uses same material and environment models 
as Nascap-2k. Available from see.msfc.nasa.gov. 

SEE Program: NASA Space Environments and Effects Program at Marshall Space Flight 
Center. 

Single Maxwellian distribution function: Distribution function appropriate to a classical gas in 
thermal equilibrium. Because the distribution function is simple (characterized by only a density 
and temperature) it is often used as an approximation to plasma distributions clearly far from 
thermal equilibrium. 

Sheath: In a dense, motionless plasma, the region of space about a charged object from which 
the repelled species is excluded. 

Sheath edge (Sheath Surface): Fictitious surface in space marking the boundary of the sheath. 
In dense, motionless plasma, the plasma thermal current times this surface area is the current 
collected. 


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SOAP: Simple Object Access Protocol: An XML-based infonnation exchange protocol. 

Space-charge-limited current collection: Collection of current by a biased probe from a 
surrounding plasma when the plasma density is such that the space charge of the attracted 
particles shields the attracting potential and thus limits the range of the potential. 

SPEAR: The Space Power Experiment Aboard Rockets series of experiments was intended to 
develop and demonstrate technology for very high voltages in space. SPEAR-I and SPEAR-III 
were experiments of the type illustrated in the “Bipolar” example. 

Special elements: Volume elements that are not empty or completely filled by the object or 
contained within a subgrid. 

Substorm: Geomagnetic event during which the density of the low energy drops and a high- 
energy (tens of kilovolts) plasma appears. Events usually last for hours and occur every few 
days. More frequent and more severe events are more likely during solar maximum. 

Sun intensity: Incident power per unit area (W/nf) of incident sunlight. The value above the 
atmosphere at 1 AU distance from the sun is 1370 W/m~. In Nascap-2k sun intensity is specified 
relative to this value. 

Surface element: An elemental surface defined by three (a triangle) or four (a quadrilateral) 
nodes. The nodes are ordered counterclockwise as viewed from an exterior point. 

Surface normal: Vector nonnal to a surface element and pointing outward. The nodes are 
ordered counterclockwise when viewed from the direction in which the nonnal points. 

Tracked current: Current to a surface element computed by tracking macroparticles. 

Wake: The ion depleted region of plasma behind a spacecraft moving at a speed higher than the 
ion thennal speed. 

Vector potential: Also known as the magnetic vector potential and generally represented by 
“A”. The magnetic field is the curl of A. 

VUFF: File used by the NXI-DEAS TMG thermal analysis program. TMG can create an ASCII 
version that includes the object description. 

WIND: NASA’s “WIND” spacecraft was launched 1 November 1994 by a Delta rocket from 
Cape Canaveral. It was designed to observe the solar wind approaching Earth, from a position 
near the Lagrangian point LI. It is part of the International Solar-Terrestrial Physics (ISTP) 
Initiative. 

XML: extensible Markup Language, a universal, simple, hierarchal text format for data. 
XMLShell: XML text editor available from http://www.softgauge.com/xmlshell/index.htm. 


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DISTRIBUTION LIST 


DTIC/OCP 

8725 John J. Kingman Rd, Suite 0944 
Ft Belvoir, VA 22060-6218 Icy 

AFRL/RVIL 

Kirtland AFB, NM 87117-5776 2 cys 

Official Record Copy 

AFRL/RVBXR/Adrian Wheelock Icy 


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