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Full text of "The electrostatics of a dusty plasma"

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Mendis, University of California, San Diego, T. G. Northrop, 
Goddard Space Flight Center. We have derived the potential 
distribution in a plasma containing dust grains where the Debye 
length can be larger or smaller than the average intergrain 
spacing. We treat three models for the grain-plasma system, with 
the assumption that the system of dust and plasma is 
charge-neutral: a permeable graih model, an impermeable grain 
model, and a capacitor model that does not require the nearest 
neighbor approximation of the other two models. We use a 
gauge- invariant form of Poisson's equation which is linearized 
about the average potential in the system. The charging currents 
to a grain are f\mctions of the difference between the grain 
potential and this average potential. We obtain expressions for 
the equilibrium potential of the grain and for the gauge- 
invariant capacitance between the grain and the plasma. The 
charge on a grain is determined by the product of this 
capacitance and the grain-plasma potential difference. 

The three models give similar but not identical results. 

i 2 

The results depend primarily on the parameter Z = 4irX NC, where X 

is the Debye length, N is the grain concentration, and C is the 

grain to plasma capacitance. When Z >> 1, the number of charges 

on a grain that is only charged by plasma currents is given by 

C-Q/e) = [(u-l)/(y+l)] [ (ii .+n ) /N] where p is the square-root of 

the Ion to electron mass ratio, and n and n are the average ion 

and electron densities. The charge on a grain in such regions is 

severely decreased from its free space value. The charge 

reduction occurs because the plasma electrons are depleted so 

that the grain does not need to be as negatively charged to 

equalize the ion and electron fluxes to its surface, despite the 

increased grain to plasma capacitance.