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Relative concentration of He+ in the inner magnetosphere 
as observed by the DE 1 retarding ion mass spectrometer 

p. D. Craven and D. L. Gallagher 

Space Sciences Laboratory, NASA Marshall Space Flight Center. Huntsville, Alabama 

R. H. Comfort 

Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville 

Abstract. With observations from the retarding ion mass spectrometer on the Dynamics 
Explorer 1 from 1981 through 1984, we examine the He"*" to H+ density ratios as a function of 
altitude, latitude, season, local time, geomagnetic and solar activity. We find that the ratios are 
primarily a function of geocentric distance and the solar EUV input. The ratio of the densities, 
when plotted as a function of geocentric distance, decrease by an order of magnitude from 1 to 
4.5 Rg. After the He"*" to H"*" density ratios are adjusted for the dependence on radial distance, 
they decrease nonlinearly by a factor of 5 as the solar EUV proxy varies from about 250 to 
about 70. When the mean variations with both these parameters are removed, the ratios appear 
to have no dependence on geomagnetic activity, and weak dependence on local time or season, 
geomagnetic latitude, and L shell. 


Solar EUV radiation at 304 A which is resonantly scattered 
from He'*' has been proposed as a possible candidate for imag- 
ing of the magnetosphere [Johnson el al., 1971; Meier and 
Welter, 1972; Weller and Meier, 1974; Waite et at., 1984]. 
The spatial distribution of the He* density in the magneto- 
sphere determines the amount of scattered 304 A energy that 
reaches the detector from an element of solid angle along a 
given line of sight. Since the distribution of He"^ ions is con- 
sidered to be optically thin, the energy reaching a detector is 
the sum of all the sources in the line of sight. Therefore some 
a priori knowledge of the average spatial and temporal distri- 
bution of the He''' would be helpful in deconvolving images 
of the inner magnetosphere. Models that have been used to 
simulate a magnetosphere image from He''' have approxi- 
mated the spatial distribution by assuming a constant He''' 
density, above some base altitude on a given L shell [Meier 
and Welter, 1972; Weller and Meier, 1974], or alternatively, 
a constant He+ to total denisity ratio; E. C. Roelof et 
al., unpublished manuscript, 1992], where total density 
in the magetosphere is assured to be represented by H+. 
Williams et al. [1992] noted that one of the important conse- 
quences of He''' following the H''' density is that images from 
He''' resonance scattering then also represent the total plasma 
and not just He'''. The behavior of the He''' to H''' ratio will be 
important in models of the inner magnetosphere, in under- 
standing the physics of the light ions, and in interpreting 
images of the magnetosphere obtained using scattered 304 A 

Observations from the retarding ion mass spectrometer 
(RIMS) on Dynamics Explorer 1 (DE 1) early in the lifetime 

Copyright 1997 by the American Geophysical Union. 

Paper number 96JA02176. 

1 48-0227/97/96JA-02 1 76$09.00 

of the satellite [Horwitz et at., 1984; Comfort et al, 1988], 
show the He* to H''^ density ratio to be of order 0.2 for the 
conditions experienced. Newberry et al. [1989] noted that the 
DE 1/RIMS He"'' to H''^ density ratios were higher than had 
previously been reported [Chappelt et at., 1972; Young et 
al., 1977; Geiss et at., 1978; Horwitz et al, 1981, 1983; 
Lennartsson et al., 1981; Waite et at., 1984] but that the 
solar activity for the DE 1 data was consistently higher than 
that for the data from these other studies. Farrugia et al. 
[1989], using data from GEOS, reported a constant He''' to H''' 
ratio of 0.1, also lower than early DE 1/RIMS results. 
However, Newberry et al. [1989], in a comparison of the 
early DE 1/RIMS data to a physical model, found that the 
ratio at 5200 km on an L=2 field line should vary with solar 
and geomagnetic activity. TTie Newberry et al. model results 
show that He"*" and H'*' have different responses to geomag- 
netic and solar activity with the effect that the solar input 
tends to dominate the behavior of the ratio. Although 
Newberry et at. [1989] found that the model consistently pro- 
duced ratios of order 0.2, it did not reproduce the near con- 
stant ratio observed above 4000 km. 

With several years of data from DE 1/RIMS now available, 
covering both high and low solar activity, it seems an advan- 
tageous time to examine the low-energy He''' to H''' density 
ratio in more detail; and, in particular, to examine how this 
ratio varies in the plasmasphere. We do this here using DE 
1/RIMS data from the first three and a quarter years of its life- 
time, between October 26, 1981, and December 31, 1984, 
during which the satellite orbit completes a full cycle of pre- 
cession back to near its original orientation. The data over 
this time cover the declining phase of the solar cycle from 
near maximum to minimum, all seasons, and most local 
times. The same instrument is used for all phases of the solar 
cycle so that it is possible to follow changes in the ratio 
with the solar cycle with no instrument cross calibrations. 
The ratio of He'*' to H''' density is used rather than the He* 




density itself, in order to check the constancy of this ratio, 
to avoid having to use separate models for the He'*' and H"^ 
density, and because in using the ratio, absolute calibrations 
for each ion are not needed. Since H"^ is the dominant ion 
above the topside ionosphere, there should be little change 
in our results if we use the H"^ density rather than the electron 
density for the total density. 


The RIMS instrument is described in detail by Chappell el 
al. [1981]. There were three RIMS heads on DE 1 and associ- 
ated with each head was a magnetic mass spectrometer, which 
had two channel electron multiplier detectors that were placed 
to simultaneously measure ion species with masses in the 
ratio of 4 to 1, for example, He"^ and H*, O* and He*. The 
ratios in this study all result from simultaneous 
measurements of He* and H*, He* in the high mass channel 
and H* in the low mass channel, from the radial head which 
looked in a direction perpendicular to the satellite spin axis. 
Densities are derived from count rate data averaged over a 
minute (each minute average is referred to as a sample in the 
following). The satellite orbit limits geocentric distances 
sampled to 4.5 Rg or less, but the distances at which 
densities are actually available are limited by the data 
reduction method. 

Densities for each sample (counts) have been derived using 
a modification of methods described by Comfort et al. [1982, 
1985], which requires that the ion distribution function be 
near Maxwellian. Because of a partial failure of the radial 
head, no energy analysis was available from this head for 
much of the time covered by the database; however, the radial 
head did provide the integral count rate, with no retarding. 
We use the energy analysis available on the two heads point- 
ing parallel and antiparallel to the satellite spin axis to 
determine the ion species temperatures, according to the 
method of Comfort et al. [1982, 1985], assuming a zero flow 
velocity to account for the orientation of the detectors trans- 
verse to the ram direction. An average of the temperatures 
from the two heads Is used for further processing. With this 
temperature and the spacecraft velocity, we are able to deter- 
mine the Mach number of the flow into the radial detector. 
The effective spacecraft potential is obtained, using the mod- 
els of Comfort and Chandler [1990], from the spin modula- 
tion of the radial detector (unretarded) count rate and this 
Mach number. The peak (unretarded) count rate in the ram 
direction from the radial head is then used with the tempera- 
ture and spacecraft potential, as described above, and instru- 
ment calibration factors to determine the density according 
to the method of Comfort et al. [1982, 1985]. 

Temperatures resulting from this method have been com- 
pared with those obtained from the radial head when it was 
fully operational to assure that it provides accurate tempera- 
tures. The density calculation in both approaches is based on 
the peak unretarded count rate of the radial head. It is assumed 
in this procedure that the ion Maxwellian distribution is 
isotropic in the plasma frame of reference, and that any flows 
are small compared with the spacecraft velocity. Also, we 
analyze only the coldest component observed, as discussed 
by Comfort et al. [1985], These conditions restrict the 
observations used to those in and near the plasmasphere 
[Comfort et al, 1982, 1985]. 

Because He* is taken from the high mass channel and H* 
from the low mass channel, corrections have to be applied to 
the count rate data to compensate for different sensitivities in 
the detectors. Since He* was paired in the 1 to 4 relation with 
both H* and O*, anytime these two ions were measured in the 
same minute. He* is obtained in both the high and low mass 
channel in the same minute. Fortunately, this was the usual 
mode of operation for RIMS. Consequently, the correction 
factor, derived from the ratio of the He* count rate in the high 
mass channel to the He* count rate in the low mass channel, 
both count rates separately integrated over the same minute, 
is a quantitative measure of the relative sensitivities of the 
high and low mass channel detectors. This ratio varied some- 
what from day to day and from measurement to measurement. 
In order to account for any day-to-day and long-term changes 
in the relative sensitivities, the correction factor for each 
data sample is used, excluding from the data set any sample 
for which there is no corresponding high-low channel correc- 
tion factor. All available data from 1981 through 1984 are 
used to find measured correction factors for each sample. 

Data taken at high latitudes (A>60°), samples with a He* to 
H* density ratio greater than 5, and samples for which the 
measured temperatures of the two ions differ by more than a 
factor of 2 have been excluded from the data set. The first 
condition is no practical limitation since there are few 
derived densities from that region because of the Maxwellian 
restriction mentioned above. The last two are considered to 
be nonphysical and reject only a few samples, but ones that 
are outliers and which, when excluded, reduce the scatter in 
the results presented here. 

We have chosen to use the proxy for the solar EUV devised 
by Richards et al. [1994] as a measure of solar activity. This 
proxy P is defined as 



where F10.7 is the daily measure of the 10.7 cm solar flux 
and F 1 0.7 A is the 81 -day average of the F10.7, with the 81- 
day average centered on the day of interest. P is a better 
proxy for the solar EUV, and therefore ion production, than 
the daily F10.7, particularly at high solar activity [Richards 
et al., 1994]; it also results in a better separation of the data 
in terms of high and low solar activity using a single value of 
P (P=150) for the separation criteria. Figure 1 shows solar 
activity in terms of the proxy P for the period of this study. 
Solar activity is seen to be generally high and highly vari- 
able in 1981, decaying in both the magnitude and variability 
into 1984. At the end of 1984, the P values are about 70 with 
small relative variations (Figure I). Because of the changing 
solar cycle, the data for high solar activity (P>150) is con- 
centrated in the early period of DE 1, 1981 into 1983, and 
low solar activity (P<150) is concentrated in 1983 and 1984. 
We use two proxies for geomagnetic activity; one, EKp, is 
the sum of Kp in the previous 24 hours from the time of the 
measurement. The other, Kp(m) is local time dependent. If 
the local time of the measurement is between midnight and 
dusk (0000-1800 hours), Kp(m) is the Kp value at the time 
the plasma was previously at midnight local time, assuming 
corotation. If the measurement local time is between dusk and 
midnight (1800-2400 hours), Kp(m) is the Kp value at the 
time of the measurement. We use these geomagnetic indices 
because in one, EKp, we get an integrated history and a mea- 






Q- 150 


Rn,(r, P) = exp(ao+a|r)exp(a2+a3P+a4P2), 


200 400 600 800 

Days since October 7, 1981 



Figure 1. The Richards proxy [Richards et al., 1994] for 
solar EUV for 1981 to 1984, the time of the DE 1 data used in 
this report. 

sure of the overall level of the geomagnetic activity. The 
other index, Kp(m), is used in recognition of the influence of 
conditions near local midnight in determining plasmaspheric 
conditions at other local times. 

We also group the ratios by season. Southern hemisphere 
summer data are grouped with the northern hemisphere sum- 
mer data and southern winter data are grouped with northern 
winter. We do this by shifting the day of year by 180 days if 
the measurement is in the southern hemisphere and within 
±45 days of the solstice. Both fall and spring equinox data 
are grouped together regardless of hemisphere. There is a 
relationship between local time and season which is 
discussed below. 

A preliminary examination of the data indicated that the 
ratio varied most with radial distance r and secondly with 
solar activity, P. The dependencies on season, local time, 
geomagnetic activity, and latitude appeared to be much 
weaker than those with r or with P. However, the spread of 
the ratios is large, due in part to the variations with r and P. 
In order to see the weaker dependencies and to model the 
behavior of the ratio, we detrend the data with respect to the r 
and P variations. We have used two methods to model the 
variations of the ratio with r and P. In the first method, the 
ratio is assumed to be separable into products of functions of 
each independent variable, that is, 

R„''(r, P, Kp,...) = f(r)g(P)h(Kp)... 


where Rm" is the modeled ratio that incorporates all the 
known dependencies. This treatment assumes that the inde- 
pendent variables are not correlated, or at least not strongly 
correlated. Each function was found successively, that is, fit 
the data to f(r), and remove this trend, then fit this detrended 
data to g(P) and remove its dependency, and so on. We found 
through this process, that the r and P dependence of the data 
could be modeled as the product of exponential functions of r 
and P, specifically, 

where now R^ is the modeled ratio that includes only the r 
and P dependencies. In the second method, rather than find- 
ing each function separately, we used multiple linear regres- 
sion to fit the data with functional forms similar to those 
used in the separable function method. In performing the 
multiple regression fit, we also used r, P, and P^ as the 
independent variables. P and P^ are, of course, not 
independent, but it is necessary to include both in order to 
model the variation of the density ratio with P. In this second 
method, the function for the model ratio was actually fit to 
the log (base 10) of the measured ratio, that is. 

log R„(r,P) =bo+b,r-Hb2P+b3P2. 


The original data set is detrended for r and P by dividing each 
measured ratio, R(r, P, Kp,...) by Rm(r, P) 

Rd(Kp,...)=R(r, P, Kp,...) / Rm(r, P), 


where Rj is the detrended ratio. The two methods yield 
approximately the same results in terms of Rj, the ratio 
detrended for r and P, but since the coefficients in the 
multiple linear regression method are determined 
simultaneously, this is the method of choice for R^,. The 
detrended ratios discussed below have been found using the 
model ratios based on the multiple linear regression fit. The 
result, Rj, has had the dependency on r and P removed, at 
least on a statistical basis, leaving the dependencies on the 
other factors, Kp, local time, season, latitude and L, to be 
determined. Because these dependencies are non linear, we 
use polynomials to fit the data to latitude, local time, and L 
shell. The latitude fit is given by a function of the form 

Rx = Xc„sinh"((>.+5)jr / (IX^)) 


where Xq = 60°. Similarly, the functional form for the fit to 
local time is given by 

RLT = SdnSin2"((LT-2.5)7t/24.). (7) 

The functional form for the fit to the remaining variable, L, 
is given by 

RL=IenL". (8) 

The final fitted ratio is given by the product of Rm and (6) 
through (8); the fully detrended ratio Rf is given by 

Rf = R(r, P, X, LT, L) / (R„{r,P)R;,RLT Rl) 


and should show no systematic variation with these vari- 
ables. We do not use the fits given by (6) through (8) in the 
discussions below because the variation of the detrended ratio 
Rj with these variables is small. However, for completeness, 
the coefficients for our best fits for (6) through (8) are given 
in Table 1 . 


In the following, we first examine the results of detrending 
the He* to H+ density ratio for r and P, and then examine the 


Table 1. Coefficients of the Polynomial Equations 





«cal Time 




L Shell 












characteristics of the detrended ratio as functions of the 
remaining variables. A statistical approach, as opposed to 
case studies, is used to determine the basic behavior of the 
ratio. Temporal characteristics are usually lost in this 
approach, as are spatial structures and boundaries. However, 
these features do add to the spread in the data. 

Two very basic characteristics of the ratio of He'*' to H* 
densities in the plasmasphere are apparent in this study: the 
ratio decreases with r in the plasmasphere, and it depends 
strongly on solar activity. The decrease with r can be seen in 
Figure 2, which shows the original He''' to H'*' density ratios 
as a function of r. All data are included in this plot, a total of 
20,338 samples. The trend for the measured ratio R to 
decrease with geocentric distance is clear, as is the large 
spread in the ratio for any given geocentric distance. R 
decreases by approximately an order of magnitude, from 
about 0.3 to 0.03, between I Rg and 4.5 R^. This decrease of 
the ratio with geocentric distance is consistent, at least quali- 
tatively, with other studies. Model results of Angerami and 
Thomas [1964] and Newberry et al. [1989] show that the 
ratio decreases with altitude along a field line. In the 
Newberry et al. [1989] study, the ratio decreases from about 1 
to about 0.1 between 1000 km altitude and the top of the L=2 
field line. The Angerami and Thomas [1964] results are for a 
constant ion temperature of 1500 °K and their He''' to H^ den- 
sity ratio decreases from about 10 at 1000 km to about 0.02 


: 1 1 . . . i 

' ' ' ' 1 










-L 1 -..,... 1 1 

' ' ' ' 1 ' ' 


12 3 4 5 

Geocentric Distance(Re) 

Figure 2. The original He'*' to H'*' ratio plotted as a function 
of geocentric distance, r (in Rg). 

at 8000 km altitude. The ratio as calculated by Angerami and 
Thomas [1964] is temperature dependent and would decrease 
more slowly with a higher ion temperature. Ratios from 
GEOS 1 measured densities of H"'" and He''' near the equatorial 
plane also indicate that the ratio falls with increasing radial 
distance [Farrugia el al., 1989]. Our choice of using the radial 
distance rather than L to examine the ratio is based on our 
observation that the data is better organized by r than by L. 
This decision is supported by the smaller linear correlation 
coefficient associated with L (see Table 2). 

The results of the multiple linear regression fit to the data 
shown in Figure 2 are given in the first 3 columns of Table 2 
in the appendix. The coefficients, b;, for (4), the linear corre- 
lation coefficients, C|, for each variable as well as the multi- 
ple correlation coefficient, €„,„!, and x^ for the overall fit are 
included in the table. The last two columns in Table 2 show 
the values of selected coefficients for L and Kp when they are 
included in the regression. They are shown in Table 2 only 
for reference since they were not used to detrend the data. 

Figure 3 shows the data plotted as a function of r after each 
point has been detrended according to (5), using (4) and the b] 
coefficients given in Table 2. The detrended ratios should 
cluster around one (the solid line across the graph at one is 
included for reference) if the trends have been removed. 
Figure 4 shows the same detrended ratios plotted as a function 
of P. No dependence on either r or P remains after detrending, 
and the scatter in the measured density ratios has been 

A third character of the ratio, which is shown in Figure 5 
and also by the correlation coefficient given in Table 2, is 
that there appears to be no correlation between the ratio and 
geomagnetic activity. The results are the same regardless of 
which of the two Kp based indices described above are used. 
Young et al. [ 1 982] found little correlation between Kp and 
the He* to H''' density ratio for higher energy particles(0.9- 
15.9 keV/e) near geosynchronous orbit (L=6.6). In the 
Young et al. study. He''' density is unaffected by Kp and the H''' 
density increases by 60 per cent over the full range of Kp so 
that the ratio decreases by less than 40 percent. Kp (or any 
other indices related to Kp) may not be a proper proxy to 
show a relation between the ratio and geomagnetic activity, 
but this seems unlikely. If the independent variables are cor- 
related, particularly Kp and P, then removal of the 
dependence of the data on P, would also decrease the variation 
with Kp. However, we find no correlation between P and Kp 
over the period of the data set. 

The variation of Rj with each of the remaining variables 
(season, local time, latitude, and L) is small relative to the 
variation with r or P. The latitudinal dependence of the ratio 
is presented in Figure 6. Rj appears to maximize near 60° lat- 
itude, the maximum occurring near a region traditionally 
associated with the outer edge of the plasmasphere. Although 



Table 2. Coefficients and Correlation Coefficients for the Multiple Linear 
Regression Fit bo = -1.541 
















r , 






not much variation between ± 40° is seen in Figure 6, the 
ratio does appear to minimize at the equator for a given pass, 
at least for the early data; this tendency is not so clear for 
later measurements. 

The orbital precession of DE 1 is such that season and 
local time are correlated. For this reason, although we exam- 
ine the behavior of the ratio with both season and local time, 
we cannot separate the influence of the two parameters. For 
reference, the intial orbit plane position for the data set 
(October 26, 1981) corresponds to the 1000 to 2200 mag- 
netic local time longitude. We have chosen to use local time 
as the variable, but could have used season just as well; the 
curve fitted to one also follows the data when plotted against 
the other. The ratio plotted as a function of season (day of 
year) is shown in Figure 7. The ratio peaks near the 
equinoxes and minimizes at the solstices, the difference 
amounting to a factor of about 2. There is a weak systematic 
variation of the ratio with magnetic local time (see Figure 8). 
An apparent dip in the ratios near 1500 hours appears to be 
the result of a concentration of measurements taken close to 
the same date. The detrended ratios Rj tend to be less than 
one from about 2200 to about 0500 hour, around one from 

0500 to about 0900, and greater than one from 0900 to about 
2200 hours, ignoring the dip at about 1500 hours, with the 
variation being a factor of about 3. The Newberry et al. 
[1989] model results indicate a diurnal variation of a factor of 
3-4 in the ratio at 5200 km (the equator at the top of the flux 
tube) in which the ratio reaches a minimum around 0300 MLT 
corresponding to a minimum in the He"^ density. The 
measured data in the Newberry et al. study appear to be 
consistent with their model results, but none of their 
observations occur at the local time minimum. Brinton et al. 
[1969] report a diurnal variation in the He'^ to H+ ratio at 
about 2700 km and at low latitudes that is similar to the 
Newberry et al. results, but they show a nearly constant ratio 
with local time at about 1200 km at midlatitudes. Bauer 
[1966] and Waite et al. [1984] note that the ratio is 
temperature dependent, so that the diurnal variation may 
decrease on the higher L shells at high altitudes, where the 
temperatures tend to show little diurnal variation; Bauer 
[1966] suggests that there should be no diurnal variation in 
the ratio at solar maximum because of the temperature 
dependence and the higher temperatures. The data shown here 
are qualitatively consistent with the Newberry et al. [1989] 
results in that the magnitude of the variation is similar and in 






12 3 4 5 

Geocentric Distonce(Re) 

Figure 3. The He"^ to H''^ ratio plotted as a function of r after 
detrending for both r and P. The line at Rd=l is drawn for 
reference only. 

100.00 F 






—\ 1 1 r- 

_i ' ' i_ 





Figure 4. The He"^ to H* ratio plotted as a function of P after 
adjusting for both r and P. 








1 1 I T I I I T I T 1 I r i I I I I I I T [ I I 1 I ! I ' I T [ I I I 1 I I I I I ■] 



100 200 300 400 500 

Sum Kp previous 24 hours 


Figure 5. The detrended He"*" to H'*' ratio as a function of thie 
sum of Kp in the 24 hours previous to the time of the 



I I I I I 

I I I [ T- T I 1 1 I I I I'T 1 I T I 1 I I T T T 1 I I I I 1 



.-J..1 I I 1 I 


Day of Year 



Figure 7. The detrended He'*' to H'*' ratio as a function of the 
day of the year. 

that the ratio is generally smaller in the midnight and dawn 
hours than during the day. 


Because the ratios presented here extend over a large num- 
ber of observations and types of conditions, some spread in 
the ratios should be expected. The spread in Figure 2 for a 
given r is greater than a factor of 5, and this variation is on 
top of a factor of 10 variation between 1 and 4.5 Rg. The 

total spread is reduced to a factor of 4 to 5 after detrending on 
r and P, indicating the strong influence of r and P on the 
ratio. The standard deviation of the data detrended on r and P 
is 0.57 measured relative to 1.0. After detrending for r, P, 
latitude, local time(season), and L shell, the standard 
deviation is reduced to 0.39. Effects contributing to the 
remaining spread are short term fluctuations in geophysical 
conditions, experimental uncertainties, and dependencies on 
geophysical parameters other than those considered here. 
Since the data in this study are analyzed by an automated 


. 1 1 1 ■ 1 1 ■ 1 1 1 1 1 

. , . , . 1 1 1 . 1 . 1 1 1 1 . 





g^^ - 


^^P'- : 




, 1 1 , 1 1 1 1 1 1 . . 

. 1 . . . i , . . 1 

-60 -40 -20 20 40 60 

Solar Magnetic Latitude(deg) 

Figure 6. The detrended He* to H* ratio as a function of 




0.10 r 


~| — r — I — I — r — I — I — I — I — i- 

' ' ' ' 

5 10 15 20 

Magnetic Locol Time (hrs) 


Figure 8. The detrended He"^ to H* ratio as a function of 
magnetic Local Time. 




l:, ' ' ' 

o) 0.8 

- X 





~::: 0.6 


U_,_^ (q) P > 150 







% 0.4 







I— 1 

i 0.2 





— L--~,-,,__ 



20 30 40 50 

20 30 


Figure 9. Histograms of the ratio after adjusting for the r 
dependence and renormalizing to the value at P=150. (a) high 
solar activity (P>150) (b) low solar activity (P<150). 

system, the "screens" built into the system may allow small 
deviations from the assumptions on which the method is 
based; these contribute to the scatter in the data after 
systematic trends with physical variables have been 
removed, as described below, but should not be systematic 
with any geophysical parameters. 


0.10 - 


2.5 3.0 3.5 
Geocentric Distance (R ) 

Figure 10. Comparison of results from the physical model 
(FLIP) with the measured He*/H+ ratios. All data are for L=4. 
The solid line shows the modeled ratio based on the DE 
1/RIMS measurements. 

A candidate geophysical parameter that may contribute to 
the remaining spread is the ion temperature. We have looked 
at the ratio as a function of scale height at the point of the 
measurement and find the scatter is not reduced by correcting 
for the point scale height. We assumed that the temperature 
of the two ions was the same [Comfort et ai, 1988; Farrugia 
et ai, 1989; Comfort, 1996] and we also ignored the polar- 
ization electric field. If the temperature of the ions varies 
along the field line or if the polarization electric field is 
included in the treatment, then the ratio at any altitude is the 
result of the integrated effects of temperature along the field 
line so that single point temperature considerations are not 
adequate. In addition, if the polarization electric field is 

Time = 61 .0 

Plate 1. Simulated 304 A plasmaspheric images (time=61.0). (a) Constant He+ to H"^ density ratio (0.15), 
(b) the ratio is a function of r and P, (c) Percentage difference in counts between images in Plate la and lb.. 


Time = 61 .0 

Time = 61.0 

Won J<4>r B 12:42:2J 199fi 

Plate 1. (continued) 

included, the ratio of the ion to the electron temperatures is 
needed [Angerami and Thomas, 1964]. That the variation 
shown in Figure 8 is not a strong function of local time may 
be related to the effect of the ion temperature on the ratio. 
Further study along these lines would have to include, at a 
minimum, an altitude profile of the ion and electron tempera- 
tures and their diurnal variation. 

Horwitz et al. [1986] noted that the ratio tends to remain 
constant even across the plasmapause. We also find that ratio 

changes across the plasmapause, in those cases for which we 
can track the change (mainly confined to the early data), are 
much smaller than the spread in the ratios for a given radial 
distance (see Figure 2), so that transitions across the plasma- 
sphere boundary at midlatitudes to low latitudes do not appear 
to be adding significantly to this spread. The ratio does 
appear to systematically increase above ±40° latitude. All the 
data points near ±60° latitude, the peak of the rise, are at geo- 
centric distances less than 2 Rg. Our detrending for r does not 



adjust the ratios in this latitude and altitude range properly, 
resulting in detrended ratios that are too high. The number of 
data points at high latitude below 2 Rg is small so that the 
total contribution to the spread is small and limited to the 
lower radial distances. The relatively small systematic varia- 
tions seen in this data with local time, geomagnetic activity, 
or latitude indicate that changes in the ratio caused by the 
processes related to these variables are small in comparison 
to the variations from processes related to r and P. 

The importance of determining the variation of the He'^ to 
H'^ density ratio to the interpretation of images of the plas- 
masphere should not be overlooked. As noted by Williams el 
al. [1992], in order for images at 304 A to represent the 
plasma density and not just He* in the plasmasphere, a rela- 
tionship between He* density and the total density must be 
known. The data presented here suggest that a relationship 
does exist and can be represented by equations 4 and 5 above. 
In order to correctly deconvolve images of He* scattered 304 
A light and represent the results as total density, this relation 
must be taken into account. Although H* is a close approxi- 
mation to the total density at altitudes above the transition 
region (where H* and O* density are equal), below this alti- 
tude, near the topside ionosphere and at lower altitudes, O* 
should properly be included in the approximation to the total 
plasma density. Very few of the measured ratios presented 
here are at altitudes at which O* is dominant, so we have not 
included it in this study 

Histograms of the He* to H* density ratios from the DE 
1/RIMS data for two levels of solar activity, P < 150 and P > 
150, show a dramatic difference in the distributions of the 
samples which emphasizes the importance of the solar input. 
For high solar activity, the peak value, after adjusting for the 
r dependence and normalizing to 0.17 at P-150 to bring the 
magnitude of the ratio back into its original range, is at 0.08 
and there is a broad distribution of values with a mean of 0. 14 
(Figure 9a). For low solar activity, the peak of the histogram 
is at 0.03 with a narrow distribution (Figure 9b). The mean 
adjusted ratio for low activity is 0.07. One of the differences 
between these two data sets, in addition to the levels of solar 
activity, is that the variability of the solar proxy P is much 
greater during the high solar activity than it is during the low 
activity. Thus it appears that at any given phase of the solar 
cycle, the range of the He* to H* density ratios that may be 
measured and the mean value of the ratio may be connected to 
the solar variability and to the mean solar activity level, 
respectively, experienced over the time the data is collected. 
However, more data, preferably following the ratio through 
another solar cycle, is needed before a definitive statement 
can be made. The phase of the solar cycle affects the ratio 
both through production and loss of He* and H*, through 
scale height effects related to ion temperature, and through 
diffusion effects. The latter two are shown in the study by 
Waite el al. [1984], in which they demonstrate the impor- 
tance of the ion temperature and density ratio at the base of 
the flux tube to the composition in the plasmasphere. 

Previous studies, [Young et al., 1982; Farrugia et al., 
1989; Lennartsson et al, 1981, 1982; Horwitz el al., 1986], 
when taken together, suggest that the He* to H* density ratio 
varies with solar activity. The data presented here covering 
half a solar cycle with a single instrument clearly show the 
relation of the ratio to the solar cycle and also show that the 
average tends to about 0.15 for high solar activity and 0.07 
for low solar activity, in approximate agreement with these 

previous studies. The ratios reported by Comfort et al. 
[1988], although plotted as a function of L, are also consis- 
tent with the results here, as they should be since that data set 
is a subset of this one. There is the question of how the ratio 
can be of order 0.2 , as suggested by early RIMS results 
[Honvitz et al., 1986], but vary an order of magnitude with r 
as shown here. The answer to this lies in the fact that the 
ratio from the early RIMS data is only approximately con- 
stant [Horwitz et al., 1986; Comfort et al., 1988] and is 
taken during a time where the average is about 0.2 due to high 
solar activity. Newberry et al. [1989] and Comfort et al. 
[1988] show that the minimum and maximum mean value of 
the ratio in the early RIMS data differ by a factor of 2 to 3, 
depending on whether the morning or evening data are being 
examined. Early analysis of the DE 1/RIMS data used 
individual orbital passes of the satellite [Horwitz et al., 
1984] or combined several months of data for statistical 
studies [Comfort et al., 1988]. The variation of the density 
ratio with geocentric distance was not identified or removed 
in the previous studies, however the range of the geocentric 
distances was limited, i.e. generally less than 3 Re. Farrugia 
et al. [1989] using GEOS/ICE data, did show that the 
equatorial He* to H* ratio decreased by a factor of about 2 
from 2 Re to 6 Re, a rate somewhat slower than that given 
here, but still within the spread of the data. 

Physical models such as the field line interhemispheric 
plasma (IT^IP) model of Richards and Torr [1985], show that 
in the plasmasphere and for given values of geophysical 
parameters such as FI0.7 and Kp, the He* to H* density ratio 
is a function of altitude along the field line, decreasing 
toward the equator from the topside ionosphere [Craven et 
al., 1995; Newberry et al. 1989]. The ratio should decrease 
with altitude along L if diffusion is the major process 
governing the distribution of density along the field line 
[Newberry et al., 1989] and if H* is the dominant ion [Waite 
et al., 1984]. The behavior of the ratio in the present study 
(Figure 2) is qualitatively consistent with the results of FLIP 
as shown in Figure 10. Figure 10 shows the results from the 
physical model (unfilled symbols) and our empirical model 
(solid symbols connected by a solid line), both for P-176 
and L-4; FLIP results for P-200 are also shown for 
comparison. A free parameter in the physical model sets 
additional plasmaspheric heating of ions as a result of the 
trapping of photoelectrons on field lines and the subsequent 
loss of their energy to the thermal electrons. From the 
comparison shown in Figure 10, some additional heating is 
required in the physical model to keep the helium to 
hydrogen ion density ratio at the measured levels for radial 
distances larger than 2 R^. Comparison of the two plots for 
F 10.7=200 in Figure 10 shows the effect of the ion tempera- 
ture on the altitude profile of the ratio. It is clear that signifi- 
cant additional heat is needed in the physical model in order 
to slow the decrease of the density with radial distance. A 
possible source of this heat in the outer plasmasphere may be 
related to interactions at the equator with ring current plasma 
[Fok et al., 1996]. The differences between the measured and 
modeled ratios for I. < r/Rg 5 2. are not entirely understood. 
Differences in the model and measured density of He* have 
previously been noted by Craven et al. [1995] and Bailey and 
Sellek [1989]. 

Quantitative agreement between physical models and the 
DE 1/RIMS data can be checked on a case by case basis or by 



averaging the data and comparing with representative model 
runs covering a variety of conditions (solar activity, geo- 
magnetic activity, time of year, etc.). Only a limited number 
of the latter have been done, for example, Newberry el al. 
[1989], but good agreement between measurement and theory 
was obtained. This was also the case in a comparison 
between data from the Atmospheric Explorers and the FLIP 
model [Craven et al., 1995], but it was also shown in that 
study that the treatment of He''' in the physical models may 
need to be revised in order to obtain better agreement with 
measurements. A more complete examination of the different 
contributions to the He''' and H''' densities is needed in order to 
explain observed He''' to H''' density ratios; that will be 
addressed in a future study. 

As a demonstration of the use of our result for the He'*' to 
H'*' density ratio, we compare simulated images of the 
magnetosphere in 304 A scattered radiation using our model 
to simulated images with a constant He"*" to H'*' density ratio 
(He"''/H'''=0.15). In both simulations, we use a total density 
model which is based on the model of Rasmussen and Schunk 
[1990]. We used each model of the density ratio to obtain 
simulated images of the magnetosphere in 304 A scattered 
solar radiation in terms of counts per sample into a instru- 
ment and these are shown in Plate I , Plate 1 a for the constant 
density model and Plate lb for our model. In each of these 
simulated images, the view is from above the pole looking 
down on the Earth, with the Sun to the left, opposite the 
shadow. The important point is the difference between them, 
since the only difference in the simulation is the distribution 
of the He"*". The quantitative differences are shown in Plate 
Ic. In this panel we show the percentage difference (error) of 
the counts between the two images. There is at least a factor 
of 2 difference in the counts on the outer edge of the plasmas- 
phere between the two models with the difference going as 
high as a factor of 1 in some places. There are also signifi- 
cant differences in the inner regions. The differences seen in 
Plate Ic could affect the design and operation of an imaging 
instrument and the interpretation of 304 A plasmaspheric 


We have shown through a statistical study, that the 
observed He''' to H"'' ratios decrease with geocentric distance 
(or altitude) and that the decrease is about an order of magni- 
tude between about 1 R^ and 4.5 Rg. Although it has been 
suggested by physical models that the ratio should decrease 
with altitude along a field line, until now it has not been 
demonstrated with observations how this behavior relates to 
radial distance. We also show that the ratio increases nonlin- 
early with solar activity. The variation of the ratio with the 
solar cycle is significant, being about a factor 5 greater for 
higher activity than for low. Taking into account the dis- 
tance and solar activity dependence, the ratio has no apparent 
dependence on geomagnetic activity and is weakly dependent 
on latitude, L shell, and with one or both of the parameters 
local time and seasons (we cannot separate the influence of 
these two with DE 1/RIMS data alone). It is clear from the 
Newberry et al. [1989] study, the study of Young et al. 
[1982], and this study that any dependence of the density 
ratio on Kp is much weaker than the dependence on P. The 
cause of the remaining spread in the ratio for any given value 
of an independent variable is unknown. Studies to determine 

the causative processes of the remaining spread will need to 
consider geomagnetic activity history, ion temperatures, and 
production of He''' and H'*' in the ionosphere. We show 
through simulated images of the magnetosphere, that the 
signal received in 304 A scattered solar radiation with our 
model is significantly different from that obtained with a 
constant density model. Such differences would affect such 
things as the integration time in the planning and operation 
phase of an imaging mission and also the inferred density 
from an image. Missions that image the magnetosphere in 
304 A solar radiation will need to use a model of the He"'' dis- 
tribution, preferably one based on observation such as we 
provide here, to help interpret the images. 

Acknowledgment. The authors gratefully acknowledge the 
support of T. E. Moore and members and the RIMS team, particularly 
B. Giles who helped make the data available to us. We thank the ref- 
erees for their helpful suggestions and comments. The work of RHC 
was partially supported under NASA grant NCC8-65 with UAH. This 
research was also supported by the Office of Space Sciences at the 
National Aeronautics and Space Administration. 

The Editor thanks C. J. Farrugia and S. A. Fuselier for their 
assistance in evaluating this paper. 


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P.D. Craven and D.L. Gallagher, Space Sciences Laboratory, 
NASA Marshall Space Flight Center, Huntsville, AL 35812. (e-mail: 

R.H. Comfort, Center for Space Plasma and Aeronomic Research, 
University of Alabama in Huntsville, AL 35899. 

(Received November 6, 
accepted July 9, 1996.) 

1995; revised July 8, 1996;