NASA-CR-204658
JOURNAL OF GEOPHYSlLAi. RESEARCH, VOL. 102, NO. A2, PAGES 2279-2289, FEBRUARY 1, 1997
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.
Introduction
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al., unpublished manuscript, 1992], where total density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
radiation.
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*
2279
2280
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
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.
Methods
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
P-(F10.7+F10.7A)/2.
(1)
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-
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
2281
300
250
200
Q- 150
100
Rn,(r, P) = exp(ao+a|r)exp(a2+a3P+a4P2),
(3)
200 400 600 800
Days since October 7, 1981
1000
1200
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)...
(2)
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.
(4)
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),
(5)
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^))
(6)
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)
(9)
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 .
Results
In the following, we first examine the results of detrending
the He* to H+ density ratio for r and P, and then examine the
2282
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
Table 1. Coefficients of the Polynomial Equations
n-O
n=l
n=2
n=3
«cal Time
0.864
1.887
-1.906
L Shell
-0.298
1.069
-0.315
0.035
Latitude
0.946
0.043
0.336
-0.169
n=4
0.049
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
10.000
: 1 1 . . . i
' ' ' ' 1
1.000
•
d:
0.100
h
-
0.010
"
0.001
-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
reduced.
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
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
2283
Table 2. Coefficients and Correlation Coefficients for the Multiple Linear
Regression Fit bo = -1.541
r
P
P2
L
Kp
bi
-0.176
8.557x10-'
-1.458x10-5
Cl
-0.648
0.744
0.731
-0.358
0.038
r ,
0.827
0.852
t
0.036
0.031
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
100.00
10.00
1.00
0.10
0.01
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
10.00
1.00
0.10
0.01
50
—\ 1 1 r-
_i ' ' i_
100
150
P
200
250
Figure 4. The He"^ to H* ratio plotted as a function of P after
adjusting for both r and P.
2284
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
100.00
10.00
1.00
0.10
0.01
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 ■]
111(11111.
■'■''■'■'■''
100 200 300 400 500
Sum Kp previous 24 hours
600
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
measurement.
100.00
10.00
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
0.10
0.01
.-J..1 I I 1 I
100
200
Day of Year
300
400
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.
Discussion
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
100.00
. 1 1 1 ■ 1 1 ■ 1 1 1 1 1
. , . , . 1 1 1 . 1 . 1 1 1 1 .
10.00
-
-
1.00
g^^ -
■"■^"/7
^^P'- :
0.10
r
0.01
, 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
latitude.
100.00
10.00
1.00
0.10 r
0.01
~| — r — I — I — r — I — I — I — I — i-
' ' ' '
5 10 15 20
Magnetic Locol Time (hrs)
25
Figure 8. The detrended He"^ to H* ratio as a function of
magnetic Local Time.
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
2285
1.0
l:, ' ' '
o) 0.8
00
- X
\^
^
ID
n
~::: 0.6
-
U_,_^ (q) P > 150
-
O
1_
c
|-i
^_^
% 0.4
-
1_^
*
cr
L_
01
I— 1
i 0.2
■J
u^.^
0.0
T
— L--~,-,,__
1.00
10
20 30 40 50
20 30
R»100
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.
E
0.10 -
0.01
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..
2286
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
Time = 61 .0
Time = 61.0
40
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
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
2287
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
2288
CRAVEN ET AL.: HE+ IN THE INNER MAGNETOSPHERE
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
images.
Conclusions
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:
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R.H. Comfort, Center for Space Plasma and Aeronomic Research,
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(Received November 6,
accepted July 9, 1996.)
1995; revised July 8, 1996;
