Coulomb collisions between ring current ions and the thermal plasma in the plasmasphere will heat the plasmaspheric electrons and ions. During a storm such heating would lead to significant changes in the temperature and density of the thermal plasma. This was modeled using a time- dependent, one-stream hydrodynamic model for plasmaspheric flows, in which the model flux tube is connected to the ionosphere. The model simultaneously solves the coupled continuity, momentum, and energy equations of a two-ion (H(+) and O(+) quasineutral, currentless plasma. Heating rates due to collisions with ring current ions were calculated along the field line using a kinetic ring current model. First, diurnally reproducible results were found assuming only photoelectron heating of the thermal electrons. Then results were found with heating of the H(+) ions by the ring current during the recovery phase of a magnetic storm

Fok, M.-C.

Guiter, S. M.

Moore, T. E.

English

NASA Technical Reports Server

NASA-TH-113075
t/,'(,
Plasmasphere Modeling with Ring Current Heating
S. M. Guiter I , M.-C. Fok 1, and T. E. Moore
Space Sciences Laboratory, NASA Marshall Space Flight Center, Huntsville, Alabama
Coulomb collisions between ring current ions and the thermal plasma in the plasmasphere will
heat the plasmaspheric electrons and ions. During a storm such heating would lead to significant
changes in the temperature and density of the thermal plasma. This was modeled using a time-
dependent, one-stream hydrodynamic model for plasmaspheric flows, in which the model flux tube
is connected to the ionosphere. The model simultaneously solves the coupled continuity, momentum,
and energy equations of a two-ion (H+ and O +) quasineutral, currentless plasma. Heating rates due to
collisions with ring current ions were calculated along the field line using a kinetic ring current
model. First, diurnally reproducible results were found assuming only photoelectron heating of the
thermal electrons. Then results were found with heating of the H+ ions by the ring current during the
recovery phase of a magnetic storm.
I. INTRODUC_ON
Significant heating of the thermal plasma in the plasma-
sphere can result from interactions with ring current ions.
This was studied by Chandler et al. [1988] using the FLIP
model; for this work the thermal plasma was assumed to be
heated by Coulomb collisions with the ring current ions,
with equatorial heating rates calculated using the methods
of Kozyra et al. [1987] and with a Gaussian profile in lati-
tude. More recently, Gorbachev et al. [1992] investigated
the heating of the thermal plasma by MHD waves which
would be generated by the ring current; they used a hydro-
dynamic model which included the heat flow equations.
For this work the heating of H ÷ ions due to Coulomb col-
lisions with ring current ions during the recovery phase of
a magnetic storm was studied. Heating rates per particle
were derived from a three-dimensional kinetic ring current
model [Fok et al., 1995a]. A time-dependent hydro-
dynamic plasmasphere model was used; the magnetic field
was assumed to be a corotating dipole. It is fully inter-
t NAS/NRC Research Associate.
Cross-Scale Coupling in Space Plasmas
Geophysical Monograph 93
This paper is not subject to U.S. copyright. Published in 1995
by the American Geophysical Union
hemispheric and no diffusive equilibrium assumptions are
made.
2. MODEL DESCRIPTION
For this work the model is essentially the same as de-
scribed in Gutter et al. (Modeling of O ÷ ions in the plasma-
sphere, submitted to J. Geophys. Res., 1995), with some
modifications. It includes the time-dependent continuity,
momentum, and energy equations for O ÷ and H ÷ ions, and
the energy equation for electrons; the plasma is assumed to
be quasineutral and currentless [cf. Gutter and Gombosi,
1990]. Ionization, charge exchange, recombination, colli-
sions, and heat conduction are included; external heat
sources are allowed. Photoelectron heating of thermal elec-
trons is described using analytic formulas which include
the effect of trapped photoelectrons. Neutral parameters
were found using the MSIS-86 [Hedin, 1987] (densities
and temperatures) and HWM-90 [Hedin et al., 1991]
(winds) models, for February 9, 1986. Also, the energy
loss of H ÷ ions due to charge exchange with H atoms was
included. This was calculated using the cross section for
this process as a function of energy, as given in Barnett
[1990].
The decay of the ring current during the February, 1986
storm was simulated using a kinetic ring current model
[Fok et al., 1995a]. In this model, the distribution function
is found as a function of pitch angle and energy; drifts, and
losses due to charge exchange and Coulomb collisions are
173
https://ntrs.nasa.gov/search.jsp?R=19970026575 2020-06-16T01:28:25+00:00Z
174 PLASMASPHEREMODELING WITH RING CURRENT HEATING
included. The initial distributions of the ring current
species are found by extrapolating from AMPTE/CCE ob-
servations on the dawn and dusk sides of the inner magne-
tosphere; boundary values on the nightside are taken from
CCE ion flux data at L - 6.75 during the storm. The ring
current fluxes along the field line are inferred from the
equatorial distribution function [cf. Fok et al., 1995a]. The
simulation began at 0300 UT on February 9, 1986. At vari-
ous times in the simulation average heating rates per parti-
cle were calculated, as a function of local time, L shell, and
magnetic latitude. It was assumed that only H ÷ ions were
heated by the ring current interactions, as the heating rate
per particle for O f is much smaller than that for H ÷
(personal communication, M.-C. Fok, 1995). For L - 2 and
L - 3, these heating rates were set to zero for magnetic lati-
tudes greater than 40 degrees, which is the boundary of the
ring current model for these L shells.
For the plasmasphere modeling, a longitude was chosen
so that 0 LT would be approximately equal to 0300 UT;
the magnetic longitude was set to 25 degrees. For the L - 2
flux tube, the model was run for several days assuming
only photoelectron heating, until the results were approxi-
mately diurnally reproducible. Then the model was
allowed to run for one day with the ring current heating of
the H ÷ ions included. For the L = 3 flux tube, results with
ring current heating were found starting from a solution
which corresponds to a partially filled flux tube.
3. RESULTS
Figure 1 shows results found when the model was run on
an L - 2 flux tube. The solid curve shows results found
assuming photoelectron heating only, the dotted line gives
results when the ring current heating started at 0 LT, and
the dashed line gives results when the ring current heating
started at 1200 LT. For the case when the heating starts at
0 LT the equatorial H ÷ temperature rises to a value of
about 35,000 K after 4 hours and then decreases more
gradually; the equatorial H ÷ density drops as the tempera-
ture increases. For this case the maximum ion heating rate
per particle is about 2 x 10 -3 eV/s. The equatorial tempera-
ture increase causes downward flows due to the increased
pressure gradients, with H ÷ velocities reaching 10 km/s
near 500 km altitude (velocity profiles not shown). In the
case when the ring current heating starts at 1200 LT the
temperature does not change much until 12 hours into the
simulation, when the temperature starts to rise. At this time
the flux tube is on the nightside, which is where the ring
current heating rates are highest. The equatorial H ÷ tem-
perature only rises to about 22,000 K in this case.
Figure 2 shows results found on an L - 3 flux tube; the
solid line gives results found assuming photoelectron heat-
ing only, while the dotted line gives results when the ring
current heating was included and assumed to start at 0 LT.
In the first four hours Teq (H +) rises to about 12,000 K, and
rises again in the afternoon, reaching a maximum of about
A
I
E
__>,
t-"
20,000 K. In addition, the plasmasphere density is lower
when the ring current heating is included.
4. DISCUSSION AND SUMMARY
We have given results found using a time-dependent
plasmasphere model when ring current heating of the H ÷
ions is included. It was found that this would lead to signif-
icant enhancements of the equatorial H ÷ temperature and
that the equatorial H ÷ density decreases when the tempera-
ture rises. A similar study [Fok et al., 1995b] was done
using the FLIP model; they found a similar time profile for
the ion temperature, although the maximum temperature in
their results is only about 14,000 K on an L - 2 field line.
This difference is probably a result of the assumption in the
40000
equatorial H÷ temperature
I I I I I I I I
(a)
30000 , , ,
20000 ,' ', '_
] ', / \
i
Q- , , /
E 10000 ,' ,\
O0 i i I l i I I I4 8 12 16 20 24 28 32 36
local time (hrs)
equatorial H ÷density
40001 ' ' ' ' ' ' ' ' I
3000
2000 , . - , \ -
1000 _.. -"
00 I I I I I 1 i i4 8 12 16 20 24 28 32 36
local time (hrs)
Fig. 1. Local time profiles of the equatorial H+ temperature (a)
and density (b) for L - 2. The solid line shows results when only
photoelectron heating of electrons is included; the dotted line
gives results when the ring current heating of H+ ions started at 0
LT; the dashed line gives results when the ring current heating of
H+ ions started at 1200 LT.
,v,
E
20000
15000
10000
5000
0
0
1200
equatorial H* temperature
1 I I J.'_. I
" (a)
/ •
/ \
/
t
t
- /
/
i
i
I I I I I
4 8 12 16 20
local time (hrs)
equatorial H* density
24
I I I I I
E
.__>,
t-
1150
1100
1050
1000
950
9000
(b)
I I I I I
4 8 12 16 20 24
local time (hrs)
Fig. 2. Local time profiles of the equatorial H + temperature (a)
and density (b) for L = 3. The solid line shows results when only
photoelectron heating of electrons is included; the dotted line
gives results when the ring current heating of H + ions started at 0
LT.
FLIP model that there is only one ion temperature, whereas
in our plasmasphere model an energy equation is solved
for each species. Assuming that the different ion species
have the same temperature implies that collisions are
strong enough to keep them in thermal equilibrium, and
that the per particle heating rates are the same for H ÷ and
O +. However, the per particle heating rates due to ring
current interactions are roughly twenty times larger for H +
than for O ÷ (personal communication, M.-C. Fok, 1995),
and the momentum transfer collision frequency of H + with
O + is inversely proportional to the H ÷ temperature raised to
the power 1.5, which means that the two ion species should
rapidly be thermally decoupled. Furthermore, to force the
ion temperatures to be the same in our model would re-
quire an enhancement of the thermal coupling between H ÷
GUITER ETAL. 175
and O +, which would be equivalent to extra energy loss for
the H ÷ ions.
The temperature rise is probably unrealistically high in
our L - 2 results. This could be a result of the ion heating
rates being too high; changing the method for obtaining the
initial ion fluxes at energies lower than the lowest energy
measured by AMPTE can reduce the heating rates by an
order of magnitude at lower L shells [cf. Fok et al., 1995b].
With the ion heating rates reduced by a factor of ten, the
maximum equatorial H ÷ temperature is about 10,000 K for
L - 2. These results show that after the main phase of a
magnetic storm ring current heating would have a signifi-
cant effect on the thermal plasma in the plasmasphere.
Acknowledgments. This work was performed while two of the
authors (S. M. Guiter and M.-C. Fok) held National Research
Council-Marshall Space Flight Center Research Associateships.
Acknowledgment is also made to Dr. Paul Craven for helpful
discussions.
REFERENCES
Barnett, C. F., Atomic Data for Fusion, vol. 1: Collisions of H,
H2, He, and Li Atoms and Ions with Atoms and Molecules,
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Fok, M.-C., T. E. Moore, J. U. Kozyra, G. C. Ho, and D. C.
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Fok, M.-C., P. D. Craven, T. E. Moore, and P. G. Richards, Ring
current-plasmasphere coupling through Coulomb collisions,
this monograph, 1995b.
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Hedin, A. E., M. A. Biondi, R. G. Burnside, G. Hernandez, R. M.
Johnson, T. L. Killeen, C. Mazaudier, J. W. Meriwether, J. E.
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formation of stable auroral red arcs, J. Geophys. Res., 92, 7487,
1987.
S. M. Guiter, M.-C. Fok, and T. E. Moore, Space Sciences
Laboratory, NASA Marshall Space Flight Center, Huntsville, AL
35812.



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