Geoscience Reference
In-Depth Information
In these equations the subscripts i, j, and e refer to ions O
C
,H
C
, and elec-
trons, respectively. The symbols par and per refer to the directions parallel and
perpendicular to the geomagnetic field. The operator
D/Dt
D
@
/
@
t
C
(
V
per
,
r
)gives
the Langrangian temporal derivatives along the electromagnetic drift trajectory
determined by Eq.
4.16
.
Q
i
,
L
i
are the production and loss rates of O
C
and H
C
ions, which take into account the photo- and corpuscular ionization, ion molecular
reactions between O
C
and O
2
and N
2
, charge exchange processes between O
C
and
H and between H
C
and O;
g
par
is a geomagnetic field-aligned component of the
sum of gravity and centrifugal accelerations; P
iQ
is the rate of the Joule heating of
the ion gas; P
iT
;P
iT
;P
iT
are the ion heat exchange rates; P
eQ
;P
eQ
are the rates of
local and nonlocal heating of the electron gas by photoelectrons and by precipitating
magnetospheric electrons; and P
eT
;P
eT
;P
eT
are the electron heat exchange rates.
For the densities of neutral hydrogen we use the barometric law with a boundary
condition at 500-km altitude from the neutral atmosphere model of Jacchia (
1977
).
Detailed description of the terms of Eqs.
4.14
,
4.15
,
4.16
,
4.17
,
4.18
,and
4.19
has
been given by Namgaladze et al. (
1988
) and Brunelli and Namgaladze (
1988
).
The integration of Eqs.
4.14
,
4.15
,
4.16
,
4.17
,
4.18
,and
4.19
is done along lines
of a dipole geomagnetic field drifting with the speed of Eq.
4.16
. The boundary
conditions are given near the bases of the field lines in Northern and Southern
Hemispheres at a height of 175 km. The atomic ion concentrations at this boundary
are obtained from photochemical equilibrium conditions. The values of the ion and
electron temperatures at this boundary are calculated from Eqs.
4.9
and
4.10
of
heat balance. We assume that geomagnetic field lines with
L
15 (
L
parameter
of McIlwain) are open and ion concentrations and heat fluxes are set equal to 0 at
r
D
15
R
E
.
Zero ion concentrations, and ion and electron temperatures equal to the temper-
ature of the neutral gas, or, alternatively, the results of preceding calculations of
the modeled parameters or input values from empirical ionospheric models, may be
chosen as initial conditions.
4.2.3
Electric Field Computation Block
The next block of our model is the electric field computation block. The equation
for the potential ® of the electrostatic field
r
® is solved numerically in this block,
taking into account the dynamo action of the thermospheric winds:
div
j D
div.
j
i
C j
m
C j
l
/
Dr
T
.
r
'
C V B
/
C j
m
C j
l
D
0 (4.20)
where
T
is the ionospheric conductivity tensor and
j
i
,
j
m
,and
j
l
are the ionospheric,
magnetospheric, and lower atmosphere current densities, respectively. The last two
are used as input parameters at the upper (175 km) and lower (60 km) boundaries of
the electric field computation block.
