Geoscience Reference
In-Depth Information
The ionospheric conductivity is a tensor, and Ohm's law for the ionospheric
current can be written as
j
i
D
par
E
par
C
p
E
per
C
h
b E
par
(4.21)
E
par
D
B.B;
E
/=B
2
;
E
per
D
B
Œ
E
B=B
2
where
h
,
p
,and
par
are the Hall, Pedersen, and along
B
conductivities,
correspondingly.
D
e
2
n
e
˝
e
=m
e
˝
e
C
en
˝
i
=m
i
˝
i
C
in
h
D
e
2
n
e
in
=m
i
˝
i
C
in
C
en
=m
e
˝
e
C
en
p
par
D
e
2
n
e
Œ1=m
i
in
C
1=m
e
en
where
m
i
,
m
e
are ion and electron masses, ˝
i
, ˝
e
are ion and electron cyclotron
frequencies, and
in
,
en
are ion-neutral and electron-neutral collision frequencies.
E Dr
'
C V B
,where® is electrostatic potential,
V
B
is the so-called
induction dynamo field, and
V
is neutral gas velocity vector.
After integrating of Eq.
4.20
over the height of the current-carrying layer
with neglect of the height dependence of the electric field components in this
layer, the problem to define the electric potential becomes two dimensional and
is solved by an iterative technique in the geomagnetic coordinate system. The
ionospheric conductivities needed to solve Eq.
4.20
are calculated using the standard
formulae with parameter values of the ionosphere and thermosphere taken from the
thermospheric and ionospheric-protonospheric blocks of the model. The 3D patterns
of the electric potential and electric field vector components are calculated using the
solution of Eq.
4.20
together with the condition of the electrical equipotentiality of
the geomagnetic field lines above 175 km.
4.2.4
Magnetospheric Block
The magnetospheric block (Volkov and Namgaladze
1996
) contains the following
equations for the magnetospheric plasma:
@n
i
=@t
Cr
.n
i
V
i
/
D
0
(4.22)
n
i
e.
E C V
i
B
/
Dr
p
i
(4.23)
d .p
i
V
/=dt
D
0;
D
5=3
(4.24)
