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)