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In-Depth Information
where b ( i )
1 and b ( i 2 are the amplitudes of the incident Alfven and FMS-waves.
By substituting electric and magnetic fields into boundary conditions (7.50),
we find the reflection matrix
R = R SS
R SA
R AS
R AA
κ s A
k 0
κ s
k 0 Y sign I
2
= 1 +
.
(7.99)
Y
sin I
ε 1 / 2
ε 1 / m S
m
Let us obtain a transformation matrix of the magnetospheric fields into
ground fields. We have from (7.50) on the upper ionospheric boundary, relation
E τ (0) = Y I b τ (+0). Then, from (7.86) and (7.94),
ζ 1
ζ 2
Y g
ζ 3
Y g
ζ 3
X
sin 2 I
Y
sin I
1
T Σ =
ζ 4
ζ 3
X
.
(7.100)
Y g
ζ 2
Y g
ζ 2
Y
sin I
|
Y I |
The following denotations are used in (7.99) and (7.100):
Y 2
= S A +
,
(7.101)
|
sin I
|
X
A = ζ 1
S = ζ 4
κ S
k 0
ζ 2 |
sin I
|−
,
ζ 3
X,
(7.102)
|
sin I
|
+ ζ 4
X ζ 1
,
Y 2
sin 2 I
X
sin 2 I
|
Y I |
=
ζ 3
ζ 2
(7.103)
X = 4 πΣ P
c
Y = 4 πΣ H
c
X = X + ε 1 / 2
m
|
sin I
|
,
,
.
(7.104)
Inclination I< 0 in the Southern Hemisphere and I> 0 in the Northern
Hemisphere. ζ i
0).
One can find, in a similar manner from (7.95)-(7.98), the transmission
matrix T :
ζ i (
Y g
Y g
ζ 3
A
ζ 3
Y sign I
2
T =
(7.105)
Y g
ζ 2 Y sign I
Y g
ζ 2 S |
sin I
|
Characteristic Parameters
In the present section the transmission and reflection matrices are studied
within a more realistic model of the distribution of the Earth's conductivity.
 
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