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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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