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is simplified and has the form
1+0
k
∗
Re
k
,
X
∆
A
=
∆
(0)
(0)
A
=
−
,
(7.120)
A
|
sin
I
|
where
X
=
X
+
√
ε
m
|
sin
I
|
.
The estimation of
k
∗
is
1
/
2
(2
T
)
−
1
/
2
σ
1
/
2
4
π
ch X
for
σ
a
T
1
|
k
∗
|≈
1
.
(7.121)
σ
a
T
a
Then, if
(2
T
)
−
1
/
2
σ
1
/
2
σ
a
T
k
∗
|
km
−
1
∼
10
−
5
1
(day)
1
,
|
×
(night)
.
10
−
4
σ
a
T
a
The simplified expression (7.120) for
∆
A
, independent of the wavenumber,
also permits us to simplify
X
K
which, for Re
k
k
∗
, no longer depends on
k
:
X
(0
K
=
X
+
Y
2
X
.
(7.122)
As a result, the problem of long-period MHD-wave reflection and trans-
formation by ionospheric plasma with an inclined magnetic field is reduced to
the study of MHD-wave propagation through a thin isotropic ionosphere with
conductivity
Σ
K
=
X
K
c/
4
π
. The transformation coecients (of '
A
'into'
S
'
and of '
S
'into'
A
') are then found by simple multiplication of the solutions
obtained by coecients proportional to
Σ
H
=
Yc/
4
π
.
Denote by
R
(0)
,
T
(0)
and
T
(0)
Σ
matrices
R
,
T
and
T
Σ
at
∆
A
=
∆
(0)
A
and
X
K
=
X
(0
K
determined by (7.120), (7.122). The introduced matrices will differ
from exact only at
|
Re
k
|≤
k
∗
.
Features of the R and T Matrices
The values of the transmitted and reflected fields depend on nine dimensional
parameters:
c
A,
Σ
P
,
Σ
H
,
g
,
a
,
ω,
,
,
H.
The consideration can be simplified by transferring to a dimensionless descrip-
tion. One can introduce six dimensionless parameters:
k
A
=
k
0
h
√
ε
m
=
ω
c
A
h,
τ
K
=
k
0
hX
K
,
d
g
=
d
g
H
d
g
,
x
=
x
H
=
k
=
kh.
h
,
h
,
(7.123)
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