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magnetosphere,
Σ
H
= 0 and the transversal dielectric permeability is
c
2
c
2
A
=
4
πρc
2
B
0
ε
⊥
=
ε
m
=
.
(6.92)
For the dipole geomagnetic field
B
0
=
M
2
(1 + 3
w
2
)
/r
6
, with the dipole mo-
ment
M
, and plasma density (6.75), then (6.92) becomes
ε
m
=
ν
2
c
2
Ω
2
w
2
)
6
1+3
w
2
−
ρ
(1
,
(6.93)
where
Ω
=
Mν
4
2
π
1
/
2
ρ
1
/
2
. Then (6.81) reduces to
e
d
2
e
2
d
w
2
ω
2
Ω
2
ρ
(1
w
2
)
6
e
2
=0
.
+
−
(6.94)
For the power distribution of the plasma density (6.76), the boundary
problem (6.94) and (6.87) becomes
d
2
e
2
d
w
2
ω
2
Ω
2
(1
w
2
)
6
−p
e
2
=0
,
+
−
(6.95)
w
=
±w
0
d
e
2
d
w
i
ω
X
±
sin
I
0
cν
(1 + 3
w
0
)
−
e
2
(
w
)
|
w
=
±w
0
.
=
(6.96)
Here the altitude dependency of the Lame coecients in the ionosphere is
neglected.
Let us also write the equations for calculating the coecient
C
0
at the
logarithmic term in the expansion of the field (6.59). From (6.73) we obtain
(1
2
d
w
Ω
ω
w
0
d
e
2
d
w
−
w
2
)
6
−p
e
2
(
w
)
−
m
2
ν
2
c
2
2
Ω
2
(1 + 3
w
2
)
ω
j
−w
0
C
0
=
.
(6.97)
w
0
d
ω
j
d
ν
e
1
(
w
)d
w
−w
0
The formulae obtained in the present section allow us to get the explicit
expressions for the leading terms describing the resonance structure of the
field. Corresponding formulae are given in the next section. For the high fre-
quency harmonics, we present the expressions for the resonance frequencies
obtained in the WKB approximation. Neglecting the dissipation and assuming
a power distribution of the plasma concentration, we find that the resonance
frequency is
jπΩ
ω
j
=
.
(6.98)
w
0
0
w
2
)
6
−p
d
w
2
(1
−
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