Geoscience Reference
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where LJ
1
and q are given by Eqs. (
5.21
) and (
5.34
). In deriving Eqs. (
5.177
)
and (
5.178
) we have neglected the terms which contain the factor .V
AI
=c/
2
10
6
1. The potential dž is derivable from Eq. (
5.177
) through
iA.
d/
0
g
dž.
d/
D
:
(5.179)
Combining Eqs. (
5.29
) and (
5.178
) we obtain
0
Ǜ
H
m.!/ cosh .kh/
2 sinh .kd/
iL
kqLJ
3
‰.
d/
D
V
AI
Ǜ
2
H
C
Ǜ
P
C
LJ
1
Ǜ
P
v
r
LJ
1
Ǜ
H
v
'
;
B
0
C
(5.180)
where the function LJ
3
is given by Eq. (
5.31
).
Applying a Bessel transform to Eqs. (
5.130
) and (
5.131
) one can express the
components of electromagnetic field through the potentials. The derivatives @
z
‰
and @
z
dž in Eqs. (
5.130
) and (
5.131
) are derivable from Eqs. (
5.114
) and (
5.146
)via
@
z
‰.
d/
D
‰.
d/ and @
z
dž.
d/
D
ik
2
c
2
A.
d/=!. On account of these
expressions we get
b
r
.
d/
D
k‰.
d/;b
'
.
d/
D
kA.
d/;b
z
.
d/
D
k
2
‰.
d/; (5.181)
e
r
.
d/
D
kdž.
d/;e
'
.
d/
D
i!k‰.
d/;e
z
.
d/
ik
2
c
2
A.
d/=!:
(5.182)
References
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Belyaev PP, Polyakov SV, Rapoport VO, Trakhtengertz VY (1990) The ionospheric Alfvén
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V (2002) Spectral properties of the ionospheric Alfvén resonator observed at a low-latitude
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1:3). J Geophys Res 107:1281. doi:10.1029/2001JA005076
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D
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