Geoscience Reference
In-Depth Information
Since there are no sources of the TE mode in the atmosphere the Maxwell
equations (
4.1
) and (
4.2
) can be written as
i!
c
2
E
'
;
@
r
ıB
z
@
z
ıB
r
D
(5.150)
@
z
E
'
D
i!ıB
r
;
(5.151)
@
r
E
'
D
i!ıB
z
:
(5.152)
Substituting Eqs. (
5.130
) and (
5.131
) into Eqs. (
5.150
)-(
5.152
), one can express the
TE mode components through the potential ‰. As a result we come to the single
wave equation for the potential ‰
!
2
c
2
‰:
r
1
@
r
.r@
r
‰/
C
@
zz
‰
D
(5.153)
Applying Bessel transform to this equation we get
@
zz
‰
k
a
‰
D
0;
.
d<
z
<0/;
(5.154)
where k
a
D
k
2
k
2
. It should be noted that if one changes the parameter
k by the perpendicular “wave number” k
?
,Eq.(
5.154
) coincides with Eq. (
5.112
)
for the case of “plane” atmosphere. Similarly, one can derive an equation for the
ground that is completely coincident with Eq. (
5.113
). This means that the solution
of the plane problem given by Eqs. (
5.115
) and (
5.116
) holds true in the axially
symmetrical case.
!
2
=c
2
The Ionosphere and Magnetosphere
In the model the space
z
>0consists of a solely cold collisionless plasma, which
is described by Maxwell equations (
4.2
) and (
5.2
) and the plasma dielectric per-
mittivity tensor (
2.18
). When the cylindrical coordinates are applied, the Maxwell
equations are split into two independent sets of equations. The first set includes the
components of the shear Alfvén waves, i.e., E
r
, E
z
and ıB
'
i!
V
A
@
z
ıB
'
D
E
r
;
(5.155)
r
@
r
rıB
'
D
1
i!"
k
c
2
E
z
;
(5.156)
@
z
E
r
@
r
E
z
D
i!ıB
'
:
(5.157)
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