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∂c
3
∂x
2
−
∂c
2
∂x
3
,
∂c
1
∂x
3
−
∂c
3
∂x
1
,
∂c
2
∂x
1
−
∂c
1
∂x
2
.
a
1
=
2
=
3
=
and
∂c
1
∂x
1
+
∂x
2
+
∂c
3
∂c
2
∇
·
c
=
∂x
3
The covariant components of
a
are
a
i
=
g
ik
a
k
,
i, k
=1
,
2
,
3. Summation here
is over repeated subscripts.
Electric (
E
) and magnetic (
b
) fields in the oblique coordinate system can
be presented as
E
=
E
1
l
1
+
E
2
l
2
+
E
3
l
3
,
b
=
b
1
l
1
+
b
2
l
2
+
b
3
l
3
.
Then for the horizontal components of
E
and
b
in the Cartesian and oblique
coordinate systems we have
E
x
=
E
1
,
y
=
E
2
,
b
x
=
b
1
,
b
y
=
b
2
.
and for the vertical
z
-component:
b
z
=
−
cot
Ib
1
+
b
3
,
j
z
=
−
cot
Ij
1
+
j
3
.
(7.4)
We begin the study of MHD-wave interaction with ionospheric plasma
by investigating the plane-layered model shown in Fig. 7.2. The complex
Fig. 7.2.
Plane model of the Earth-magnetosphere system. The magnetosphere
is a dielectric with the transversal dielectric permeability
ε
m
. The ionosphere is
taken as a thin layer with the Pedersen
Σ
P
and Hall
Σ
H
components of the tensor
height integrated conductivity. The atmosphere is a conductor with complex dielec-
tric permeability. The ground is a conductive layer of thickness
H
and the specific
conductivity
σ
g
1
underlain by the half-space of conductivity
σ
g
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