Geoscience Reference
In-Depth Information
dielectric permeability tensor
ε
is a function only of
z
. First consider the
magnetosphere to be a homogeneous half-space filled with collisionless mag-
netized cold plasma. Such a medium becomes strongly anisotropic. Across the
magnetic field the medium can be approximated as a dielectric with transverse
dielectric permeability
c
2
c
2
A
ε
m
=
,
where
c
is the light velocity and
c
A
is the Alfven velocity
B
0
√
4
πρ
0
c
A
=
.
B
0
is the geomagnetic field strength,
ρ
0
is the cold plasma density. Along the
magnetic field this medium can be considered as a perfect conductor.
Ohm's law for the ionospheric plasma has the form (see Chapter 1)
j
⊥
=
σ
⊥
E
⊥
=
σ
P
E
⊥
+
σ
H
B
0
×
E
⊥
,
j
=
σ
E
,
B
0
where
j
⊥
,
E
⊥
are transversal current density and the electric field,
j
,
E
are
the field-aligned current density and electric field. The tensor of conductivity
σ
⊥
in the coordinate system connected with
B
0
is
σ
⊥
=
σ
P
.
−
σ
H
σ
H
σ
P
Here
σ
P
and
σ
H
are the Pedersen and Hall specific conductivities, respectively.
The relationship of
σ
P
and
σ
H
with ionospheric parameters was obtained in
Chapter 1. Note that
σ
H
>
0. Components of
j
in the coordinates
x
,y
,z
}
{
are
j
x
=
σ
P
E
x
−
σ
H
E
y
,
j
y
=
σ
H
E
x
+
σ
P
E
y
,
j
z
=
σ
E
z
.
The atmosphere and the ground are considered as isotropic conductors
with conductivities
σ
a
(
z
)and
σ
g
(
z
)
.
In this case, the dielectric permeability
tensor is reduced to scalar
ε
a,g
(
z
)=
ε
a,g
+
i
4
πσ
a,g
(
z
)
.
ω
In the lower part of the atmosphere (the first 10 kilometers), at frequencies
ω
10
−
1
s
−
1
, the magnitude of the displacement currents is much larger than
the conduction currents. The extremely low value of atmospheric conductivity
enables us to regard it as a perfect insulator. Only one exception is known
when the atmospheric conductivity must be taken into account: that is the
excitation of the so-called
TEM
wave mode (see Chapter 8).
1
−
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