Geoscience Reference
In-Depth Information
It is possible to omit some terms in (1.92)-(1.94) and (1.97) for specific
magnetospheric regions and obtain the equations for an estimate of the cor-
responding electrodynamic plasma parameters.
In the atmosphere and lower
D
-layer, the collision frequencies are so high
that the electron and the ion are non-magnetized, i.e.
β
e
1. Then
the conductivity becomes isotropic. In the lower
D
-layer, neglecting the ion
conductivity, we get
1
,β
i
ω
pe
4
πν
e
σ
≈
σ
⊥
≈
σ
0
=
and
σ
H
≈
0
.
(1.99)
In the
D
- and lower
E
-layers, at the altitudes between
≈
≈
80 and
100 km,
electrons are strongly magnetized
β
e
1 but
β
e
β
i
<
1. Here both
the Pedersen
σ
P
and Hall
σ
H
conductivities are determined by electrons and
reduce to
1and
β
i
σ
0
/β
e
2
,
σ
P
=
σ
Pe
≈
H
=
σ
He
≈
σ
0
/β
e
This is an important special case of the different sensitivity of
σ
P
and
σ
H
to
the magnetic field. It can cause an anomalous effective Pedersen conductivity
of the ionosphere containing small random inhomogeneities. This is discussed
in Chapter 10.
Above, in the
E
-layer, there is an intermediate case of low but finite ion
magnetization and high electron magnetization, so that
β
i
<
1,
β
e
1, and
β
i
>β
−
e
. Then (1.93) and (1.94 ) become
ω
pi
4
πν
i
,
β
i
c
Ne
B
0
σ
P
≈
=
H
≈
σ
0
/β
e
.
(1.100)
This means that the Pedersen conductivity is predominantly ionic and the
Hall conductivity is determined by the electrons' drift in crossed electric and
magnetic fields.
The polarization conductivity
σ
pol
, which determines the polarization cur-
rent, is equal to the imaginary part of
σ
xx
.If
β
i
<
1, (1.92) becomes
ω
pi
ν
i
2
iω
4
π
σ
pol
=
i
Im(
σ
xx
)
≈
.
(1.101)
From this equation and (1.100), the ratio of the polarization current to the
Pedersen current is
|
σ
pol
/σ
P
|
=
ω/ν
i
. Joining of the inequalities (1.89) and
β
i
1. So that the polarization
conductivity can be neglected in comparison with Pedersen conductivity.
Now, let both magnetization parameters be large,
β
i
1 gives
ω
ω
ci
ν
i
. Hence
ω/ν
i
ω/ω
ci
1.
These inequalities are met in the
F
-layer and in the magnetosphere. Omitting
small terms
1and
β
e
β
−
2
i
c
2
A
≈
c
2
A
.
∼
, one can see that the modified Alfven velocity
Then (1.92) may be rewritten
c
2
4
πc
2
A
σ
xx
≈
(
ν
i
−
iω
)
,
xy
≈
0
.
(1.102)
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