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 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 e 2 ,
σ P = σ Pe
H = σ He
σ 0 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 e . Then (1.93) and (1.94 ) become
ω pi
4 πν i ,
β i c Ne
B 0
σ P
=
H
σ 0 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
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 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
) ,
xy
0 .
(1.102)
 
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