Geoscience Reference
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by Dreizin and Dychne [11] for electron plasma. An analogous expression for
the effective conductivity σ e xx of a two-component plasma containing electrons
and ions is ([5], [8]):
σ e xx =
+ δσ e xx ,
σ xx
(10.27)
where
δσ e xx = σ 0 ε
4 / 3
σ xx
σ xxe
σ xxi
,
,
=
+
β e
and
= σ 0 en
σ 0 = Ne 2 /mν en ,
= σ 0 e ,
σ xxe
σ xxi
in ,
m and M denote electron and ion mass.
Taking into consideration that ( 10.27 ) is obtained without using pertur-
bation theory, it is possible to consider the case
σ xx
<<δσ e xx . Then from
(10.27) we have
σ e xx = σ 0 ε
4 / 3
+
σ xxi
.
(10.28)
β e
The relative value of the part of effective conductivity caused by inhomo-
geneities for a 3-dimensional model of a medium with stochastic inhomo-
geneities is
δσ e xx
( β e ε 2 ) 2 / 3
=
.
(10.29)
σ xx
1+
σ xxi
/
σ xxe
β 1 / 2
) 3 / 4 the contribution of the fluctu-
ating part δσ e xx becomes comparable with the background conductivity
We notice that for ε
(
σ xxi
/
σ xxe
e
.
Expression (10.26) is obtained under very general assumptions about the
magnetic field. Therefore, it is valid for both strong and weak fields.
σ xx
Weak Field
For weak fields when β e
. The main con-
tribution to (10.26) is provided by δσ xx ( q ) . From (10.26) we obtain equation
that
1 , the component
σ xx
σ xy
δσ xx =
q
δσ xx (
q ) q x B x ( q )
(10.30)
σ mn
q m q n
In the lowest-order approximation to the fluctuations δσ xx ( q ) , it follows from
(10. A.3) that
B x ( q )
≈−
δσ xx ( q ) q x .
(10.31)
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