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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
mν
en
σ
0
=
Ne
2
/mν
en
,
=
σ
0
/β
e
,
σ
xxe
σ
xxi
Mν
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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