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From (10.24) follows
σ
e
xx
=
σ
xx
+
δσ
xx
(10.25)
where
δσ
ij
=
q
δσ
il
(
−
q
)
q
l
B
j
(
q
)
,
(
i, j
≡
x, y
)
.
(10.26)
σ
mn
q
m
q
n
Equation (10.26) was analyzed in details in series of papers (see, e.g., [11],
[19]) for strong magnetic fields
β
e
1
.
Let
σ
0
is the longitudinal conductivity. Then taking into account that
=
σ
0
/β
e
and
=
σ
0
/β
e
one can suppose that the fluctuations
δσ
xxe
(
q
)and
δσ
xye
(
q
) in (10.26) are proportionally respectively to
β
−
e
and
β
−
e
. It follows that the fluctuations of the electron Hall conductivity will be es-
sentially stronger than the fluctuations of the electron Pedersen conductivity.
Formally, the anisotropy of a partially ionized gas under the strong magnetic
field leads to that the electron terms, including the Hall's part, prevail in
(10.25) and (10.26).
The influence of
B
0
on
σ
Pi
is extremely weak when
β
i
<<
1. The av-
erage ion Pedersen conductivity
σ
xxe
σ
xye
σ
xxi
in this case is independent of
B
0
.
Hall ion conductivity
σ
xyi
is proportional to the parameter of
β
i
. This is
. In so doing, the fluctuations
δσ
Pi
will be propor-
tional to the fluctuations of the relative electron concentrations
δσ
xxi
(
q
)
σ
xyi
=
σ
xxi
β
i
<<
σ
xxi
ε
and the perturbations of Hall component of the ion conductivity
δσ
xyi
will be
lesser than Pedersen conductivity because of weak ion magnetization, this is
δσ
xyi
(
q
)
∝
εβ
i
. This means that
δσ
xxi
gives the main contribution to the fluc-
tuated ion part. It independent of the magnetic field and gives the correction
to
σ
e
P
∝
proportional to
ε
2
<<
1, that is considerably lesser than
.
The crossed terms with the products of the correlation functions of the
fluctuations of ion and electron conductivities appear also during the calcula-
tions of
δσ
e
xx
. It follows from estimations that their contribution is essentially
smaller than the “pure” electron contribution.
Thus, the main contribution to the expression for
δσ
eff
σ
xxi
ik
in (10.25) is de-
fined by electrons. Let us write out the first term in the series for
δσ
e
xx
substituting the first approximation of
B
k
(
q
) in ( 10.25 ) from ( 10.26 ) :
B
k
(
q
)=
δσ
ik
(
q
)
q
i
.
Instead of
δσ
il
we consider only electron Hall compo-
nent
δσ
xye
. An estimate of the first order correction
δσ
(1)
ef f
−
gives [11]:
xx
σ
0
ε
2
β
e
δσ
(1)
ef f
xx
.
As a result, we have:
+
δσ
(1)
ef f
xx
(1 +
β
e
ε
2
+
σ
xxe
+
···
=
σ
xxe
···
)
.
That means that even for weak inhomogeneities
ε
2
1 in the strong magnetic
1) the product
β
e
ε
2
may be greater than 1. The last circumstance
forces us to take into account all serial terms. The summing was performed
field (
β
e
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