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And the addition to Pedersen conductivity can be written as
q
)
δσ
xx
(
q
)
q
x
δσ
xx
(
−
δσ
xx
≈−
.
σ
mn
q
m
q
n
q
We obtain, in view of
σ
xx
σ
xy
,
that
δσ
xx
(
r
)
δσ
xx
≈−
(10.32)
σ
xx
Substituting (10.32) into (10.25), we get an expression for the effective con-
ductivity in the form of (10.9) in which
=
σ
0
/
(1 +
β
e
)
.
It is clear that the effective conductivity is less than the average
conductivity in the case of a weakly magnetized plasma (
β
e
<
1).
σ
should be replaced by
σ
xx
Strong Field
In strong magnetic fields (
β
e
1) but (
β
i
1) from (1.93, 1.94) follows
σ
0
β
e
σ
0
β
e
.
σ
xx
≈
,
xy
≈
(10.33)
The main term in (10.26) is defined by the perturbed Hall component
δσ
xy
.
Therefore, the correction
δσ
xx
is
δσ
xy
(
−
q
)
q
y
B
x
(
q
)
δσ
xx
≈
(10.34)
σ
mn
q
m
q
n
q
and
B
x
(
q
)
≈−
δσ
yx
(
q
)
q
y
.
Noting the asymmetry of
δσ
ij
for
i
=
j
, that is
δσ
xy
=
−
δσ
yx
,
we obtain
2
q
y
+
q
|
δσ
xy
(
q
)
|
δσ
xx
≈
.
σ
mn
q
m
q
n
Hence, it follows that the contribution from inhomogeneities is positive and
in the case of
β
e
1
,
the effective conductivity always exceeds
σ
xx
.
Effective 2D Medium
We have found relations appropriate for distributed inhomogeneities. We now
return to
σ
eff
, and use the method of 'effective medium' ([10], [20]) for a brief
treatment of a thin conductive layer model containing a binary mixture of
circle inhomogeneities with conductivities
σ
1
and
σ
2
.
The second term on
the right-hand side of (10.2) are
r
-and
ϕ
-components of a dipole moment of
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