Geoscience Reference
In-Depth Information
10
−
5
equatorial ionosphere with
B
=
2
.
5
×
tesla (0.25 gauss). The transition
from a molecular ion plasma (NO
+
and O
2
)
to an atomic ion plasma (O
+
) has
been included in the calculation of
κ
. The absolute value of
κ
e
passes through
unity near 75 km, while
κ
i
does so at 130 km. In making the plot of
κ
e
, we have
used the total electron collision frequency
v
e
v
ei
. This is not entirely
consistent with the preceding discussion, which assumes
v
e
=
=
v
en
+
v
en
. However, the
modification is of little importance, since the absolute value of
κ
e
is very large
above 100 km.
The relationship between
J
and
E
may now be determined from the definition
J
, with
V
j
given by (2.37a,b) and (2.35). The result may be
expressed through a tensor relationship
J
=
σ
·
V
i
−
V
e
)
=
(
ne
E
, where
⎛
⎞
σ
P
−
σ
H
0
σ
H
σ
P
0
00
⎝
⎠
σ
=
(2.38)
σ
0
To obtain this form,
B
has been taken to be parallel to the
z
-axis, and we have
defined
σ
0
=
ne
(
b
i
−
b
e
)
(2.39a)
ne
b
i
1
i
b
e
1
e
2
2
σ
P
=
+
κ
−
+
κ
(2.39b)
e
1
e
i
1
i
2
2
2
2
σ
H
=
(
/
)
κ
+
κ
−
κ
+
κ
ne
B
(2.39c)
The three conductivity parameters,
σ
H
, are called the specific,
Pedersen, and Hall conductivities, respectively. (Remember that
b
e
is negative.)
Plots of
σ
0
,
σ
P
, and
σ
H
for a typical daytime midlatitude ionosphere are given
in Fig. 2.6. These plots correspond to the daytime collision frequencies in Fig. 2.3
and a magnetic field of 5
σ
0
,
σ
P
, and
10
−
5
tesla (0.5 gauss). The specific or parallel conduc-
×
σ
0
is dominated by the high electron mobility and is equal to
ne
2
tivity
mv
e
to a
good approximation. At high altitudes when electron-neutral collisions become
rare, the plasma density factor in
v
ei
cancels the same factor in the numerator
of
/
σ
0
is independent of density above 400 km. The variation
above that height displayed in Fig. 2.6 is related to the electron temperature,
since according to (2.29b),
v
ei
is very nearly proportional to (
T
e
)
−
3
/
2
. The par-
allel conductivity is so high that the ratio
σ
0
, and therefore
10
4
above
σ
0
/σ
P
is greater than 1
×
130 km. Above about 75 km,
κ
e
is very large, and in the plane perpendicular to
B
0
, the electrons only move perpendicular to the forces that act on them. Then
the Pedersen conductivity may be written in the form
ne
2
Mv
in
1
i
2
σ
P
=
+
κ
(2.40a)
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