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where
L
−
1
=
1
/
n
(
dn
/
dy
)
,
C
s
is the ion acoustic speed,
ν
in
and
ν
ei
are the ion-
neutral and electron-ion collision frequencies,
e
and
i
are the electron and ion
gyrofrequencies,
E
0
⊥
is the component of the perpendicular electric field in the
∇
B
direction, and the ratio of parallel to perpendicular wave numbers for
maximum growth,
n
×
θ
max
, is given by
E
0
⊥
BV
1
/
2
E
0
⊥
BV
ν
in
i
2
ν
in
i
2
ν
in
/
i
i
/ν
in
+
i
/ν
en
θ
max
=−
±
+
||
||
(10.11)
θ
max
=
If we let
V
go to zero in (10.11) and choose the negative sign, then
0.
||
This result yields the flute mode (
k
||
=
0)
E
×
B
instability. Indeed, if we set
θ
0 in (10.10), it reduces to the growth rate of the gradient drift instability.
Thus, as already noted, a field-aligned current can serve to destabilize a plasma
configuration that is otherwise stable to the
E
=
max
B
instability, or to enhance
the growth rate of an already unstable situation. Choice of the negative sign in
(10.11) corresponds to a damped acoustic mode.
The linear local theory described here has a preferential tendency to create
unstable conditions at low plasma densities, since for a fixed
J
×
is inversely
proportional to
n
. The region above the F peak is therefore a region of high
growth rate. However, the generalized process could very easily be
stable
on the
same magnetic field line at or below the F peak. It is very clear then that a local
theory is not very suitable. Such nonlocal effects in general reduce the growth
rate. Note also that E-region shorting is every bit as important to the current
convective instability as it is to the
E
,
V
||
||
B
instability and is not included in (10.10).
Also, the growth rate given in (10.10) uses a perpendicular diffusion coefficient
corresponding to a nonconducting E region, which may also underestimate the
damping. Taken together, these negative aspects have led to the conclusion that
although it is an interesting physical process, the current convective instability
can only rarely overcome the stabilizing effects of an unfavorable
E
×
B
geometry.
Finally, it should be noted that the instability only occurs when the current is
carried by thermal plasma and does not apply when energetic electrons carry the
bulk of an upward current.
Erukhimov and Kagan (1994) proposed a thermal instability mechanism
(which they named thermomagnetic) in which a strong field-aligned electric field
is set up by conversion of the field-perpendicular electric field by a geomagnetic
field-perpendicular magnetic perturbation. The induced field-aligned electric field
is prevented from shorting out by electron inertia and is sustained by the plasma
drift. Such type of electric field conversion takes place in stationary Alfvén wave
(Knudsen, 1996). The induced field-aligned electric field is much stronger than
usual and leads to the thermal instability generation discussed in (Erukhimov
et al., 1982). The E-region analogue of the latter, based on ion heating, is devel-
oped by Kagan and Kelley (2000). The main idea is that temperature fluctua-
tions provide a feedback that enhances the electric field in plasma depletions and
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