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therefore lead to further plasma forcing out from the plasma-depleted regions.
Similar to the current-convective processes, a finite field-aligned wave vector is
essential. The instability criterion and the growth rate are
1
d
(
ln V d )/
dy
k B (
T e +
T i )
2
V d V
+
V d
>
λ
p k
k
,
||
||
δ e ν e
m e
v e
v en ,
d
(
ln V d )
dy
γ =
δ eff ν e +
V d
where
c m e
4
λ p =
e 2 n
π
is the wavelength of the plasma wave,
δ eff ν e involves the heating loss caused
by collisions and the field-aligned electron thermal conductivity, V d is the
plasma drift velocity in E
×
B 0 fields, and V
is the field-aligned electron
||
velocity.
Analyses of coordinated scintillation observations using orbital satellite
beacons and the EISCAT radar by Kagan et al. (1995) showed that the ther-
momagnetic instability is the most probable candidate for F-region 1 km-scale
irregularities inside the trough. It is interesting that the same type of field-aligned
electric field associated with stationary Alfvén waves seems to be responsible for
ion outflows from auroral ionosphere that are observed above stable auroral
arcs and are accompanied by strong electron temperature enhancements (Kagan
and St.-Maurice, 2005).
10.2.2 Turbulent Mixing as an Alternative to Plasma Instabilities
It is well known that the magnetospheric flow pattern is seldom laminar but
rather is usually somewhere between turbulent and extremely turbulent (Crow-
ley and Hackert, 2001; Earle and Kelley, 1993). The effect of this turbulence is to
mix any existing density gradient due to solar production or particle impact ion-
ization regardless of the sign of the gradient. We can estimate the turbulence level
necessary to accomplish a higher level of density structure than that provided by
the E
B process as follows. We assume that the layer has the appropriate sign
for instability, but, of course, this will happen only 50% of the time. The simple
form of the linear growth rate for the E
×
γ EB , given previously.
If that same gradient is structured by a spatial electric field pattern characterized
by some wave number spectrum E
×
B instability is
(
k
)
, then we may use the continuity equation
n
/∂
t
=−
V
·∇
n
 
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