Geoscience Reference
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This is very similar to the result found earlier for the Rayleigh-Taylor instability
[i.e., (4.24b)]. The wavelength at which the magnitudes of the first and second
terms in (4.43) are equal for
T
i
=
T
e
(i.e.,
C
s
=
2
k
B
T
e
/
M
)
is given by
C
s
(
λ
c
=
π
+
0
)
ν
i
V
D
1
Setting
0
=
0
.
22 at an altitude of 105 km
,
C
s
=
V
D
=
360m
/
s and
ν
i
=
10
3
s
−
1
yields
2
4m. This wavelength is thus quite small and for
most wavelengths of interest we may use (4.44) to relate the perturbed electric
field to the density.
Using these results, the instability process can now be understood from
Fig. 4.32a. The figure is drawn for daytime conditions with the vertical elec-
tric field upward. The sinusoidal wave can thus represent both
.
5
×
λ
c
0
.
δ
n
/
n
and
δ
E
x
for
λ
λ
c
. That is, the eastward perturbation
n
is positive.
The two quantities are in phase with net positive or negative charges built up
as shown, where these charges are associated with the perturbation electric field
(i.e.,
δ
E
x
is positive when
δ
n
/
ρ
c
=
ε
0
(
∇·
E
)
=−
ε
0
ik
δ
E
x
)
.
E
z0
n
.
0
n, 0
n. 0
V
D
B
E
East
West
E
E
Pressure gradient force (2ikk
B
T
i
n)
Ion inertia force (
2
nMi
V
ix
)
(a)
V
5
E
3
B
E
z0
0
n. 0
n
,
n.
0
V
D
B
E
East
West
E
E
(b)
Figure 4.32a
Schematic diagrams showing the linear instability mechanism in (a) the
two-stream process and (b) the gradient drift process for daytime conditions.
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