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where
ν
i
V
D
A
=
i
L
−
2
α
n
0
2
2
(
1
+
0
)
C
s
2
0
V
D
(
+
0
)
−
2
B
=
−
1
/
ν
i
(
1
+
0
)
Substituting (4.55) and (4.58) into (4.57) yields
dk
k
4
I
3
/
2
k
V
−
D
kI
k
A
Bk
2
d
/
∝
−
(4.59a)
This differential equation may readily be solved to yield
x
−
8
/
3
1
x
4
/
3
1
2
S
2
x
−
2
/
3
I
(
x
)
=
−
−
−
/
(4.59b)
V
0
k
c
/
A
2
where
x
=
k
/
k
cc
,
k
c
is some long wavelength cutoff,
I
(
x
)
=
(
)
I
k
, and
Bk
c
)
S
γ
k
we see that
A
represents growth and
B
damping, so
S
is therefore a “strength parameter” for the process.
A plot of the quantity
xI
=
A
/(
. From the definition of
is given in Fig. 4.37 for values of
S
equal to 10
4
(
x
)
and
and for negative values. The latter correspond to drifts greater than the
primary two-stream value. For positive large values of
S
, the curve rises to a peak
∞
I
II
III
10
21
E
M
10
22
x
25/3
10
23
10
24
10
25
V
d
.C
s
V
d
,C
s
x
21
10
26
k
k
L
S510
4
S
5
V
d
5
C
s
x
∗
5
x
M
x
m
10
27
10
2
10
3
10
4
1
10
X
Figure 4.37
Theoretical one-dimensional power spectrum of the electrojet turbulence.
[After Sudan (1983). Reproduced with permission of the American Geophysical Union.]
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