Geoscience Reference
In-Depth Information
4.4 Linkage of Large and Small Scales in CEIS
4.4.1 Evidence for a Diffusive Subrange
We turn now to the studies of the power spectra of convective ionospheric storms
and examine the information they contain concerning the physics of these phe-
nomena. First, the relationship between density perturbation and electric field
structure may be derived from (4.13a), which may be written
−
δ
=−
δφ(
/
)
ikQ
n
ik
Pk
i
(4.24a)
or
Q
P
δ
n
n
δ
E
x
=
which may also be written
gB
ν
in
δ
n
n
δ
E
x
=−
(4.24b)
where
E
x
represents the electric field amplitude. In (4.24b) the electric field
is proportional to the density perturbation and thus the shape of the power
spectrum of the two quantities,
δ
δ
E
x
and
δ
n
/
n
0
, should be the same—that is,
gB
ν
in
2
2
|
δ
|
E
=
(4.24c)
2
(δ
n
/
n
)
n
0
is different for different plasma
phenomena, the ratio may be used as a test for sorting out what processes domi-
nate the physics as a function of altitude and wave number. The ambipolar
electric field due to diffusion (see Chapter 10) is given by
Since the relationship between
δ
E
x
and
δ
n
/
=
k
B
T
e
(
∇
δ
E
/
n
/
n
)
=−
i
k
(
k
B
T
/
e
)(δ
n
/
n
)
(4.25)
rather than by (4.24b). This expression predicts that the electric field and density
fluctuation power spectrum differ by a factor of
k
2
due to the presence of the
gradient operator.
The ratio of simultaneously measured power spectra is presented in Fig. 4.19
for a rocket experiment. The ratio has been plotted to have the units of electric
field squared. For the three likely driving sources (gravity, electric field, wind),
the corresponding electric field would be
gB
/ν
in
,
E
,or
uB
. The flat portion of
the plot corresponds to the result in (4.24c); that is,
2
and
2
have the
(δ
)
(δ
/
)
E
n
n
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