Geoscience Reference
In-Depth Information
That the medium is linearly stable at m scales in the direct RT process now
can be seen by comparing the growth
g
/ν
in
L
to the classical perpendicular dif-
fusive damping rate, as in (4.26). Experiments show that the 3m structures are
highly elongated along the magnetic field (Farley and Hysell, 1996; Hysell and
Farley, 1996). Parallel diffusion is so fast that the only structures that can be
maintained have
k
so perpendicular and parallel diffusion is comparable.
As indicated in (4.29),
D
c
⊥
⊥
k
||
may range from a minimum of
D
e
⊥
to as large as
D
i
⊥
depending on the conductivity of the E region. The wavelength at which
the RT process is marginally stable, that is, where linear growth equals diffusive
damping, is then
π
D
c
⊥
ν
in
L
g
1
/
2
λ
c
=
/
2
(4.30)
λ
where
c
is the critical wavelength at marginal stability. This parameter exceeds
10m for reasonable F-region parameters, even using the smallest value of
D
c
⊥
(i.e.,
D
e
⊥
)
. The RT process is thus linearly stable in the range where most of the
radar observations have taken place—that is, for backscatter from waves with
λ
≤
3m. If no other wave generation process exists, the 3m waves must receive
energy from the longer scales via a cascade process of some sort.
Another possible candidate for meter-scale structure is the collisional drift
wave. These waves are driven only by gradients, so they could be a secondary
instability due to the primary Rayleigh-Taylor irregularities. However, linear
instability studies based on the rocket observations show that such waves are
linearly stable (Huba and Ossakow, 1981a, b). This fact, coupled with the fea-
tureless
k
−
5
spectrum for
100m, seems to rule out unstable drift waves as
a source of 3m waves. As we shall see next, it appears that classical diffusion
may be sufficient to explain the spectrum, provided energy can be coupled from
growing large-scale waves to small-scale modes damped by diffusion.
λ
≤
4.4.3 Toward a Unified Theory for the Convective Equatorial
Ionospheric Storm Spectrum
Hysell and Kelley (1997) observed the fluctuation spectrum for several sets of
plasma bubbles seen on consecutive orbits of the AE-E satellite, one occurring in
the 2200-2300 LT period and the next after midnight LT. This is in the period
of decay, and the authors estimated the decay of each range of
k
space using the
model
δ
2
δ
2
k
2
De
2
γ(
k
)τ
n
n
n
(
k
,
t
+
τ)/
=
n
(
k
,
t
)/
(4.31)
s
−
1
and virtually indepen-
dent of
k
. For reference the classical diffusion time constant for
D
c
⊥
=
10
−
4
Remarkably,
γ(
k
)
was the order of
−
(
2
×
)
4m
2
0
.
/
s
equals this value for
700m. So for wavelengths greater than about 500m, the
structures decay faster than the classical rate, and for
λ
=
λ
≤
500m, the structures
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