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That the medium is linearly stable at m scales in the direct RT process now
can be seen by comparing the growth g
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
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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