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we reproduce their plots of altitude dependences of dimensionless parameters
ξ
AT
=
δ
e
ν
e
(adiabatic with thermal corrections over inelastic
electron energy exchange, shown by dashed lines) and
3
(ω
r
−
k
·
u
0
⊥
)/
2
k
2
/δ
e
ν
e
(ther-
mal conduction and thermal diffusion over inelastic electron energy exchange,
shown by solid lines) that define the dominating physical process for inelastic
electron cooling rates of
ξ
T
=
CD
e
⊥
003 (gray lines)
for each of three radar frequencies. Here,
C
is a coefficient and is given follow-
ing. From Fig. 4.32b, after essentially dominating all altitudes at 16MHz, this
transitional process clearly covers a smaller altitude range and moves to higher
altitudes at 50MHz, then disappears completely at 146MHz. A direct transi-
tion from super-adiabatic to isothermal processes results in a sudden drop in the
phase velocity of two-stream waves that could be observed if the radar altitude
resolution were less than the height of the transitional region (of about 2 km).
This was first reported at 50MHz by Swartz (1997). Kagan et al. (2008) also
observed a sudden change in
V
ph
with the newly employed Prototype Advanced
Modular Incoherent Scatter Radar (AMISR-P) at the Jicamarca Radio Obser-
vatory. AMISR-P was operated at 430MHz and had an altitude resolution of
0
δ
e
=
0
.
007 (black lines) and
δ
e
=
0
.
6 km at vertical incidence. Range-velocity-intensity plots and individual nor-
malized spectra of these AMISR-P data are shown in the left-hand column of
Fig. 4.32c. In the right-hand column of Fig. 4.32c, these observations, plotted
together with theoretically predicted phase velocities, show good correspondence
between theory and experiment.
For an equatorial electrojet between 100 and 120 km altitudes, Kagan and
Kissack (2007) offer a simpler and more explicit expression for a phase veloc-
ity of Farley-Buneman waves, that is valid with less than 3% uncertainty. Since
observational uncertainty is usually much more than 3%, the Kagan and Kis-
sack (2007) formula is handy for quick estimates and is easy to program. Their
Eq. (4.47) following allows easy tracking of wave phase velocity dependence on
its wave number and facilitates thermal corrections to the classical expression,
contributions fromnon-zero flow angles, and dominating physical processes such
as thermal conduction and inelastic electron cooling.
.
V
ph
=
)η
CD
e
⊥
k
2
⊥
+
η
+
1
g
2
A
2
T
(
+
T
)
2
u
0
k
2
DS
C
sj
k
T
e
0
χ
(
2
/
3
+
1
k
⊥
+
η
2
u
i
0
±
1
+
.
)
T
(
+
T
)
2
u
0
k
2
)
CD
e
⊥
(
T
e
0
+
T
i
0
)
k
2
(
3
/
2
1
+
(
2
/
3
(4.47)
Here,
u
0
=
V
i0
−
V
e0
is a current velocity—that is, a relative velocity between
ions and electrons;
δ
e
ν
e
is the inelastic volume electron-neutral energy exchange
rate, where the dimensionless energy ex
change factor,
δ
e
, is essentially constant
k
B
(
over the altitudes of interest;
C
sj
M
is the isothermal ion-
acoustic speed where
T
e
0
and
T
i
0
are background electron and ion temperatures,
respectively;
k
is the magnitude of the wave vector; and
k
=
T
e
0
+
T
i
0
)/
is the magnitude
⊥
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