J. Geophys. Res., 101, 2279-2295, 1996
(received March 20, 1995; revised August 18, 1995;
accepted August 21, 1995.)
Copyright 1996 by the American Geophysical Union.
Paper number 95JA02587.
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Appendix
As noted in the body of the text,
CO
is the dominant
neutral at low altitudes in the Venus ionosphere. Morrison and
Greene [1978] have investigated the cooling of electrons through
collisions with CO,
and we use their work as a basis for
parameterizing the collision cross-section, and vibrational cooling
rate. Figure A1 shows the cooling rates from Morrison and Greene
[1978], as indicated by the symbols. It is assumed that the neutral
gas temperature is 200 K. The solid lines in
Figure A1 show least
squares regression lines through the data. The functional forms for
the regression were chosen to best fit the data, with the constraints
that the curves approach an asymptotic form at high temperature,
and that the functions are positive definite for all temperatures.
Figure A1.
Cooling rates for electron-CO
collisions [after
Morrison and Greene, 1978]. The symbols give the cooling rates
for vibrational (squares), electronic (diamonds), and rotational
(triangles) excitation of CO,
and for elastic, momentum transfer
(circles), collisions. The solid lines give least squares fits used to
parameterize the vibrational cooling rate and momentum transfer
collision cross section.
Turning to the momentum transfer cooling rate first, from
(5) and (7),
(A1)
where temperatures are in eV, and densities are in
cm
. Thus the
explicit temperature dependence in (A1) is removed prior to
performing the fit. Note that (A1) has been expressed
in eV cm s
, for direct comparison with Figure A1,
1 eV cms
= 1.6 
10
erg
cm s
= 1.6
10
W/m
.
The fit yields a collision cross section for momentum
transfer of the form
(A2)
The fit to the vibrational cooling rate curve is
(A3)
Thus at high temperatures (> 0.3 eV)
Q
/Q
~ 1.34
10/T
and the vibrational cooling generally exceeds the momentum transfer
cooling by about 3 orders of magnitude.
However, while electrons lose most of their energy through
inelastic collisions, they lose most of their momentum through
elastic collisions. If we denote the effective collision frequency for
momentum loss through vibrational excitation of
CO as
v then
(A4)
and since m
/
m = 8
10
, even though
Q/Q
~ 1.34
10/T,
the electron momentum loss collision frequency is essentially that
due to elastic collisions. Thus it is the collision frequency for
elastic collisions that gives the Joule dissipation rate, while the
cooling due to inelastic collisions is the dominant collisional
cooling term. This further emphasizes the relative inefficiency of
cooling through elastic collisions.
Another consequence of the relative efficiency of
vibrational cooling was alluded to in section 4, where we showed
that the vibrational cooling rate exceeded the Joule dissipation rate
at most altitudes. Even in the absence of waves, the vibrational
cooling operates, and may require unrealistically high topside
electron temperatures to provide the heat flux required to offset the
cooling, depending on the assumed ionospheric density profile.
This is shown in
Figure A2
, where we plot solutions of the heat
budget equation (1)
, but with the Joule dissipation turned off, and
cooling through vibrational excitation of
CO (A3)
turned on. The
thick curves to the right of the figure show the temperature and
cooling rate profile obtained for the same density profile shown in
Figure 6.
Since downward heat flux is the only source of heat in
the model, (1)
requires unrealistically high topside electron
temperatures. When obtaining a solution of
(1) in this case, we
required that the electron temperature at lowest altitude be the
same as the neutral gas, and allowed the topside temperature to
float.
Figure A2.
Electron temperature profiles and associated cooling
rates for different ionosphere minimum altitudes. The temperature
(thick solid line) and collisional cooling rate (thick dashed line) are
plotted to the right for an ionospheric density profile that vanishes
at 125 km altitude. The peak density is at 140 km, with a value of
20,000 cm.
The thin lines show the temperature and cooling rate
for the same peak density and altitude, but with the ionospheric
minimum altitude at 130 km.
Because the vibrational cooling rate is proportional to
N ,
while the thermal conductivity is inversely proportional to
N
(through the collision frequency), small changes in the
minimum altitude of the ionosphere can have marked changes in
the vibrational cooling rate. The thin curves to the left of
Figure A2
show the temperature and cooling rate when we assume that the
electron density vanishes at an altitude of 130 km. Clearly, while
slightly elevated, the temperatures are much more reasonable. Thus
in section 5, where we discuss wave transmission including
vibrational cooling, we assume the bottom of the ionosphere is at
130 km.
As a last remark on inelastic cooling, we have not included
other cooling processes, such as the fine structure excitation of
atomic oxygen [Hoegy, 1976]. Except at higher altitudes (> 150
km), this cooling is relatively unimportant in comparison to the
cooling by CO.
However, a complete analysis of the electron heat
budget should in the future include this and other cooling terms
due to inelastic collisions with atomic oxygen.
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Text and figures by R.J. Strangeway
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Last modified: Feb. 10,1996
