*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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6. Conclusions

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4. Joule Dissipation: Self-Consistent Altitude Dependence

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Title and Abstract

Figures
4a, 4b,
4c, 4d,
5a, 5b,
5c, 5d,
6a, 6b,
6c & 6d
show that the electron cooling rate due to the
vibrational excitation of
is about 3 orders of magnitude larger
than the cooling due to elastic collisions. As such this cooling
should be included in the heat budget. However, as noted in the
appendix, the vibrational cooling operates even in the absence of
any wave heating, and a downward heat flux is required to offset
this cooling. Consequently, unless *Morrison and Greene* [1978]
significantly overestimate the cooling rates, the bottom of the
ionosphere may be as high as 130 km. In assessing the effect of
vibrational cooling we will therefore assume that the
*z* = 130 km,
instead of 125 km as used in the previous section. Prior to
presenting results of the wave attenuation calculations, however,
we note that attempts to obtain solutions for
*z* = 125 km resulted
in unrealistically high topside temperatures, unless intense waves
( ~ 0.1 V/m amplitude) were applied at the bottomside of the
ionosphere. These waves provide enough heat to offset the
vibrational cooling, without requiring any additional downward
heat flux. Less intense waves did not supply enough heat at the
bottomside when *z*= 125 km.

In Figure 7 we plot solutions of the wave attenuation calculation for four cases: 10 mV/m applied field, weak attenuation (Figure 7a); 100 mV/m applied field, weak attenuation (Figure 7b); 10 mV/m applied field, strong attenuation (Figure 7c); and 100 mV/m applied field, strong attenuation (Figure 7d). For the weakly attenuated waves we assumed a peak electron density of 1000 cm and an ambient field strength of 30 nT. For strong attenuation we assumed a peak density of 20,000 cm and a field of 5 nT. The wave amplitudes have been chosen to reflect the average and extreme amplitudes expected at the bottomside. Since many of the features of the model have been shown in Figures 4a, 4b, 4c, 4d, 5a, 5b, 5c, 5d, 6a, 6b, 6c & 6d , we only show the heat budget terms, and the temperature and wave electric field profile in Figure 7.

Figure 7a shows the results for moderate amplitude, weakly attenuated wave field. In this case the vibrational cooling is large enough to offset the Joule dissipation, at least for some of the altitude range. The peak cooling rate is ~ 5 10 W/m ~ 3 10 eV cm s . For larger amplitude waves, Figure 7b shows that the vibrational cooling is insufficient to balance the Joule heating. The temperature is therefore elevated, in comparison to Figure 7a. Throughout the altitude range shown Joule heating is balanced by electron heat conduction. Thus only about 10% of the energy released through Joule dissipation actually causes vibrational excitation of CO , one cannot simply equate the Joule dissipation rate to a neutral atmosphere heating rate. The peak vibrational cooling rate is ~ 3 10 W/m, roughly an order of magnitude larger than that obtained for a 10 mV/m applied wave field. It should also be noted that the strongest cooling, i.e., the most rapid transfer of heat to the neutrals, does not occur where the electron temperature is highest.

Figures 7a & 7b, Figures 7c & 7d. Heat budget, electron temperature, and wave amplitude as a function of altitude, including vibrational cooling in the heat budget. (a) Weakly attenuated, moderate amplitude signal; (b) weakly attenuated, high amplitude signal; (c) strongly attenuated, moderate amplitude signal; (d) strongly attenuated, high amplitude signal.

An applied field of 100 mV/m is extremely large,
corresponding to the very intense burst observed by the Pioneer
Venus Orbiter, at ~ 128 km on Orbit 5055, assuming a 100 Hz
bandwidth. Moreover, most of the incident wave electric field is
reflected. For Figure 7b
, the incident wave field is ~ 5 V/m, which
is typical for electric fields due to terrestrial lightning at 100 km
away from the lightning strike [*Uman*, 1987]. Since the spectral
peak of lightning is usually in the few kHz range, we might expect
the wave amplitude at 100 Hz to be typically about a factor of 10
less. Furthermore, while wave fields incident on the dayside or
dusk ionosphere might be expected to be of this amplitude, since
this is the local time range over which lightning appears to occur
on Venus [*Russell*, 1991], in the nightside the waves are thought to
have traveled some distance in the surface-ionosphere waveguide
[*Strangeway*, 1995b], and we expect lower amplitudes. Last, if as
we suggest here, the ionosphere is above 130 km altitude, it is
possible that the spacecraft was below the ionosphere for the
lowest-altitude measurements, and the wave fields measured at ~
128 km may include vertical electric fields that are shielded from
higher altitudes.

Figures 7c and 7d show the wave attenuation and heat budget for strongly attenuated signals. The decoupling of the bottomside from the topside is shown clearly in Figure 7c, where there is a temperature minimum at ~ 136 km. At higher altitudes, where the thermal conductivity is higher, a relatively weak positive temperature gradient provides the heat flux necessary to offset the vibrational cooling. At lower altitudes, where the Joule dissipation is occurring and the conductivity is lower, a stronger negative temperature gradient provides the upward heat flux. In Figure 7d, where the applied field is 100 mV/m, the topside electron temperature is slightly elevated. However, in Figures 7c and 7d the maximum vibrational cooling occurs at altitudes above the maximum Joule dissipation.

From Figure 7c one could perhaps come to the somewhat surprising conclusion that a modest amount of wave Joule dissipation is required to offset the vibrational cooling. In Figure A2, where there is no wave heating, we find a topside temperature of 0.5 eV is required to provide the necessary downward heat flux. Because of the wave heating in Figure 7c, less heat flux is required from above, and a more reasonable topside temperature of 0.1 eV is obtained.

We can use
Figure 7c
as a guide for how much heating of
the neutral atmosphere is reasonable. The peak cooling rate in
Figure 7c
is ~ 10 W/m,
where the electron density is ~ 20,000
cm
, and *T*
~ 0.1 eV (again in a region where there is no wave
Joule dissipation). Unless the vibrational cooling rate is severely
overestimated, it seems reasonable to assume that the neutral
atmosphere can readily absorb heat supplied at this rate, ~ 6
10
eV cm
s
, since the plasma parameters are consistent with in
situ observations. At 140 km both O and CO
have densities of
~ 2
10 cm,
and assuming that the vibrational energy is
ultimately converted to thermal energy [*Cole and Hoegy*, 1995],
we get a heating rate of 0.04 K s
atom, which for a neutral gas
temperature of ~ 100 K, gives a doubling time of 2500 s, a little
over 40 min.

Taking an electron cooling rate of 10
W/m as a rate that
does not seriously perturb the atmosphere, only the strongly
attenuated large amplitude waves (
Figure 7d) appear to be capable
of perturbing the atmosphere when we incorporate vibrational
cooling in our calculation. Even then, the net heating rate is only ~
0.4 K s atom.
However, we have not included other inelastic
processes, specifically electronic excitation of
CO and O, which
are likely to be important when electron temperatures are a few eV.
Enhanced ionization may even be possible. Such processes are
thought to occur at the Earth [*Taranenko et al*., 1993a, b] in
association with lightning, and it appears reasonable to expect
similar effects at Venus for the most intense waves.

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6. Conclusions

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4. Joule Dissipation: Self-Consistent Altitude Dependence

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Text and figures by R.J. Strangeway

Converted to HTML by Chris Casler

Last modified: Feb. 10,1996