Collisional Joule dissipation in the ionosphere of Venus: The importance of electron heat conduction

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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5.       Cooling Through Inelastic Collisions

      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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Text and figures by R.J. Strangeway
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Last modified: Feb. 10,1996