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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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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