Earlier analysis [Strangeway, submitted, J. Geophys. Res., 1995] has shown that plasma waves could heat the bottomside of the Venus ionosphere. This analysis showed that electron heat conduction provided a means for balancing the heating due to the plasma waves. At the same time, the low thermal conductivity at very low altitudes decoupled the region where most of the Joule dissipation occurred from the higher altitudes. However, the earlier analysis neglected the effects of inelastic collisional cooling. In this poster we will include this additional cooling process.
The cooling due to inelastic collisions tends to further reduce the effects of wave Joule dissipation. However, the inclusion of inelastic cooling has important consequences for the basic structure of the ionosphere. We find that in the absence of any additional heat sources the electron heat flux can only balance the inelastic cooling at altitudes above ~ 135 km.
From the momentum transfer cooling rate, and Equations (3) and (5), we have derived the electron - CO2 cross-section shown in the bottom panel of Figure 1. This cross-section has an asymptotic value of ~ 1.5 x 10^15 cm^2. Atomic oxygen, which is the second most abundant neutral has a cross-section ~ 2 x 10^15 cm^2.
Figure 1 shows that the cooling due to vibrational excitation of CO2 is the most important collisional cooling process for temperatures typically associated with the ionosphere of Venus. However, before including this cooling we will investigate the role of the electron heat conduction in balancing the heating due to collisional Joule dissipation of waves propagating through the ionosphere of Venus.
The other ionospheric parameters are fixed. We assume a neutral density profile as given by Kasprzak et al. [Geophys. Res. Lett., 20, 2747-2750, 1993], with CO2 being the dominant neutral at lowest altitude, O being dominant around 150 km. We assume the ions are O2+ [Grebowsky et al., Geophys. Res. Lett., 20, 2735-2738, 1993]. The electron density peak is assumed to be at 140 km altitude, and we further assume that the density goes to zero at 125 km altitude, where we start the wave transmission calculation.
Figures 2a,b and 2c,d shows the results of this calculation. We have assumed a 100 Hz wave. Most of the whistler-mode waves attributed to lightning are detected in the 100 Hz channel of the Pioneer Venus Orbiter. We have further chosen a relatively low peak density and high magnetic field strength, and the waves are weakly attenuated ( Figure 2c ). From Figure 2a we see that the bottomside electron temperature is elevated to ~ 7 eV. The resultant temperature gradient allows the heat flux to balance the Joule dissipation ( Figure 2d ).
Figure 3 shows the wave amplitude at 150 km for the range of likely peak densities and magnetic field strengths observed at Venus. Assuming a 100 Hz bandwidth, the Pioneer Venus wave instrument threshold correponds to a wave amplitude of ~ 10^-4 V/m. Clearly a strong magnetic field and low density is required for the waves to be detected by the Pioneer Venus Orbiter.
In Figure 3 we assume a net applied field of 0.01 V/m. Most (~ 97%) of the incident wave electric field is reflected, and the incident wave field is ~ 0.3 V/m. More intense electric fields could be present, but these fields would cause even more heating of the bottomside. We find that for the case shown in Figure 3, where we have neglected vibrational cooling, Te ~ 0.4LE eV, where L is the temperature gradient scale length (~ 2 km), and E is the net applied field in V/m.
Figures 4a,b and 4c,d show results of the wave transmission calculation, including vibrational cooling. Following the discussion above, we start the calculation at 135 km. The waves do cause some heating, the bottomside temperature is elevated to about 0.4 eV ( Figure 4a). However, because the neutral density is much lower, the collision frequencies are relatively low ( Figure 4b), and the wave attenuation is very weak ( Figure 4c). Figure 4d shows that the Joule dissipation is balanced by both vibrational cooling and thermal conductivity.
In Figure 5 we show the wave amplitude at 150 km, and we find that waves would be detectable by the Pioneer Venus Orbiter for a much larger range in density and magnetic field strength than shown in Figure 3.
Figure 6 shows the bottomside temperature. For the assumed wave amplitude we find the temperature is elevated to typically ~ 1 eV. More intense waves will cause more heating.
The actual nightside ionosphere of Venus probably lies somewhere between these two extremes. However, both limits indicate that while waves are attemuated as they propagate through the ionosphere, measurable fields are detectable at higher (~ 150 km) altitudes for sufficiently strong ambient fields and low enough peak densities. Moreover, the resultant heating can be absorbed within the ionosphere, primarily through the introduction of negative temperature gradients. Thus the bottomside ionosphere heats up, but the temperature gradient is sufficiently steep that the topside remains thermally decoupled. Very intense waves may cause additional heating at higher altitudes.
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Created by R. J. Strangeway
Last modified: February 8th, 2000.