Collisional Joule Dissipation of Lightning Generated Plasma Waves in Planetary Ionospheres

R. J. Strangeway and C. T. Russell
Institute of Geophysics and Planetary Physics
University of California at Los Angeles

Spring AGU, May 1995

1. Introduction

Following the suggestion of Cole and Hoegy [personal communication, 1994], we have explored the effects of collisional Joule dissipation of plasma waves in the nightside ionosphere of Venus. This study has particular relevance for the interpretation of plasma waves detected at low altitudes in the Venus ionosphere as being due to atmospheric lightning. Depending on the amount of energy deposited into the ionsophere by the waves, we may find that the waves modify the ambient ionosphere sufficiently to yield detectable effects. For example, local "hot-spots", enhanced ionization, and perhaps even visible or ultraviolet radiation.

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.

2. Heat Budget Equations

3. Electron - CO2 Collisions

The dominant neutral species at low altitudes within the Venus ionosphere is CO2. It is therefore necessary to determine the CO2 cross-section and the elastic and inelastic cooling rates for electron - CO2 collisions. We base our analysis on the results of Morrison and Greene [J. Geophys. Res., 83, 1172-1174, 1978], who give tables and figures of the various electron cooling rates. These are summarized in the upper panel of Figure 1, where the symbols show the rates given by Morrison and Greene. The curves through the points are least-squares fits to the data that we have calculated for use in our wave propagation analysis.

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.

4. Wave Attenuation Without Vibrational Cooling

We perform wave transmission calculations following the method of Huba and Rowland [J. Geophys. Res., 98, 5291-5300, 1993]. In this method the wave electric field is calculated as a function of altitude, using finite differences. We have extended the scheme to also calculate the Joule dissipation rate. The temperature profile is then iteratively modified so that Equation (1) is satisfied. We impose an upper boundary condition of Te = 0.1 eV at the top of the model, at 150 km altitude.

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.

5. Wave Attenuation Including Vibrational Cooling

When we include the vibrational cooling we can no longer assume the density profile shown in Figure 2a. This is because the cooling is so large that the thermal electron heat flux is insufficient to balance the cooling at the lower altitudes, as can be seen on inspection of Figure 1 and Equations (2) and (5). From Figure 1, the cooling rate is proportional to Nn, while from Equations (2) and (5) the thermal conductivity is inversely proportional to Nn. Both are proportional to ne. The CO2 density scale height is ~ 2 km for the nightside ionosphere of Venus. If the heat flux gradient and the vibrational cooling are in equilibrium at one altitude, say 140 km, then at an altitude of 135 km the temperature gradient scale length must be roughly an order of magnitude smaller. Using the vibrational cooling rate shown in Figure 1, we have found that we can only maintain electron thermal equilibrium if we assume that the electron density is zero below an altitude of ~ 135 km.

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.

6. Conclusions

The results presented here can be taken as two limiting cases for the nightside ionosphere of Venus. The first, where we neglect inelastic cooling, corresponds to the case where some additional (as yet unknown) heat source balances the inelastic cooling. In that case, any heating due to plasma waves is balanced by divergence of the electron heat flux. In the second case, where we have included the effects of inelastic cooling, only the thermal electron heat flux balances the inelastic cooling in the absence of any wave heating. This results in a higher altitude bottomside ionosphere. As a consequence any waves propagating through the ionosphere are less strongly attenuated.

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.

IGPP/SSC home page     Pioneer Venus Orbiter OMAG/OEFD home page     Bob Strangeway's home page

Created by R. J. Strangeway


Last modified: February 8th, 2000.