Joule Dissipation in Planetary Ionospheres: Implications for Planetary Lightning

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

Fall AGU Meeting, 1994

Introduction

Recently, Cole and Hoegy [personal communication, 1994] and Hoegy and Cole [this meeting] have suggested that collisional Joule dissipation limits the allowed VLF wave amplitudes observed within the Venus ionosphere. In particular, they suggested that the VLF waves attributed to atmospheric lightning are of sufficient intensity to cause significant heating of the ionosphere, much more than is apparent in any in situ data.

In coming to this conclusion, it was assumed that Joule dissipation is only balanced by electron cooling through collisions with ions and neutrals. Electron heat conduction was ignored. We demonstrate here that electron heat conduction is a critical component in the energy budget within the ionosphere. Once this is included the energy deposited through Joule dissipation is easily absorbed by the ionosphere.

To do this we first present the heat budget equations. We then perform an order of magnitude estimation of the relative importance of the various heating and cooling terms. We find that collisional Joule dissipation is only important at low altitudes in the ionosphere of Venus.

In carrying out the order of magnitude estimates of the heating and cooling rates we do not take into account the attenuation of the waves themselves. To do this we perform detailed wave transmission calculations, which give both the attenuation of the waves, and the associated Joule dissipation rates. These calculations show that the wave bursts detected in the nightside ionosphere of Venus are consistent with lightning, this interpretation is not precluded through considerations of Joule dissipation.

Heat Budget Equations

Heat Budget Equations (12k gif)

Figure - Collision Frequencies (8k gif)

Wave Attenuation and Heating: Order of Magnitude Estimates

It is useful to estimate the relative importance of the various terms in Equation (1) prior to calculating detailed wave transmission characteristics. To this end, we assume that the electron temperature varies with a scale length L. Further, for simplicity, we assume that the ions and neutrals are cold when estimating the amount of collisional cooling in Equation (4).

There are two limits we consider here. One when electron-ion collisions dominate, the second when electron-neutral collisions dominate. The former mainly applies at higher altitudes, i.e., at the dayside ionopause and altitudes ~ 150 km in the nightside. The latter assumption is more appropriate for very low altitudes, i.e., the bottomside ionosphere.

Equations - Order of Magnitude Estimates (6k gif)

Figure - Dayside Ionopause - Heating Estimates (9k gif)

Figure - Nightside Ionosphere - Heating Estimates (11k gif)

Wave Attenuation and Heating: Detailed Calculations

To take into account the attenuation of the waves as they enter the ionosphere from below, we perform wave transmission calculations following the method of Huba and Rowland [JGR, 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, given by - div S||, where S|| is the parallel Poynting Flux. The temperature profile is then "bootstrapped" 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. [GRL, 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., GRL, 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.

To take into account the different ionospheric conditions encountered at Venus we use three different models:

1) Weakly attenuated 100 Hz waves. The peak density is 1000 cm-3, and the ambient magnetic field is 30 nT - a deep ionospheric hole.

2) Moderately attenuated 100 Hz waves. The peak density is 5000 cm-3, and the ambient magnetic field is 20 nT - a moderate hole.

3) Strongly attenuated 100 Hz waves. The peak density is 20000 cm-3, and the ambient magnetic field is 5 nT - typical ionosphere.

For all three cases we assume that the wave amplitude at 125 km is 10 mV/m. This amplitude is the sum of both incident and reflected waves. The amplitude reflection coefficient is typically ~0.98, and so the incident wave amplitude is ~ 0.5 V/m.

We find that the waves do deposit energy into the ionosphere, but only at very low altitudes, where the density is low. The electron temperature is elevated (~ 6 eV) at these lowest altitudes, but the low thermal conductivity allows for a steep temperature gradient, and no significant heating occurs at higher altitudes. Note that the Joule dissipation rates calculated using the divergence of Poynting flux are essentially identical to those computed using Equation (3).

Figure - 100 Hz, Weak Attenuation - Ionospheric Characteristics (10k gif)

Figure - 100 Hz, Weak Attenuation - Wave Parameters and Heat Budget (9k gif)

Figure - 100 Hz, Moderate Attenuation - Ionospheric Characteristics (10k gif)

Figure - 100 Hz, Moderate Attenuation - Wave Parameters and Heat Budget (9k gif)

Figure - 100 Hz, Strong Attenuation - Ionospheric Characteristics (10k gif)

Figure - 100 Hz, Strong Attenuation - Wave Parameters and Heat Budget (8k gif)

Conclusions

Any analysis of the importance of Joule dissipation in the ionosphere of Venus must include electron heat conduction. Heat conduction is much more effective in balancing the energy input from Joule dissipation.

At Venus, Joule dissipation due to electron collisions is unimportant at the dayside ionopause, or at moderate to high altitudes in the nightside ionosphere (~ 150 km).

Collisional Joule dissipation of lightning generated VLF signals could heat the bottomside ionosphere. However, the heating rate is small, and can be balanced through heat conduction. Joule dissipation does not preclude a lightning source for the VLF bursts in the nightside ionosphere of Venus.

The amplitude and attenuation scales of the VLF bursts detected at very low altitudes (~ 130 km) during the Pioneer Venus Orbiter entry phase [Strangeway et al., GRL, 23, 2771-2774, 1993] are consistent with the wave analysis presented here. Collisional Joule dissipation does not preclude a lightning source for these waves.

Addendum

Through conversations with Walt Hoegy, Tom Cravens, and Jane Fox at the Fall AGU Meeting, it has become clear that the neutral atmosphere can cool electrons very efficiently. In our calculations we neglected any cooling due to inelastic collisions (e.g., vibrational and rotational excitation of neutrals). The cooling due to inelastic processes can be quite large, perhaps sufficient to further reduce the temperature enhancements required to balance the Joule dissipation. The temperatures may be even lower than shown in this poster. We are currently revising our calculations to include inelastic cooling.


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