Plasma Wave Evidence for Lightning on Venus

J. Atmos. Terr. Phys., 57, 537-556, 1995
(Received in final form 19 May 1994; accepted 27 June 1994)
Copyright © 1995, Elsevier Science Ltd

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3.       Lightning or Whistler-Mode Instability

      Several authors have suggested that the VLF bursts detected at low altitudes in the Venus nightside ionosphere are generated locally, rather than through lightning in the Venus atmosphere. In addition to comments on the association of 100 Hz waves with holes, Taylor et al. [1987] noted that the waves detected at 100 Hz were observed primarily when the spacecraft velocity vector was perpendicular to the ambient magnetic field. They argued that the waves were in fact short wavelength waves propagating parallel to the ambient field which could be Doppler-shifted to higher frequencies and the selection criterion used by Scarf and Russell [1983] requiring bursts at 100 Hz only artificially excluded those waves that had been Doppler-shifted through spacecraft motion. Figure 8, from Ho et al. [1992], shows that the burst rate for 100 Hz waves was largest when the magnetic field was vertical. The data are plotted as a function of the angle between the magnetic field and the radial direction (), and the angle between the magnetic field and the spacecraft velocity vector (). Since the spacecraft motion is nearly horizontal around periapsis, a vertically oriented magnetic field will be perpendicular to the spacecraft velocity vector. In determining the dependence on magnetic field orientation, no selection criteria, other than an intensity threshold, were applied to the data. Thus, that the waves are observed for vertical field is an intrinsic property of the signals, and is not due to some selection criteria artificially rejecting those events for which the spacecraft velocity vector is parallel (not perpendicular as stated in the published version of this paper) to the field. It is hence unlikely that the 100 Hz bursts are parallel propagating ion acoustic waves. Alternative wave instabilities that have been suggested are cyclotron resonant whistler-mode instabilities [Maeda and Grebowsky, 1989] and short wavelength lower hybrid waves [Huba, 1992]. Both these instabilities generate waves that would be detected in the 100 Hz channel of the OEFD.

Fig. 8.     100 Hz burst rate dependence on the magnetic field orientation [after Ho et al., 1992]. The upper plot shows the time spent as a function of (the angle between the magnetic field and the radius vector) and (the angle between the magnetic field and the spacecraft velocity vector). Note that, for 0°, 90°. The lower plot shows the burst rate, which peaks at 0°. At higher there is no dependence on .

      In this section we will concentrate on whistler-mode instabilities. Maeda and Grebowsky [1989] argued that the signature of VLF saucers, which occur at low altitudes in the Earth's auroral zone ionosphere, would be similar to the bursts detected at Venus by the OEFD, if the same instrument were to be flown at the Earth. However, this argument neglects a fundamental difference between the terrestrial and Venusian ionosphere. At the Earth, there is a strong internal magnetic field that ensures that the plasma is low ( = , the ratio of thermal to magnetic energy density, where is the permeability of free space, n is the plasma number density, k is the Boltzmann constant, T is the plasma temperature, and B is the ambient magnetic field strength). At Venus, on the other hand, the magnetic field is relatively weak and the plasma can have a high , as noted by Strangeway [1990].

      This point was discussed further by Strangeway [1992]. For the sake of discussion, we will assume that the electron density in an ionospheric hole 3 10 cm, and the magnetic field 30 nT. For these values the electron plasma frequency - gyro-frequency ratio (/) 500. This ratio will be higher outside of holes since the magnetic field is weaker and the density is higher. Whistler-mode dispersion curves for this ratio are shown in Figure 9. The figure shows that the highest parallel phase speed is 300 kms, corresponding to an electron energy of 0.26 eV. Thus we expect whistler-mode waves to be damped by thermal electrons in the nightside ionosphere of Venus, and this damping will suppress any whistler-mode instability.

Fig. 9.     Whistler-mode dispersion curves for different propagation angles [after Strangeway, 1992]. Wave frequencies are normalized to the electron gyro-frequency, while the parallel wave vector is normalized to the inverse of t he plasma skin depth. The shaded regions show where thermal electron Landau and gyro-damping are expected to occur.

      To demonstrate this point more clearly, in Figure 10 we plot the damping rate of 100 Hz waves as a function of the normalized electron thermal velocity (v/c)(/), where v is the thermal velocity of the electrons. We have used the convention that 1/2mv = kT. The normalized thermal velocity = , where is the electron beta. In calculating we have used 2-s averages of the electron density and temperature measured by the Langmuir probe onboard the Pioneer Venus Orbiter, and the magnetic field. The data were acquired from orbits 484 - 560, and we have restricted the altitude range to < 300 km. The convective damping rate has been calculated for parallel propagating waves at 100 Hz. We find that for = 1, the damping decrement is 5 dB/km. Thus the wave intensity will have decreased by ten orders of magnitude after propagating some 20 km in the nightside ionosphere. Clearly whistler-mode waves cannot propagate any great distance in the high regions of the nightside ionosphere. Thus ionospheric holes, which are low , are where whistler-mode waves are more likely to be found. The magnetic fields within holes also have a large vertical component, allowing vertical propagation of whistler-mode waves from below the ionosphere. That 100 Hz wave bursts are found within ionospheric holes is entirely consistent with the lightning hypothesis. Strangeway [1992] further showed that the 100 Hz wave intensity was largest in regions where the thermal electron damping was lowest.

Fig. 10.     The convective damping rate of 100 Hz whistler-mode waves as a function of the normalized electron thermal velocity (= ). The observed magnetic field strength, electron density and temperature are used to calculate the damping rate for parallel propagating whistler-mode waves at 100 Hz, assuming an isotropic plasma. The thick line passing through the data gives the median as a function of the damping rate, binned every half decade. A damping rate of 8.686 dB/km corresponds with 1 e-folding of the wave amplitude/km.

      As a last comment on the work of Maeda and Grebowsky [1989], Strangeway [1992] also investigated a beam driven instability. He assumed a beam density of 5 cm, parallel drift speed = parallel thermal velocity = 0.007c (12.5 eV), and a temperature anisotropy T/T = 2. This beam represented precipitating solar wind electrons that had gained access to the nightside ionosphere of Venus. He found growth rates less than 0.1 dB/km, requiring growth paths of at least 1000 km for a gain of 100 dB. It is hence very difficult for whistler-mode waves to grow to appreciable intensities within the nightside ionosphere, especially at low altitudes.

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