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


Next: 6. Conclusions
Previous: 4. Lightning or Density Fluctuations
Top: Title and Abstract


5.       Lightning or Lower Hybrid Instability

      While the Langmuir probe anomalies are not strongly associated with the 100 Hz wave bursts, here we address the likelihood that the lower hybrid drift instability discussed by Huba [1992] and Huba and Grebowsky [1993] could be responsible for the 100 Hz bursts. Huba [1992] pointed out that although the lower hybrid resonance frequency is only a few Hz in the nightside ionosphere, sufficiently short wavelength waves can be Doppler-shifted to 100 Hz by the spacecraft motion. The spacecraft velocity 10 kms, and a wave with wavelength 100 m will be Doppler-shifted to 100 Hz. For an electron temperature of 0.1 eV, and a magnetic field strength of 30 nT the electron Larmor radius () is 35 m. Thus k 2, where k is the wave vector. Huba [1992] found that this wavelength range is typically unstable to the lower hybrid drift instability.

      The lower hybrid drift instability is generated by the relative drift between electrons and ions caused by a density gradient. The magnitude of the particle drift is determined by the gradient perpendicular to the ambient magnetic field; a parallel gradient does not cause a drift. The drift is perpendicular to both the magnetic field and the gradient, and the waves propagate in the direction of the drift. For a particular species the density gradient drift is given by

            (1)

where v is the thermal velocity of the species, L is the scale length of the density gradient and is the species gyro-frequency. For a magnetic field gradient the drift is given by

            (2)

where L is the scale length for the change in magnetic field magnitude.

      If the plasma is in pressure balance then it can be shown that

            (3)

where the subscript e and i denote electrons and ions respectively. If the ion and electron temperatures are equal then L = -L. Thus, as increases, the magnetic field gradient drift becomes comparable to the pressure gradient drift, but is in the opposite direction, and the instability is quenched for > 1. Low is therefore a necessary condition for both the lower hybrid drift instability and whistler-mode propagation in the nightside ionosphere of Venus.

      However, unlike the whistler-mode, low is not the only requirement for the lower hybrid instability. As noted above, the lower hybrid resonance frequency is only a few Hz, and the electron collision frequency can be large enough to damp the instability, especially for high densities and weak magnetic fields. The electron collision frequency v = 2.91 10nT s, where is the Coulomb logarithm 15, the density is expressed in cm and the temperature is in eV [Huba and Grebowsky, 1993]. For a density of 10 cm and a temperature of 0.1 eV, v = 15 s, while the lower hybrid resonance frequency () 30 rads when B = 30 nT. Thus, the collision frequency can be comparable with the wave frequency.

      Another condition that applies to the 100 Hz waves, but not to the density fluctuations, is the requirement that the wavelength be 100 m, so that the wave can be Doppler-shifted to 100 Hz through spacecraft motion. Huba and Grebowsky [1993] found maximum growth occurred for k 2, although the actual value depended on the choice of the plasma parameters, and the gradient scale length. As noted above, this implies an electron Larmor radius 35 m, which for T = 0.1 eV requires a magnetic field strength of 30 nT. If the field strength is smaller than this, then the k required for Doppler-shift to 100 Hz becomes too large, and the waves tend to be damped.

      Thus, the lower hybrid drift instability requires low , low collision frequencies, and small electron Larmor radii to generate short wavelength waves that can be Doppler-shifted to 100 Hz. In Figure 11 we show where the burst intervals used in determining the burst rates discussed above occur as a function of electron density and magnetic field strength. In order to explore whether or not these bursts correspond to lower hybrid drift waves, we have plotted several reference curves. Above, we discussed the various parameters relevant to the lower hybrid instability assuming an electron temperature of 0.1 eV. However, the temperature is not constant, and we find that T = 0.188 (n/2.45 10) for the burst intervals, using a least squares regression, where T is in eV, and n is in cm. The correlation coefficient is 0.686, with 1234 points. This regression line allows us to specify the temperature for a given density, and so determine the following reference curves as a function of density and magnetic field strength: = 1, v/ = 0.25, and k = 3. As an approximate rule of thumb, we expect the lower hybrid drift instability to generate Doppler-shifted 100 Hz waves in regions for smaller values of these parameters.

Fig. 11.     Scatter plot of burst occurrence as a function of electron density and magnetic field strength. Various limiting curves are also shown. The lower hybrid drift instability is most likely to occur for low , low v/, and low k. The whistler-mode requires low only. At any particular density, lower values of , v/, and k lie above the limiting curves shown.

      Figure 11 indicates that there are large regions of the B-n parameter space where bursts occur, but the approximate conditions for lower hybrid instability are not satisfied. However, most of the bursts occur in the region where < 1, as we expect for the whistler-mode. A word of caution is in order when interpreting Figure 11. The various limiting curves are indicative of the likely region of lower hybrid drift instability, but we have not performed an instability analysis. Huba and Grebowsky [1993] present instability limits in a similar format. They find that for sufficiently high drift speeds, corresponding to short gradient scales, the collision frequency and constraint can be relaxed for high densities, while the Larmor radius restriction is less important for low densities. The maximum drift speed used is twice the ion thermal velocity, i.e., v 2 kms. From (1) v/v = /2L, implying that L 0.25. The ion Larmor radius is 10 km for B 30 nT, and the high drifts invoked by Huba and Grebowsky [1993] correspond to gradients scale lengths 2.5 km. This is an extremely short scale length; with this scale length, the density changes by two orders of magnitude in 12 km which, for a spacecraft velocity of 10 kms, would correspond to a two order of magnitude change in density in just over 1 s. Another possible restriction of the applicability of the lower hybrid drift instability at Venus is the extremely narrow propagation angle because the plasma composition is mainly O. Huba and Grebowsky [1993] note that electron Landau damping will become important for angles ~ 0.33° away from perpendicular propagation.

      In summary, it is possible that the lower hybrid drift instability can operate in the Venus nightside ionosphere. However, the gradients required are extremely steep, and electron Landau damping is likely to be important. In addition, we noted earlier that the association between Langmuir probe anomalies and 100 Hz bursts is low, about 20%. Thus, the lower hybrid drift instability may explain the anomalies reported by Grebowsky [1991], but it only explains a small fraction of the 100 Hz bursts observed at Venus. The 100 Hz waves are more likely to be whistler-mode waves.


Next: 6. Conclusions
Previous: 4. Lightning or Density Fluctuations
Top: Title and Abstract


To R. J. Strangeway's homepage

Text and figures by R. J. Strangeway
Converted to HTML by R. J. Strangeway
Last modified: Feb. 16, 1996