VLF Waves in the Foreshock

R. J. Strangeway* and G. W. Crawford**

*Institute of Geophysics and Planetary Physics,
University of California at Los Angeles

**Radio Atmosphere Science Center
Kyoto University at Kyoko 611, Japan
Now at SRI International, Menlo Park, California 94025, U. S. A.

Adv. Space Res., vol 15, (8/9)29-(8/9)42, 1995
Copyright 1995 by COSPAR

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Down-shifted Plasma Oscillations

      In addition to the emissions at the plasma frequency that occur close to the tangent field, VLF waves are also observed at frequencies below the plasma frequency in the terrestrial foreshock /34, 35/. These waves are referred to as down-shifted plasma oscillations. It should be noted that "down-shift" does not mean that the waves are shifted in frequency due to a frame transformation, as opposed to ion acoustic waves, for example, which are "up-shifted" to several kHz in the ion foreshock because of their short wavelength. The down-shift is too large to be accounted for simply by Doppler-shift /35/. An example of down-shifted plasma oscillations is shown in Figure 7 The top panel shows wideband electric field data from the ISEE-1 spacecraft. The bottom panel shows the distance behind the tangent field line ("Diff"). The sign convention for Diff is the opposite of the convention we have used in discussing the PVO observations, with negative Diff corresponding to locations behind the tangent field line. A narrow-band intense wave emission is observed when the spacecraft is close to the tangent line. Just behind the tangent line this emission tends to increase in frequency, but at much greater depths the emission moves to lower frequencies. Typically the plasma frequency wave amplitude is a few mV/m, while the down-shifted emission is much weaker, only a few 100V/m /34/. In terms of wave power, the plasma frequency emission can be as intense as 10-10 V2/m2/Hz, and the down-shifted emission is typically less than 10-12 V2/m2/Hz /34/.

Fig. 7. Example of down-shifted plasma oscillations observed in the terrestrial electron foreshock (after /35/).

      The most energetic reflected electrons are found close to the tangent field line. At greater depths the energy decreases. This decrease in the electron beam energy appears to explain the down-shift, as shown in Figure 8 (after /35/). This figure shows the results of a linear stability analysis where the ambient electrons are represented by a Maxwellian distribution, and the beam electrons are modeled by a Lorentzian distribution. The left panel of the figure shows that the maximum growth rate decreases as the beam velocity decreases with respect to the ambient electron thermal velocity. In addition, the frequency at which the maximum growth occurs shifts to progressively lower frequencies with respect to the plasma frequency. This conclusion is reinforced in the right panel which shows the frequency of maximum growth as a function of beam velocity for different beam temperatures.

Fig. 8. Solutions of the beam-plasma dispersion relation. The left panel shows growth rate versus frequency for different beam velocities. The right panel shows the frequency at which maximum growth occurs as a function of beam velocity for different beam temperatures (after /35/).

      Given many of the similarities of the terrestrial and Venusian bow shock and electron foreshock, it appears reasonable to expect that down-shifted plasma oscillations should also be present at Venus, but Figures 5 and 6 show no evidence of these waves. The lack of down-shifted oscillations appear to be mainly due to the limitations of the PVO wave instrument /26, 32/. First, the large frequency spacing between channels (5.4 kHz and 30 kHz), coupled with the relatively narrow bandwidth of the frequency filters (30%) implies that down-shifted waves will not be well sampled by the instrument. Second, and perhaps more importantly, the short antenna length reduces the sensitivity of the PVO instrument. The background level of the color plots in Figures 5 and 6 is the instrument background. At 30 kHz this level is 5 10-13 V2/m2/Hz. The peak intensities at the tangent field line are 5 10-10 V2/m2/Hz, which is comparable to the terrestrial observations, while the instrument threshold is comparable to the down-shifted wave intensities /34/. Thus the PVO instrument is not likely to observe the down-shifted waves. However, such waves are present at Venus. The much more sensitive Galileo wave instrument detected down-shifted plasma oscillations during the flyby of Venus. These emissions depended on depth in a manner similar to the terrestrial observations /36/.

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