**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
Plasma waves observed in the VLF range upstream of planetary bow shocks not only modify the particle distributions, but also provide important information about the acceleration processes that occur at the bow shock. Electron plasma oscillations observed near the tangent field line in the electron foreshock are generated by electrons reflected at the bow shock through a process that has been referred to as Fast Fermi acceleration. Fast Fermi acceleration is the same as shock-drift acceleration, which is one of the mechanisms by which ions are energized at the shock. We have generated maps of the VLF emissions upstream of the Venus bow shock, using these maps to infer properties of the shock energization processes. We find that the plasma oscillations extend along the field line up to a distance that appears to be controlled by the shock scale size, implying that shock curvature restricts the flux and energy of reflected electrons. We also find that the ion acoustic waves are observed in the ion foreshock, but at Venus these emissions are not detected near the ULF foreshock boundary. Through analogy with terrestrial ion observations, this implies that the ion acoustic waves are not generated by ion beams, but are instead generated by diffuse ion distributions found deep within the ion foreshock. However, since the shock is much smaller at Venus, and there is no magnetosphere, we might expect ion distributions within the ion foreshock to be different than at the Earth. Mapping studies of the terrestrial foreshock similar to those carried out at Venus appear to be necessary to determine if the inferences drawn from Venus data are applicable to other foreshocks.
Collisionless shocks provide a myriad of phenomena that occur on many different scales, from ion inertial lengths, through ion Larmor radii, to scales of many planetary radii. At the same time, the physics involved may be expressed by simple magnetohydrodynamics, or particle trajectory analysis, or fully kinetic plasma theory. The tools employed include analytic theory, simulations, and data analysis. In this paper we will discuss just one aspect of collisionless shocks, that is the VLF waves that are observed upstream of a planetary bow shock in the region known as the foreshock. Although primarily based on data analysis, we will also discuss some wave instability theory, and the mechanisms by which particles gain energy at a shock.
VLF wave generation is a microscale phenomenon, but the morphology of the waves allows us to make inferences concerning the energization processes that occur at a shock. Moreover, we will show that while the energization occurs on mesoscales, the macroscale of the shock itself appears to be a limiting factor on this process. This will be most clear through analysis of the waves observed in the electron foreshock, and we will devote much of this paper to the electron foreshock, although we will also discuss ion foreshock waves. Our understanding of the electron dynamics within the shock and foreshock appears to be much firmer /1, 2, 3/. While there has been significant progress in our understanding of the ion dynamics /4, 5, 6, 7/, how the ion distributions within the foreshock interact, how they evolve, and nature of their relationship with both ULF and VLF waves is still a topic of some debate /8, 9, 10/.
Before discussing the VLF observations we will briefly review some of the basic theory on electron reflection and energization at a shock. This will not be a comprehensive review of particle dynamics and energization. In particular we will not discuss in detail why electron dynamics are best investigated in the de Hoffman-Teller (HT) frame /11/, while ion dynamics are more readily understood in the normal incidence frame (NIF). Instead we refer the reader to the excellent articles that discuss why the presence of a non-coplanar magnetic field allows the magnetized electrons to be only affected by the HT frame cross-shock potential, while the unmagnetized ions respond to the full potential in the NIF /12, 13, 14/. Having reviewed the electron reflection process at the shock, we will present some examples of VLF wave data, obtained by the Pioneer Venus Orbiter (PVO). We will then present images of the VLF emissions in the ion and electron foreshock generated from statistical studies of the foreshock at Venus. The most significant result of the imaging is the observation of a finite extent to the electron foreshock emissions, which we attribute to the scale size of the shock acting to restrict the availability of energetic electrons far from the shock. We will then discuss why the limitations of the PVO wave instrument do not allow us to observe down-shifted plasma oscillations in the foreshock. Lastly, we will summarize the results presented in the paper, including some comments on the apparent disparity between the ULF and VLF waves within the ion foreshock.
The energetic electrons responsible for the generation of VLF waves in the electron foreshock are mainly of solar wind origin. While energetic electrons could possibly be of magnetospheric origin at the Earth, the presence of electron foreshock VLF waves upstream of the bow shock of Venus, for example, implies that the electrons are indeed accelerated at the shock. Leroy and Mangeney /15/, amongst others, discussed the acceleration of electrons at a bow shock, using the de Hoffman-Teller (HT) transformation /11/ to facilitate their discussion of acceleration, transmission and reflection. The HT transformation is carried out by moving along the shock surface with the velocity that aligns the upstream flow velocity and magnetic field in the transformed frame. In this frame the motional electric feld has been transformed away. Thus there can be no energization of reflected electrons in the HT frame, assuming a time stationary shock structure.
The HT frame is a particularly useful frame for discussing the processes involved in electron transmission and reflection at the shock, as can be seen in Figure 1. The left of this figure, after /15/, shows phase space contours of the incident and reflected solar wind electrons. The solar wind has been transformed into the HT frame, and the incident flow is field-aligned, with positive velocities corresponding to flow into the shock from upstream. The dashed hyperbola in the figure gives the boundary between transmitted and reflected electrons. In the HT frame only the jump in the magnetic field causes electron reflection at the shock. In the absence of a field-aligned electric field within the shock, the boundary between transmitted and reflected electrons is a cone. The shock electric field, which retards the ions, accelerates the electrons through the shock, widening the transmission cone into the hyperbolic shape sketched in panel a) of Figure 1 The portion of the incident solar wind that lies outside of this boundary is reflected at the shock and travels back upstream. It is this reflected population that is believed to generate electron plasma oscillations in the electron foreshock.
Fig. 1. a) Phase space contours of the incident and reflected solar wind electron population, in the de Hoffman-Teller frame (after /15/). b) Reflected electron flux and energy as a function of bn (after /15/).
The de Hoffman-Teller velocity in the observer's frame (which is assumed to be at rest with respect to the shock surface) is given by
where n is the shock normal, v0 is the solar wind velocity in the observer's frame, b is the unit vector along the magnetic field,vn is the angle between the solar wind velocity vector and the shock normal, and bn is the angle between the magnetic field and the shock normal. Taking primed vectors to be measured in the HT frame, the transformation from shock frame to HT frame is given by v' = v - vHT.
In the HT frame the solar wind moves towards the shock with a speed given by v0' = v0 cos vn/cos bn along the magnetic field. Since the magnetic field increase at the shock acts as a mirror, the solar wind sees a magnetic mirror moving with the speed v0', and particles reflected by this moving mirror gain twice this speed in the solar wind frame. Thus this process has been named Fast Fermi acceleration /16/. At first sight, it appears that electrons can gain an arbitrary amount of energy, depending on bn. As bn 90°, v0' , ignoring relativistic effects. However, as pointed out in /15/, the mirror efficiency 0 as bn 90°. This can be seen on consideration of Figure 1 As v0' increases, the whole solar wind population moves to higher parallel velocity, and more and more of the solar wind population lies within the transmission cone. This is further demonstrated in panel b) of Figure 1.
Another point alluded to in /15/ and /16/, but not discussed in detail, concerns the effect of shock curvature. In carrying out the HT frame transformation we assume an infinite planar shock. In reality, planetary bow shocks are curved. This affects the reflection process in two ways. First the area of the curved bow shock over which reflection occurs becomes vanishingly small as bn 90°, and so the net flux of reflected particles must 0. Second, the amount of energy gain will be restricted by the curvature of the shock. In the HT frame the reflected particles gain no energy, but in the shock frame the particles have gained energy, corresponding to the moving mirror speed. This energy gain can only come from the motional electric field -v0 B. Furthermore, the electrons gain this energy by drifting along the shock, i.e., shock-drift acceleration /4, 5/. Although shock-drift acceleration is usually discussed in the context of ion acceleration at the shock, the same principles apply to electron acceleration. Taking a solar wind flow velocity of 400 kms-1, and an upstream magnetic field strength of 10 nT, the motional electric field is 4 mV/m. The tangential electric field is continuous across the shock, and so a particle gains an energy of the order 25 keV/Re in drifting along the shock surface. For a shock, such as the terrestrial bow shock, whose radius of curvature is of the order 20 Re, electrons can gain moderately high energies before shock curvature effects become significant. However, for smaller shocks, such as the Venus bow shock, whose radius of curvature 2 Rv (1 Rv = 6052 km, 1 Re = 6371 km), curvature effects are likely to limit the energy gain of the electrons. At Mars, with an even smaller radius of curvature, and weaker magnetic field, we would expect the effect of shock curvature to be even more significant.
Since shock curvature changes bn along the bow shock, we expect electrons which encounter the shock further downstream to in general gain less energy than those electrons that encounter the bow shock near the point of where the IMF is a tangent to the shock surface. This tangent field line also marks the limit of accessibility for reflected particles, since they are convected downstream by the solar wind motional electric field. The lower energy particles take longer to travel any given distance along the field, and so they are convected further downstream by the solar wind electric field. This time-of-flight effect was first used by Filbert and Kellogg /17/ to explain the presence of electron plasma oscillations in the electron foreshock. In Figure 1 all the particles outside of the transmission cone are reflected. However, at any particular location in the foreshock, there exists a critical parallel velocity, below which the particles are convected downstream before they can propagate from the shock to the point of observation. The resultant low energy cut-off in the reflected population introduces a positive slope in the reduced distribution function (i.e., the distribution function integrated over v ), which can generate plasma oscillations through the bump-on-tail instability.
Fitzenreiter et al. /18/ developed a model for electron distributions in the foreshock. In their work they took into account the curvature of the shock through changes in the HT speed as a function of bn, and through kinematic restrictions on the allowed trajectories. Figure 2 shows some results of their modeling. Two effects are clear from the figure. The first is that the reflected distribution lies at oblique angles with respect to the magnetic field. The boundaries of the "earlike" structure are given by the transmission cone at high energy, and the time-of-flight cut-off velocity at low energy. As discussed in /18/, the distribution is built up from reflected electrons from different portions of the shock. The net effect of this is to steepen the time-of-flight gradient in the distribution. The second effect in Figure 2 is that the instrument sampling smears any gradients in the phase space distribution. Thus, because of instrument sampling, and also the smoothing that occurs in response to the wave generation, the typical signature of the reflected electrons tends to be a high energy tail. The break in the distribution marks the cut-off velocity.
Fig. 2. Foreshock electron distributions (after /18/). The left panels (a) show theoretical phase space density contours, together with the reduced distribution function. The right panels (b) show the same phase distributions, but sampled in a manner similar to a particle instrument. In this case the reduced distribution functions (solid curves) are compared with actual observations (dotted curves).
The basic concepts of "Fast Fermi" acceleration at the bow shock and time-of-flight cut-offs appear to be sufficient to explain many of the features of VLF waves in the electron foreshock, as we shall see below. However, there are still some effects not yet incorporated into theory, primarily the restriction on electron energization imposed by shock curvature, as briefly discussed above. This can best be seen through studies of the electron foreshock at Venus.
In order to understand VLF wave phenomena in the Venus foreshock it useful to make use of a coordinate system first derived for terrestrial observations /17, 19/, shown in Figure 3 for the Venus bow shock /20, 21/. This figure shows the IMF, solar wind, bow shock, and the observing spacecraft (PVO) in the aberrated Venus Solar Orbital (VSO) coordinate system. (VSO coordinates are analogous to Geocentric Solar Ecliptic Coordinates.) In Figure 3 we have assumed that the plane containing the solar wind and IMF, the B-v plane, also contains the center of the planet. For convenience we refer to this as the equatorial plane. In general, the observing spacecraft need not lie in the equatorial plane, but the geometry is similarly defined, except that the B-v plane containing the spacecraft intersects the bow shock in a plane parallel to the equatorial plane. The tangent field line then intersects the shock further downstream from the point of tangency in the equatorial plane.
Fig. 3. Foreshock coordinate system at Venus (after /20, 21/).
Depending on the phenomenon of interest, various coordinates systems can be chosen. However, given the discussion in the previous section, we use the distance along the tangent field line and the depth downstream from the tangent field line to the point of observation as the foreshock coordinate system. For a reflected particle the distance depends primarily on the parallel reflection velocity, while the depth is governed by the solar wind flow. An alternative coordinate system could use the time-of-flight angle (), and the distance traveled along the time-of-flight velocity vector, indicated by the dashed line. Other parameters of interest include the shock normal direction (bn) as measured at the point of intersection on the bow shock of the field line passing through the spacecraft, and the distance along the field line from the bow shock to the spacecraft. Note that as drawn in Figure 3 the shock normal lies in the B-v plane, but this is not the case when the B-v plane containing the spacecraft lies above or below the equatorial plane.
An example of the VLF emissions observed in the foreshock of Venus is shown in Figure 4 /20, 21/. This figure shows 1 hr 45 min of data acquired by PVO when it was in the solar wind, some 5 Rv behind and the terminator and about 7 Rv from the Venus-Sun line. The top four panels show wave electric field intensity, measured at 30 kHz, 5.4 kHz, 730 Hz, and 100 Hz, which are the four frequency channels of the Orbiter Electric Field Detector (OEFD). The OEFD was restricted to these four frequencies because of the power, weight, and telemetry restrictions of the Pioneer Venus Orbiter /22, 23, 24/. Because the OEFD antenna is so short, 0.76 m, the wave instrument suffers from high levels of interference when the spacecraft is in sunlight and the plasma Debye length is large, as occurs when the spacecraft is in the solar wind. The 100 Hz channel is most susceptible to this interference. However, in Figure 4 we have applied a noise removal scheme based on Bayesian statistical methods /25/ to the data, and much of the noise has been removed. The middle four panels in Figure 4 show the magnetic field components in VSO coordinates and total field strength. The bottom two panels show depth behind the tangent field line, and bn at the bow shock intersection point of the field line passing through the spacecraft. When the depth is negative the spacecraft is upstream of the tangent field line, and bn is not defined. On the other hand, depth is not defined if the magnetic field becomes sufficiently close to radial that there is no field line that is tangent to the bow shock, although bn is defined. The changes in depth and bn are mainly due to changes in the IMF orientation, rather than spacecraft motion.
Fig. 4. Example of VLF emissions observed in the foreshock at Venus (after /20, 21/).
In Figure 4 waves are observed at 30 kHz for the first 20 min of data shown. At this time depth is small and positive, while bn is > 45°, indicating that the spacecraft is in the electron foreshock. Around 0605 UT there is a rotation in the IMF, and from 0605 UT to 0627 UT most of the wave activity occurs in the 5.4 kHz and 730 Hz channels. Depth is generally larger than before this time, and the waves are most intense when bn drops below 45°. This suggests that at this time the spacecraft is in the ion foreshock. Also some ULF waves are present when the VLF waves are most intense, again indicative of the ion foreshock. After 0630 UT depth is mainly negative until 0645 UT, at which time the rotation in the IMF causes the electron foreshock to rapidly sweep over the spacecraft, and we observe a brief burst of 30 kHz noise. From 0650 UT until the end of the data the spacecraft is deep in the ion foreshock, and intense 5.4 kHz, 730 Hz, and ULF waves are observed. Throughout most of the interval after 0650 UT the spacecraft is upstream of a quasi-parallel bow shock.
Figure 4 provides a succinct overview of the types of wave phenomena observed by PVO in the foreshock at Venus. The VLF waves observed in the foreshock of Venus have been analyzed in terms of polarization, intensity as a function of location within the foreshock, and dependence on solar wind plasma density /20, 21, 26/. The 30 kHz wave intensity peaks at the tangent field line, with a peak amplitude around 10 mV/m /26/, comparable to plasma oscillations detected at the Earth /17/. Using the variation in plasma density to scan in frequency, the 30 kHz wave intensity is centered on the local plasma frequency /26/, and the waves are polarized parallel to the magnetic field /21, 26/. It is hence clear that the waves generated at the tangent field line are indeed plasma oscillations. The 5.4 kHz and lower frequency waves, on the other hand, tend to be observed further downstream from the tangent field line /21/. Comparisons with terrestrial observations shows a similar spectral shape, with the wave power extending up to 10 times the ion plasma frequency, with intensities comparable to those observed by the ISEE-2 spacecraft /21/. Through comparison of wave power as observed on both the ISEE-l and -2 spacecraft it was concluded that the wavelength of the VLF waves in the terrestrial foreshock was >30 m (the length of the ISEE-2 antenna), but less than 215 m (ISEE-l) /27/. The PVO antenna is even shorter than the ISEE-2 antenna, but since the wavelength is greater than the antenna length in both cases, the observed wave power is independent of wavelength. At Venus the 5.4 kHz waves were found to be parallel polarized /21/, which contradicts a terrestrial study /28/ that used wave interference patterns to show that the wave vector direction was typically 40° away from the magnetic field. This apparent contradiction has yet to be resolved, but may be a consequence of the spin averaging used for determining wave polarization in the PVO studies.
Although the PVO plasma wave instrument suffers from a lack of frequency resolution, there are advantages to studying VLF data at Venus. First of all, the PVO orbit had apoapsis around 12 Rv, much larger than the size of the Venus obstacle, and so the spacecraft spent a significant amount of time on each orbit in the unshocked solar wind. Furthermore, the spacecraft was in the solar wind both in the sub-solar region, and also well past the planetary terminator, thus allowing a much larger area of the foreshock to be mapped. Last the spacecraft was in orbit around Venus for 14 years, and we can carry out large statistical studies. A preliminary study /29/ using data from nearly one Venus year (200 orbits) showed the usefulness of imaging the Venus foreshock using VLF data. Subsequently /20/, this study was extended using a separate set of 650 orbits. The results of this study are presented in Figures 5 and 6.
Fig. 5.VLF map of the Venus foreshock for nominal Parker spiral (after /20/).
Fig. 6.VLF map of the Venus foreshock for perpendicular IMF (after /20/).
In Figure 5 the data have been restricted to those intervals for which the IMF was within 10° of the nominal Parker spiral in the B-v plane. As discussed in /20/ and /29/, the technique employed in generating the maps is to calculate for each observation the distance along the tangent field line and depth behind the tangent line using the instantaneous IMF, and a model bow shock that has been scaled to the observed bow shock location for each orbit. In scaling the bow shock, we have only changed the semilatus rectum (L) of the conic of revolution that specifies the shock. This conic of revolution is given by
where R is radial distance from the focus, is the eccentricity, and sz is the solar zenith angle with respect to the focus. In generating the maps we used a bow shock model with = 1.03, and focus at 0.45 Rv sunward of the planet /20, 21, 30/. When matching bow shock models to actual observations, it is preferable to keep the shock shape (specified by ) and focus fixed, and allow the size (specified by L) to change /31/.
Having calculated depth and distance, these are then converted to a Cartesian coordinate location with respect to the point of tangency in the B-v plane by assuming the IMF is at the nominal Parker spiral angle (35° at Venus), even though the instantaneous IMF may be at some other angle. This is done to prevent "smearing" of the tangent field line, which would occur if the instantaneous IMF orientation was used to specify the location. Finally, all the parallel B-v planes are mapped to the equatorial plane, using the point of tangency in each plane as the common reference point. Although we have mixed flank bow shock intersections with sub-solar intersections, this does not appear to drastically alter the statistical results /20/. Once the data have been mapped to a common foreshock geometry, the data are accumulated in bins with l l Rv resolution.
At the top left of Figure 5 we show the 9th decile of the 30 kHz wave intensity. Although the data have been accumulated in l l Rv bins we have interpolated the data in generating the maps. The color scale shows the log 10 of the wave intensity. The small black dot is the point of tangency. At the bottom left of the figure we show the log 10 of the number of samples per l l Rv bin. Throughout most of the distribution we have over 100 samples per bin, and thus we have high stastitical confidence in the results. In the bottom panel we have superimposed the reference bow shock model used in generating the maps, given by L = 1.69 Rv /21, 26/.
It is clear that the 30 kHz emissions occur mainly along the tangent field line. In addition, the wave intensity only reaches a maximum a few Rv away from the point of tangency. Moreover, the wave intensity shows a marked decrease some 15 Rv upstream of the point of tangency. Similar mapping studies using ISEE-3 data show wave emissions extending up to ~ 100 Rv along the tangent field-line /32/. Thus the electron foreshock emissions seem in part to be controlled by the scale size of the shock, consistent with limits being imposed on the Fast Fermi process through shock curvature, as noted earlier. If the drop-off was due to some inherent properties of the plasma instability and subsequent saturation processes, we would expect the drop-off scale to be independent of shock-size, instead being controlled by some scale dependent on the ambient plasma parameters. Since the solar wind is very similar at the Earth and Venus, such a scale factor would be the same at both planets.
We also note that in Figure 5 the electron foreshock emissions that are upstream of the tangent point appear to be stronger than the emissions in the downstream region. This could be attributed to two possible causes /20/. The first is that the solar wind electron distribution is asymmetric, there is a heat flux from the sun, and electrons energized at the bow shock will be flowing in the same direction as this heat flux in the downstream foreshock, thus reducing the slope in the distribution function, and hence the growth rate for instability. The second possibility can be seen on inspection of (1). While the electrons are coming from regions with roughly the same bn, the shock normal is almost parallel to the solar wind flow in the sub-solar region, while the shock normal is more nearly perpendicular along the flanks. The vndependence of the de Hoffman-Teller velocity implies that the electron acceleration will be weaker for the downstream foreshock. However, the interplay between changes in vn and changes in bn requires further analysis, similar to /18/, but taking into account both upstream and downstream foreshocks.
In this paper we have concentrated on the electron foreshock emissions, but one or two remarks are in order concerning the ion foreshock emissions at Venus, as revealed in the Figure 5 At the right of Figure 5 we include maps of the 9th decile of wave intensity measured at 5.4 kHz, and the standard deviation of the trace of the magnetic field. The 5.4 kHz channel is used to monitor the ion acoustic emissions in the foreshock, while the magnetic field deviation is a proxy for the presence of ULF waves. The line intersecting the model bow shock behind the tangent field line is the ULF boundary obtained from terrestrial studies /33/, but modified for the nominal Parker spiral orientation at Venus /21/. The ULF waves are most intense near the bow shock, and tend to be confined to locations behind the ULF boundary. The 5.4 kHz emissions, on the other hand, appear to be confined to locations even further downstream of the model ULF boundary. It is normally assumed, and Figure 4 appears to bear this out, that the ULF waves and VLF ion acoustic waves are both seen together. However, Figure 5 implies that this is only the case for observations deep in the ion foreshock. This suggests that different plasma populations are responsible for the different waves. Unfortunately, no similar mapping studies of the terrestrial ion foreshock have been carried out to determine if this result is unique to Venus. The smaller shock scale size at Venus will probably result in weaker Fermi and shock-drift acceleration, This, together with the lack of magnetosphere to act as a reservoir of energetic leakage particles, leads us to expect that the ion foreshock at Venus will be populated by lower energies and fluxes than at the Earth.
In Figure 6 we repeat the foreshock analysis, but now for IMF orientations nearly perpendicular to the solar wind flow. We find that the electron foreshock emissions are still present, but with intensities that lie between those observed in the upstream and downstream foreshock as shown in Figure 5 That the 30 kHz emissions are weaker than in the upstream foreshock of Figure 5 is consistent with our arguments concerning the vn dependence of the electron reflection process. The ion foreshock VLF emissions are almost completely absent. There is perhaps a hint of ULF emissions close to the shock behind the model ULF boundary.
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/.
VLF waves observed in the electron foreshock that is present upstream of planetary bow shocks appear to be a useful diagnostic of the energization processed that occur at the bow shock. First, the waves themselves provide a very clear marker of the tangent field line. As such they can be used for remote sensing of the bow shock /37/, although some care must be exercised in inferring the bow shock location /31/. Some of the more extreme shock shapes in /37/ arise from allowing the focus of the shock to change, rather than the semi-latus rectum. Varying the latter parameter is more physically realistic since it determines the size of the forward part of the shock near the obstacle, which will vary as a function of Mach number, while the focus is mainly fixed by the obstacle.
Second, the evolution of the waves as a function of both depth and distance provide information on the energization process. The changes that are a function of depth are clearly related to the decrease in reflection energy, and provide confirmation of both the time-of-flight models, and also the validity of Fast Fermi (or alternatively, electron shock-drift) acceleration. The dependence on distance observed within the Venus foreshock may also have important lessons concerning the effects of curved shocks on the electron energization. It appears that the shock radius of curvature is an important controlling factor in limiting the availability of energetic electrons in the foreshock. As such we might expect the plasma emissions to be observed at progressively larger distances as the shock radius of curvature decreases. Studies of the terrestrial foreshock appear to confirm this /32/.
A comparison with foreshock data from the outer planets and also from interplanetary shocks would be useful. Unfortunately, it is only statistical studies, such as shown in Figures 5 and 6, that allow us to determine the spatial extent of the foreshock emissions. Most wave observations at the outer planets are from flybys, or from relatively close orbiters such as the Phobos spacecraft at Mars /38, 39/.
The ion foreshock appears to be much more complicated than the electron foreshock. As other papers in this issue indicate /8, 9, 10/, our understanding of the ion foreshock is far from complete. This is not only the case for the VLF waves, but also for the source of the ions in the foreshock, and the role that ULF waves have to play in modifying the ion distributions. From our studies of the ion foreshock at Venus we are drawn to the conclusion that the ULF and ion acoustic waves are not necessarily observed at the same time, especially further away from the shock. Figure 5 indicates that the VLF waves in the ion foreshock are generated well downstream of where ion beams are expected to be present, rather they are observed where we might expect diffuse ions to be present. Unfortunately, the solar wind instrument on PVO was not able to provide detailed distributions within the foreshock. Also, since similar studies have not been carried out at the Earth, we do not know if this separation of ULF and VLF signatures is specific to the Venus foreshock, or if such features are also present at the Earth.
In conclusion, VLF waves observed in planetary foreshocks can provide information about the underlying plasma that generates the waves. The waves of course indicate the presence of free energy within the plasma. However, through maps of the wave emissions we may be able to infer more about the mechanisms that are responsible for the free energy. This appears to be the case for the electron foreshock, where maps of the VLF emissions suggest that shock curvature limits the energization of the electrons. For the ion foreshock, on the other hand, it may be necessary to reconsider the source of the VLF waves. Rather than being generated by ion beams /40/, the waves may be generated by the more diffuse distributions, implying that the waves are generated through pitch angle anisotropy within the ion distribution. Maps of the ion foreshock emissions at planets other than Venus would probably help in determining the validity of this speculation.
2. Fitzenreiter, R. J., The electron foreshock, Adv. Space Res., this issue.
3. Scudder, J. D., A review of the cause of electron temperature
increase in collisionless
shocks, Adv. Space Res., this issue.
4. Forman, M. A., and G. M. Webb, Acceleration of energetic
particles, in Collisionless
Shocks in the Heliosphere: A Tutorial Review (eds. R. G. Stone, and B. T. Tsurutani),
pp. 91-114, Geophysical Monograph 34, American Geophysical Union, Washington,
5. Armstrong, T. P., M. A. Pesses, and R. B. Decker, Shock drift acceleration, in Collisionless
Shocks in the Heliosphere: Reviews of Current Research (eds. B. T. Tsurutani, and R.
G. Stone), pp. 271-285, Geophysical Monograph 35, American Geophysical Union,
6. Gosling, J. T., and A. E. Robson, Ion reflection, gyration, and
dissipation at supercritical
shocks, in Collisionless Shocks in the Heliosphere: Reviews of Current Research (eds.
B. T. Tsurutani, and R. G.Stone), pp. 141-151, Geophysical Monograph 35, American
Geophysical Union, Washington, 1985.
7. Thomsen, M. F., Upstream suprathermal ions, in Collisionless
Shocks in the Heliosphere:
Reviews of Current Research (eds. B. T. Tsurutani, and R. G. Stone), pp. 253-270,
Geophysical Monograph 35, American Geophysical Union, Washington, 1985.
8. Greenstadt, E. W., G. Le, and R. J. Strangeway, ULF waves in the
Space Res., this issue.
9. Fuselier, S. A., Ion distributions in the Earth's foreshock
upstream from the bow shock,
Adv. Space Res.,this issue.
10. Scholer, M., Interaction of upstream diffuse ions with the
solar wind, Adv. Space Res.,this
11. de Hoffman, F., and E. Teller, Magneto-hydrodynamic shock, Phys. Rev., 8O, 692 (1950).
12. Goodrich, C. C., and J. D. Scudder, The adiabatic energy change
of plasma electrons and
the frame dependence of the cross-shock potential at collisionless magnetosonic shock
waves, J. Geophys. Res., 89, 6654-6662 (1984).
13. Scudder, J. D., A. Mangeney, C. Lacombe, C. C. Harvey, and T.
L. Aggson, The resolved
layer of a collisionless, high b, supercritical, quasi-perpendicular shock wave 2.
Dissipative fluid electrodynamics, J. Geophys. Res., 91, 11,053-11,073 (1986).
14. Ellison, D. C., and Jones, E. C., Non-coplanarity magnetic fields in shock transition layers,
Adv. Space Res., this issue.
15. Leroy, M. M. and A. Mangeney, A theory of energization of solar
wind electrons by the
Earth's bow shock, Annales Geophysicae, 2, 449-56 (1984).
16. Wu, C. S., A fast Fermi process: Energetic electrons accelerated by a nearly perpendicular
bow shock, J. Geophys. Res., 89, 8857-8862 (1984).
17. Filbert, P. C., and P. J. Kellogg, Electrostatic noise at the
plasma frequency beyond the
Earth's bow shock, J. Geophys. Res., 84, 1369 (1979).
18. Fitzenreiter, R. J., J. D. Scudder, and A. J. Klimas, Three-dimensional analytical model for
the spatial variation of the foreshock electron distribution function: Systematics and
comparisons with ISEE observations, J. Geophys. Res., 95, 4155-4173 (1990).
19. Greenstadt, E. W., and L. W. Baum, Earth's compressional foreshock boundary revisited:
Observations by the ISEE 1 magnetometer, J. Geophys. Res., 91, 9001-9006 (1986).
20. Crawford, G. K., A Study of Plasma Waves Arising from the Solar
Wind Interaction with
Venus, Ph. D. Thesis, University of California at Los Angeles, 1993.
21. Crawford, G. K., R. J. Strangeway, and C. T. Russell, VLF emissions in the Venus
foreshock: Comparisons with terrestrial observations, J. Geophys. Res., 98, 15,
22. Scarf, F. L., W. W. L. Taylor, and P. V. Virobik, The Pioneer
Venus Orbiter plasma wave
investigation, IEEE Trans. Geosci. Remote Sens., GE-18, 36-38 (1980).
23. Scarf, F. L., W. W. L. Taylor, C. T. Russell, and R. C. Elphic,
Pioneer Venus plasma wave
observations: The solar wind-Venus interaction, J. Geophys. Res., 85, 7599-7612
24. Strangeway, R. J., Plasma waves at Venus, Space Sci. Rev., 55, 275-316 (1991).
25. Higuchi, T., G. K. Crawford, R. J. Strangeway, and C. T.
Russell, Separation of spin
synchronous signals, Annals of the Institute of Statistical Mathematics 46, 405-428,
26. Crawford, G. K., R. J. Strangeway, and C. T. Russell, Electron
plasma oscillations in the
Venus foreshock, Geophys. Res. Lett., 17, 1805-1808 (1990).
27. Anderson, R. R., G. K Parks, T. E. Eastman, D. A. Gurnett, and
L. A. Frank, Plasma
waves associated with energetic particles streaming upstream into the solar wind from
the Earth's bow shock, J. Geophys. Res., 86, 4493-4510 (1981).
28. Fuselier, S,. A., and D. A. Gurnett, Short wavelength ion waves
upstream of the Earth's
bow shock, J. Geophys. Res., 89, 91-103 (1984).
29. Crawford, G. K., R. J. Strangeway, and C. T. Russell, VLF
imaging of the Venus foreshock,
Geophys. Res. Lett., 20, 2801-2804 (1993).
30. Slavin, J. A., R. E. Holzer, J. R. Spreiter, and S. S. Stahara,
Planetary Mach cones: Theory
and observation, J. Geophys. Res., 89, 2708-2714 (1984).
31. Farris, M. H., and C. T. Russell, Determining the standoff
distance of the bow shock: Mach
number dependence and use of models, J. Geophys. Res, 99, 17,681-17,689 (1994).
32. Greenstadt, E. W., G. K. Crawford, R. J. Strangeway, S. L.
Moses, and F. V. Coroniti,
Spatial distribution of electron plasma oscillations in the Earth's foreshock at ISEE-3,
in preparation, personal communication, 1994.
33. Le, G., and C. T. Russell, A study of ULF wave foreshock
morphology-1: ULF foreshock
boundary, Planet Space Sci., 40, 1203-1213 (1992).
34. Etcheto, J., and M. Faucheux, Detailed study of electron plasma
waves upstream of the
Earth's bow shock, J. Geophys. Res., 89, 6631-6653 (1984).
35. Fuselier, S. A., D. A. Gurnett, and R. J. Fitzenreiter, The
downshift of electron plasma
oscillations in the electron foreshock region, J. Geophys. Res., 90, 3935-3946 (1985).
36. Hospodarsky, G. B., D. A. Gurnett, W. S. Kurth, M. G. Kivelson,
R. J. Strangeway, and S.
J. Bolton, Fine structure of Langmuir waves observed upstream of the bow shock at
Venus, J. Geophys. Res., 99, 13,363-13,371 (1994).
37. Cairns, I. H., C. W. Smith, W. S. Kurth, D. A. Gurnett, and S.
Moses, Remote sensing of
Neptune's bow shock: Evidence for large scale shock motions, J. Geophys. Res., 96,19,
38. Skalsky, A., R. Grard, S. Klimov, C. M. C. Nairn, J. G. Trotignon, and K. Schwingenschuh,
The Martian bow shock: Wave observations in the upstream region, J. Geophys. Res., 97,
39. Trotignon, J. G., A. Skalsky, R. Grard, C. Nairn, and S.
Klimov, Electron density in the
Martian foreshock as a by-product of the electron plasma oscillation observations, J.
Geophys. Res., 97, 10,831-10,840 (1992).
40. Fuselier, S. A., S. P. Gary, M. F. Thomsen, S. J. Bame, and D. A. Gurnett, Ion beams and
the ion/ion acoustic instability upstream from the Earth's bow shock, J. Geophys. Res.,
92, 4740-4744 (1987).
Return to the top of the document
Go to R. J. Strangeway's Homepage
Converted to HTML by Shaharoh Bolling
Last modified: Jan 18, 2000