Pages 673-682


D. Burgess

Astronomy Unit, Queen Mary and Westfield College, London, United Kingdom E1 4NS,


I present a short review of waves observed in the terrestrial foreshock. The observed frequencies span several orders of magnitude, from mHz to tens of kHz. The foreshock has a complex morphology, ordered mainly by magnetic connection to the bow shock, and particle energy and species. The observational characteristics of the different categories of upstream waves will be summarized, and the currently accepted notions of their production will be mentioned. A comprehensive review of generation mechanisms will not be given.


Waves and disturbances upstream of the Earth's bow shock have been studied ever since observations of the solar wind were first taken. The existence of a foreshock is a natural consequence of the lack of collisions in the solar wind. Particles suitably energized at the shock can stream into the upstream region, and there present particle distributions functions which can be unstable to a wide variety of plasma wave types. The observed particle distributions, and associated waves, vary considerably through the foreshock. The terrestrial foreshock is then a fascinating subject, as a precursor to the bow shock, and as a ``zoo'' in which a wide range of plasma wave species can be studied.

In this paper, after a brief introduction to our knowledge of the overall structure of the foreshock, I will present a reasonably complete catalogue for the wave zoo, organized by observed frequency. The emphasis will be observational, since one of the motives behind this review is that furthering our knowledge of the foreshock depends on building on the understanding of earlier authors. There are so many different kinds of wave phenomena, that it is all to easy to rediscover the wheel. Furthermore, since a single phenomenon may present different aspects when observed with different instruments (or different data analysis techniques), it is also important that any discovery claim is tested against the existing body of knowledge.

Implicit in this review is the understanding that has resulted from a large amount of theoretical, modelling and simulation work. These studies underpin many of the statements made here. Unfortunately, to give full justice to this body of work would more than double the material here. So, with apologies, citations in this area will be partial.

The scientific endeavour is incomplete without controversies, either genuine or synthetic. My aim is to present only the most widely accepted results. Thus controversies, divergent points of view, inconsistencies, will all be, unfairly, pushed to the sidelines.

Finally, at least in terms of restricting the scope of this review, only the terrestrial foreshock will be discussed. The foreshocks of other interesting solar system bodies (comets, unmagnetized planets) are ignored, as is what can be learnt from the comparisons with foreshocks of the other magnetized planets. After the catalogue of species, I will make a few points which I believe should orient future progress in this area.

The subject of upstream waves has, in general, seen declining activity over the last few years. Thus the reviews presented at the 1994 COSPAR meeting [Adv. Space Res., 15(8-9), 1995] remain useful, as do early reviews such as (Greenstadt, 1985, Onsager and Thomsen, 1991, Russell and Hoppe, 1983, Tsurutani and Rodriguez, 1981). The ``historical'' papers are also still a valuable resource (Heppner et al., 1967, Holzer et al., 1966, Scarf et al., 1970, Scarf et al., 1971).


The foreshock global morphology is organized by the interplanetary magnetic field direction (IMF), the bow shock shape, and, crucially, particle cross field drift relative to particle parallel velocity. Particles energized at the shock with high speeds will tend to more closely follow a field line parallel to the tangent field line. This leads to a velocity filter which organizes the foreshock spatially, so that one can distinguish an electron foreshock, and an ion foreshock. In each case one expects, and sees, the fastest beams occurring on the upstream edge. Electron distributions vary from energetic beams to a backstreaming heat flux (Fitzenreiter, 1995). Ion distributions vary from ``field aligned beams'' (FAB, with beam temperature similar to the solar wind), through ``intermediate,'' to ``diffuse'' ions (near isotropic, hot, with low drift speed) (Fuselier, 1995).

Given this spatial structuring, what governs the waves that can be seen? First, as our basic tenet: upstream particles cause upstream waves. (It has also been suggested that the particle gradients are important (Parks et al., 1981).) So we must take account of particle distributions as a function of space and time. Then, given these, one can consider the issues of wave instability and damping. Once a wave is created (via an instability, or perhaps by the modulation of the injected particle distribution), it then propagates, and so its continued existence relies on it remaining in a region where it is undamped. Observationally, the wave propagation is superimposed on the convection of the plasma frame, which introduces Doppler shifts in frequency, and possible reversal of polarization sense.

The foreshock wave modes may be very different from those of an isotropic maxwellian plasma because of energetic particle; they may be merely modified, or entirely different modes may be introduced (e.g., beam modes). And that is not the end of the story, since on must take account of the feedback of the waves on the particle distribution function, any possible nonlinear wave-wave processes, and even the possibility that the bow shock injection of particles into the foreshock is modulated either by intrinsic processes or even by the foreshock waves themselves. And there are are certainly even more possible processes to complexify the foreshock!


The Wave Zoo: ULF Electromagnetic Waves

The ULF range here spans (very roughly) 5mHz to 0.1Hz, and has been characterized largely by DC magnetometer observations (Fairfield, 1969, Greenstadt et al., 1995b, Russell and Farris, 1995). This frequency range corresponds to what some call ``MHD-like,'' a term which is colloquial and potentially misleading. The generation and properties of waves in this category can only be explained with kinetic theory. Within the overall ULF category there are different classes of waves which are distinguished by their waveform appearance, and sometimes also the associated particle signatures and/or presumed generation mechanisms. In all cases the waves are generally large amplitude (B/B ~ 0.2 - 1.0).

The waveforms can appear monochromatic (with many cycles) or more complex (``developed'') showing steepened edges or ``shocklets.'' Some steepened edges have whistler wave packets (f ~ 0.4Hz) associated with them (Russell et al., 1971). A third class is ``intermediate'' with characteristics, strangely enough, intermediate between the first two. The peak frequency of the ULF spectrum is about 0.02 Hz, corresponding to ~ 0.1cp(Le and Russell, 1996). Using two spacecraft observations (Hoppe and Russell, 1983, Hoppe et al., 1981) it has been found that these waves are propagating (in the plasma frame) upstream, or rather, away from the shock, at about 20° - 40° to the magnetic field direction. However, their propagation speed is less that the flow speed, and they are swept back towards the shock. This has implications for the observed, as opposed to plasma frame, polarization properties. Again, using two spacecraft observations, is it possible to disentangle the observed and plasma frame polarizations. The results (Hoppe and Russell, 1983, Elaoufir et al., 1990, Blancocano and Schwartz, 1995) are not as clearly differentiated as one might hope from simple expectations. But that might just show that simple expectations are wrong! The monochromatic waves tend to be RH circularly polarized (in plasma frame) whereas the developed waveforms show mixed polarizations. In both cases, the super-wave speed of the flow causes a reversal of the sense of polarization.

Using an unusual foreshock passage when the IMF was remarkably constant, the evolution of the ULF waves has been studied (Le and Russell, 1992a, Le and Russell, 1992b) (but see also, Russell et al., 1987, Sugiyama et al., 1995), showing that the monochromatic waves occur towards the foreshock upstream edge, amd that the spectrum broadens (mainly to lower frequencies, but also with appearance of shocklet whistler wave packets) with decreasing distance to the shock. The waves are associated with, and presumably generated by the different types of foreshock ion distributions: monochromatic/intermediate waves with field aligned beams and intermediate distributions; developed waves and shocklets with diffuse distributions (Bavassano-Cattaneo et al., 1983, Hoppe et al., 1981, Hoppe et al., 1982, Paschmann et al., 1979, Scarf et al., 1970). It is accepted that the waves are driven by electromagnetic ion beam instabilities with the RH resonant instability for fast/cold beams and LH and RH nonresonant and resonant instabilities for diffuse distributions (Akimoto et al., 1991, Akimoto et al., 1993, Gary et al., 1985, Gary, 1991, Gary et al., 1981, Gary et al., 1984, Gary et al., 1985, Gary et al., 1986a, Omidi and Winske, 1990, Sentman et al., 1981, Smith et al., 1985, Smith and Gary, 1987, Watanabe and Terasawa, 1984, Winske and Leroy, 1984, Winske and Quest, 1986). This latter complexity could help explain the observed mixed polarization, but one should not neglect the role of wave evolution with distance from the foreshock edge. The terms ``resonant'' and ``nonresonant'' are defined via a quantity which parameterizes the distance of the cyclotron resonance from the driving population. However, it should be realized that in all cases the physical mechanism of the instabilities is cyclotron resonance. One open issue is the fact that EM ion beam instabilities have maximum growth rate for waves with k parallel to B, but the observed propagation direction is between 20° - 40°. There is no clear explanation for the discrepancy, although wave refraction has been suggested (Hada et al., 1987). In these instabilities, coupling is via gyrophase bunching of the ions in the wave field so that such bunching, when observed is a direct signature of the particle-wave coupling (Fazakerley et al., 1995, Fuselier et al., 1986, Gary et al., 1986b, Hoshino and Terasawa, 1985, Thomsen et al., 1985). One notes that gyrophase bunching could also result from direct injection at the shock, although there is no clear observational case for a separate related ULF wave class (Brinca et al., 1993, Killen et al., 1995).

In parallel with the linear instability approach there is a body of work which treats the large amplitude ULF waves of the diffuse ion foreshock as an example of nonlinear ``MHD-like'' turbulence. For example, one can look for signatures of nonlinear processes in the density characteristics (Spangler et al., 1988), or compare observations with models of turbulence (Labelle et al., 1994, Mann and Luhr, 1991), as well as study the nonlinear theory per se (Longtin and Sonnerup, 1986, Vinas and Goldstein, 1991, Terasawa et al., 1986, e.g.,).

The Wave Zoo: Large Amplitude Pulsations

Large amplitude pulsations (sometimes called SLAMS: short, large amplitude magnetic structures) are related to the ULF waves in that they have a similar period, or rather observed duration, of 10-20s (Greenstadt et al., 1993, Mann et al., 1994, Schwartz et al., 1992, Thomsen et al., 1988, Thomsen et al., 1990, Wilkinson et al., 1993). They have, indeed, large amplitudes, with B/B ~ 5, but they appear as a coherent structure embedded in ``normal'' ULF wave solar wind material. They are also like ULF waves in that they propagate upstream (in the plasma frame) but are convected downstream, they have mixed polarization signatures, and can have attached whistler wave packets. It is believed that they grow from the upstream ULF field, and that this growth is associated with proximity to the bow shock. Indeed, it is thought that they form a vital part of the quasi-parallel pulsation shock, even though they can appear like ``upstream'' entities (Burgess, 1995, Dubouloz and Scholer, 1995, Scholer and Burgess, 1992, Scholer et al., 1993, Schwartz and Burgess, 1991, Thomsen et al., 1988).

The Wave Zoo: 3 Second Waves

We now move up in frequency to a rather singular class of low frequency electromagnetic waves. There has only been one comprehensive study of this class (Le et al., 1992), and this indicates that they are relatively rare and tend to appear only for certain solar wind conditions. Their observational properties can be summarized as: appear as wave packets, with variable peak amplitude; RH circularly polarized in the spacecraft frame; propagating in the direction of B; convected downstream by solar wind flow; tend to be observed when the solar wind plasma beta is high. These waves are similar (in frequency and narrow bandwidth) to the discrete wave packets associated with steepened ULF waves, except for the fact that the polarization is in the opposite sense. It has been concluded, that these are LH (in plasma frame) ion cyclotron wave. These waves appear in both intermediate and developed ULF wave intervals (corresponding to upstream of quasi-perpendicular and quasi-parallel portions of the bow shock). The waves are very planar and nearly circularly polarized, and their propagation directions are within about 20° of the magnetic field direction. The source of these waves is one of the puzzles of the foreshock.

The Wave Zoo: ``1Hz'' Whistlers

The name for this class is essentially a misnomer, since one now includes waves in the frequency band 0.5 - 4 Hz, and it is thought that, in the plasma frame, the spectrum is broad band up to 10 - 20 Hz. Their amplitude is small (B/B ~ 0.2) and they have propagation directions between 20° - 40° to the magnetic field direction (Fairfield, 1974, Orlowski et al., 1990, Orlowski et al., 1995, Orlowski and Russell, 1995). They are observed to be more ``persistent'' close to the quasi-perpendicular shock (Fairfield, 1974). Their polarization is either LH or RH (spacecraft frame) depending on their propagation direction relative to the flow direction. If the identification of these waves with whistlers is correct, then they will have group velocities high enough to propagate upstream ahead of the shock, with possibly sub-flow phase speeds. The waves are found to be consistently RH polarized in the plasma frame, with wavelengths in the region of 100 km.

The reversal of polarization from RH (plasma frame) to LH (spacecraft frame) has been shown to be accompanied by by a peak in the power spectrum at about 1 Hz, with a sharp cutoff at higher frequencies. It is this characteristic spectrum that most catches the eye, and which has probably led to the term ``1 Hz whistlers.'' Actually it might be added that even the term ``whistler'' is rather loosely used, since at these plasma frame frequencies the RH Fast-Magnetosonic mode, although dispersive like a whistler, does not yet have the resonance cone of the classic whistler.

The wavelength, propagation direction, and proximity to the quasi-perpendicular shock, and attempts to find suitable particle distributions and corresponding instabilities (Sentman et al., 1983, Wong and Goldstein, 1987, e.g.,), indicates that the waves are emitted by the bow shock itself, and not necessarily via any energized particle population (Fairfield, 1974, Greenstadt et al., 1981, Krauss-Varban et al., 1995). As supporting evidence, one can note that the observe wavelengths are typical of the width of the ramp of the supercritical quasi-perpendicular shock. The waves are then observed upstream because of the dispersive nature of the mode, perhaps aided by electron heat flux from the shock which lessens the Landau damping operating on them (Orlowski et al., 1995). The emission process is not entirely clear, with two candidate processes: either intrinsic modulation (instability?) of the shock ramp, or some linear instability at the shock driven by, for example reflected gyrating ions.

Coherence Lengths

Using two spacecraft observations it is has been possible to measure the correlation coefficients transverse to the solar wind flow, for the different wave classes discussed above (Le and Russell, 1990, Le et al., 1993). The results are not entirely surprising given the wavelengths of the waves, their production mechanisms and bandwidths. The ULF waves (period ~ 30s) have wavelengths of about 1 RE and a similar coherence length. For the 3s waves, which are early monochromatic, the coherence length is again about 1 RE, corresponding to several wavelengths. For the upstream propagating whistler waves the coherence length is only ~ 100 km, roughly the same as their wavelength. One important conclusion to be drawn is that different spacecraft separations are required when studying the different classes of wave.

The Wave Zoo: Whistler Bursts

Also in the category of whistler mode waves we go up in frequency to roughly 40 - 100 Hz (Anderson et al., 1981, Hayashi et al., 1994). Whistler waves at these frequencies are observed as short (2 - 10 s) bursts of drifting tones. They are weak and impulsive during energetic ion enhancements, but also seen coincident with low energy electron heat flux enhancements (i.e., in electron foreshock). Indeed, they are sometimes seen simultaneously with electron plasma oscillations and without energetic ion enhancements. This species of whistler wave emission has been little studied. The observations indicate that either electron heat flux, electron beams, or ion beams could all be responsible for wave growth (Tokar and Gurnett, 1985, e.g.,). Further work needs to be done observationally to correlate wave activity with particle signatures, as well as theoretically to differentiate the signatures of the various possible instabilities.


The Wave Zoo: Ion Acoustic Waves

We again step up in frequency to what have been identified as electrostatic ion acoustic waves. These are observed in the frequency range 1-10 kHz, and are ubiquitous in the diffuse ion foreshock, at the bow shock, and in the magnetosheath (Gurnett and Frank, 1978, Rodriguez, 1981). They attain their highest amplitudes at the shock and in the sheath. High time resolution foreshock data reveals that the emissions are in fact bursty, and narrowband, but fluctuating in frequency (Anderson et al., 1981). Important in the identification of these waves has been the fact that observations using antennae of different lengths have different characteristics. With a long antenna (200 m) one observes an antenna interference pattern (as the spacecraft spins, and the antenna changes angle with the electric field of the waves), but a shorter antenna (30m) does not show such an interference pattern (Fuselier and Gurnett, 1984). The implication is that the wavelength is somewhere between the lengths of the two antennae, which is of the order of 5D. Given this short wavelength, it then follows that almost all of the observed frequency is due to Doppler shift from the solar wind flow, and it is presumed that the plasma frame frequency of the waves is near to the ion plasma frequency (~ 500 Hz). Using the antenna interference pattern, and the ion acoustic dispersion relation, the propagation angle relative to the magnetic field has been found to be in the range 10° - 80°.

Despite their ubiquity, or even maybe because of it, there is no one clear mechanism for the source of these waves, although there are several suggestions. The problem with most suggested instabilities is that they require Te >>Ti for significant wave growth. One attractive, suggestion is that ion beams with fine structure (steep gradients) in velocity space are responsible (Fuselier et al., 1987). It has also been suggested that electron acoustic waves are present (Marsch, 1985).

The Wave Zoo: Electron Plasma Oscillations

Electron plasma oscillations (also sometimes called Langmuir waves), with frequencies at, or around the electron plasma frequency, are seen throughout the electron foreshock (Etcheto and Faucheux, 1984, Filbert and Kellogg, 1979, Fuselier et al., 1985, Lacombe et al., 1988, Onsager et al., 1989, Scarf et al., 1971). They are observed to be narrowband, and most intense at the upstream foreshock edge, where one expects the most energetic electron beams. The waves are broader band and downshifted in frequency as observations are taken deeper in the foreshock. This is also demonstrated when the emissions are mapped into a foreshock coordinate system (Greenstadt et al., 1995a). It is clear that the waves are related to electron beams backstreaming from the shock, but unstable distributions are only occasionally seen. This may be an observational artifact, or a feature of the electron acceleration process, or, indeed, a fundamental part of the electron-wave interaction process. Recent observational data where the actually waveform is captured, reveals that the waves are in arranged in wavepackets lasting only a few milliseconds (Bale et al., 1996, Kellogg et al., 1996, Cairns, 1994).

The theory of the linear and nonlinear evolution of electron beam instabilities has been studied by many authors (Cairns, 1994, Cairns and Fung, 1988, Canu, 1990, Dum, 1990a, Dum, 1990b, Dum, 1990c, Goldman et al., 1996, Marsch, 1985, Muschietti et al., 1996, Robinson and Newman, 1991). The source of the electron plasma oscillations is accepted to be electron beams, and studies of the linear dispersion properties show that the downshifted oscillations are associated with lower electron beam speeds. However, the electron beams are at low densities and with such time variability, that it is difficult to make a one-to-one correspondence with particle observations

The Wave Zoo: 2fp Electromagnetic Emission

We finally step up in frequency to where the foreshock eventually becomes a radio source. In the region upstream from the foreshock, and in the electron foreshock, an emission line at twice the foreshock electron plasma frequency(i.e., 20 - 100kHz) is observed (Hoang et al., 1981, Lacombe et al., 1988, Reiner et al., 1996). The radiation is electromagnetic, and freely propagating. It is clear that the source is associated with the electron foreshock (Lacombe et al., 1988). The most widely accepted theory is that the radiation is formed by the nonlinear coalescence of two (oppositely directed) Langmuir waves in the electron foreshock (Cairns, 1988a, e.g.,). Although widely accepted, there are alternative theories, (e.g., Yoon et al., 1994).

In the context of harmonics of the plasma frequency, one can note that higher harmonics are sometimes observed. Sometimes these are clearly instrumental, related to the intense Langmuir wave emission, but there are examples where it appears they are naturally generated (Cairns, 1986, Cairns, 1988b, Klimas, 1983).


Our knowledge of waves in the foreshock bounded forward with the data from the ISEE mission. In recent years progress has slowed. On the other hand there are still some exciting areas where I believe we could advance. More effort needs to be made to apply refined nonlinear data analysis and physics. One might mention the use of high order spectral methods and nonlinear dispersion relations (Dewit and Krasnoselskikh, 1995, Dewit et al., 1995) and other techniques (Muret and Omidi, 1995). Mapping the global morphology of the foreshock is required to actually test the facts against our cartoons. In this respect large scale simulations could reveal the interactions between different parts of the foreshock.

Observationally, the most important next step is higher resolution, both in terms of waveforms (where one can apply modern spectral methods), but also in terms of particle distributions, so that the wave-coupling processes can be examined in detail. Finally, as ISEE has shown us, the importance of multi-point measurements cannot be exaggerated.


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