Earth's Foreshock Research Articles

Characteristics of electrostatic solitary waves in the Earth's foreshock region: Geotail observations

We observed electrostatic solitary waves (ESW) in the Earth's foreshock region by the Geotail spacecraft. The foreshock region is classified into electron foreshock and ion foreshock regions, which are dominated by energetic electrons and superthermal ions, respectively. The Geotail waveform observations show the existence of ESW in both electron and ion foreshock regions. To understand the wave features of ESW, we examine the waveform and perform statistical analyses on the spatial distribution of the ESW. The results show that the occurrence and amplitude of ESW decrease as the distance from the bow shock transition increases. In the electron foreshock region, we find that ESW and electron beams are observed simultaneously. The plasma conditions are similar to those in the plasma sheet boundary layer (PSBL), in which ESW were first discovered by the Geotail spacecraft. In the ion foreshock region, ESW are simultaneously observed with superthermal ions reflected by the bow shock. We find two types of ESW in the ion foreshock region based on the orientation of their bipolar waveforms. We examine the angle between the magnetic field and the shock normal dependence of the occurrences of ESW in the ion foreshock region. The results show that ESW observed in the quasi‐parallel shock have characteristics that differ from those observed in the quasi‐perpendicular shock. From waveform and statistical analyses, the most plausible generation mechanism of the first type of ESW is the Buneman instability based on the superthermal ions and background electrons. A possible mechanism of the second type of ESW is the positive potential ESW propagating from the upstream region to the bow shock due to the reflection by the negative potentials or the negative potential ESW generated by the reflected superthermal ions.

Beam‐plasma interaction in randomly inhomogeneous plasmas and statistical properties of small‐amplitude Langmuir waves in the solar wind and electron foreshock

A numerical model for wave propagation in an unstable plasma with inhomogeneities is developed. This model describes the linear interaction of Langmuir wave packets with an electron beam and takes into account the angular diffusion of the wave vector due to wave scattering on small‐amplitude density fluctuations, as well as suppression of the instability caused by the removal of the wave from the resonance with particles during crossing density perturbations of relatively large amplitude. Using this model, the evolution of the wave packets in inhomogeneous plasmas with an electron beam is studied. To analyze data obtained both in space experiments and numerical modeling, a Pearson technique was used to classify the spectral density distributions. It was shown that both experimental distributions obtained within the Earth's foreshock aboard the CLUSTER spacecraft and model distributions for the logarithm of wave intensity belong to Pearson type IV rather than normal. The main reason for deviations of empirical distributions from the normal one is that the effective number of regions where the waves grow is not very large and, as a consequence, the central limit theorem fails to be true under the typical conditions for the Earth's electron foreshock. For large amplitudes, it is suggested that power law tails can result from variations of wave amplitudes due to changes of group velocity in the inhomogeneous plasma, in particular due to reflection of waves from inhomogeneities.

Statistical properties of small-amplitude Langmuir waves in the Earth's electron foreshock

We present the results of a statistical study of Langmuir waves observed by the Cluster spacecraft in the Earth's electron foreshock. To classify the probability density distributions of the logarithms of the wave energies, a Pearson technique is used. We show that experimental distributions can be better approximated, in a statistical sense, by Beta distribution or Pearson Type IV distribution rather than by a normal distribution predicted by the stochastic growth theory. This conclusion agrees with the results of numerical simulations that were previously performed with the use of a model for Langmuir wave propagation in unstable plasma with random inhomogeneities. The main reason for deviations of empirical distributions from a normal distribution is probably related to the effective number of regions, where the waves grow, which is not sufficiently large for the central limit theorem to be applicable under typical conditions in the Earth's electron foreshock. For two of seven events such deviations may be partially attributed to the effects of thermal Langmuir waves.

Experimental evidence of phase coherence of magnetohydrodynamic turbulence in the solar wind: GEOTAIL satellite data

Magnetohydrodynamic (MHD) turbulence is commonly observed in the solar wind. Nonlinear interactions among MHD waves are likely to produce finite correlation of the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in the quasi-linear theory) or have a finite coherence. Using a method based on the surrogate data technique, we analysed the GEOTAIL magnetic field data to evaluate the phase coherence in MHD turbulence in the Earth's foreshock region. The results demonstrate the existence of finite phase correlation, indicating that nonlinear wave-wave interactions are in progress.

Macrostructure of collisionless bow shocks: 2. ULF waves in the foreshock and magnetosheath

We perform global hybrid (kinetic ions and fluid electrons) simulations of the solar wind coupling with magnetic dipoles of different strength and study foreshock morphology and its influence on the bow shock and magnetosheath. The advantage of the hybrid code over fluid codes is that it treats ion‐scale microphysics in the context of the global interaction. We study the characteristics of the ultralow‐frequency (ULF) waves generated by kinetic instabilities and find two types of waves: (1) sinusoidal almost parallel propagating waves and (2) highly compressive obliquely propagating fluctuations. In contrast to suggestions made in the past, we show that compressive waves found near the shock do not evolve from the sinusoidal wave population but rather are generated by a different ion population. We find that the sinusoidal waves are generated by field‐aligned backstreaming ions, while the compressive waves near the shock are generated by gyrating ion beams closer to the shock. Our results show that, for low dipole magnetization, noncompressive waves dominate the foreshock, while compressive waves grow just in a very small region and do not have time to evolve, so no quasi‐parallel shock is formed. In contrast, when the system scale size is much larger than an ion inertial length, highly compressive waves convect into the quasi‐parallel region, evolving into large steepened structures that eventually form the shock transition. These waves play an active role in shock dissipation processes and eventually form part of the wave spectra in the magnetosheath. Comparison of our results with observations shows that the characteristics of sinusoidal waves in our simulations resemble the properties of 30‐s sinusoidal quasi‐monochromatic waves in the Earth's foreshock, while compressive waves have similar properties to the observed right‐handed steepened fluctuations. Downstream from the shock, the magnetosheath is permeated by a variety of waves that result from the convection of upstream waves and also from local generation. The wave characteristics are different in the quasi‐parallel and quasi‐perpendicular parts of the magnetosheath.

INTERBALL-1 observations of plasma and energetic particle fluxes upstream of the Earth's bow shock

In this paper, we follow our recent statistical examinations of solar wind plasma fluctuations in the Earth's foreshock and their relationship to measurements of energetic ion ( ∼ 25 keV) fluxes under different solar wind and interplanetary magnetic field conditions, based on the INTERBALL-1 data obtained during 1995–2000. We study in detail the influence of more energetic particles ( ∼ 50 and 110 keV energy channels) and their energetic and angular distributions. We compare the intervals of upstream observations outside the foreshock and inside the foreshock of different strengths and relate plasma fluctuations to observed energetic particle spectra and anisotropy at different distances to the bow shock. We discuss possible physical explanations of observed phenomena.

Electric field distributions for Langmuir waves in planetary foreshocks

This paper addresses several key issues regarding the statistics of Langmuir wave fields E in planetary foreshocks by presenting (1) a detailed theory for the electric field strength probability distributions averaged over Earth's foreshock and (2) the first analyses of the distributions observed in the outer planets. First, existing theory is extended and generalized, describing in detail how lognormal distributions of P(log E) for a specific location can be aggregated over foreshock location to give power law distributions (log E). The extended theory is in good agreement with the observations of power law distributions (log E) for Earth's foreshock, and implies that stochastic growth theory (SGT) is likely to be relevant. The statistics of the Langmuir wave fields of the outer planets Saturn, Uranus, and Neptune are then analyzed and compared. The characteristics of the observed distributions (logE) agree qualitatively with each other and Earth, and these distributions collapse onto a single curve when scaled on the assumption that the ratio of the wave energy density to thermal plasma energy density is constant with heliocentric distance. The extended theory developed for Earth is also found to agree well with the scaled (log E) distributions for each outer planet. The evidence is thus that the physics of electrons and Langmuir waves in all planetary foreshocks is essentially identical and that the distributions (log E) are consistent with SGT.

Statistical behavior of foreshock Langmuir waves observed by the Cluster wideband data plasma wave receiver

Abstract. We present the statistics of Langmuir wave amplitudes in the Earth's foreshock using Cluster Wideband Data (WBD) Plasma Wave Receiver electric field waveforms from spacecraft 2, 3 and 4 on 26 March 2002. The largest amplitude Langmuir waves were observed by Cluster near the boundary between the foreshock and solar wind, in agreement with earlier studies. The characteristics of the waves were similar for all three spacecraft, suggesting that variations in foreshock structure must occur on scales greater than the 50-100km spacecraft separations. The electric field amplitude probability distributions constructed using waveforms from the Cluster WBD Plasma Wave Receiver generally followed the log-normal statistics predicted by stochastic growth theory for the event studied. Comparison with WBD receiver data from 17 February 2002, when spacecraft 4 was set in a special manual gain mode, suggests non-optimal auto-ranging of the instrument may have had some influence on the statistics.

A Quantitative model for terrestrial foreshock radio emissions: 1. Predicted properties

We present detailed quantitative results from a theoretical model for fundamental (fp) and second harmonic (2fp) radio emission generated in Earth's foreshock by beam‐driven Langmuir waves. The model is the first to self‐consistently incorporate all key aspects of foreshock physics: reflection and acceleration of incident solar wind electrons at the bow shock, generation of unstable electron beams in the foreshock, stochastic growth of Langmuir waves and their conversion to electromagnetic waves via nonlinear processes. The physical properties of the foreshock electron beams, Langmuir waves and electromagnetic emissivities are calculated as a function of position for nominal solar wind conditions. Variations in the bow shock's location and characteristics with changes in the solar wind parameters are included. The predicted fluxes of fp and 2fp radiation are explored over a wide range of solar wind conditions. We find that the 2fp flux is most sensitive to the electron and ion temperatures and the solar wind speed and that the radio fluxes of both fp and 2fp radiation also vary significantly with the solar wind electron number density, and proportion of nonthermal electrons. Our macroscopic model provides a powerful and unique diagnostic tool with which to interpret observational data from various spacecraft under a range of solar wind conditions.

Pressure‐pulse interaction with the magnetosphere and ionosphere

We reexamine traveling convection vortices (TCVs) seen by the Magnetometer Array for Cusp and Cleft Studies on 9 November 1993. IMP‐8 energetic ion observations confirm that the solar wind pressure variations previously associated with these TCVs were generated by kinetic processes within the Earth's foreshock. As expected during this interval of spiral IMF orientation, fast mode waves launched by the pressure variations first arrived in the equatorial ionosphere near dusk and propagated dawnward. We derive a model for the field‐aligned currents generated by transient compressions of the magnetopause and show that it accounts for the number of TCVs seen in the prenoon ionosphere, their sense of rotation, the latitude at which they occur, and their absence in the postnoon ionosphere.

Phase coherence of MHD waves in the solar wind

Large amplitude MHD waves are commonly found in the solar wind. Nonlinear interactions between the MHD waves are likely to produce finite correlation among the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in quasi-linear theories) or they have a finite coherence. Using a method based on a surrogate data technique and a fractal analysis, we analyzed Geotail magnetic field data (provided by S. Kokubun and T. Nagai through DARTS at the Institute of Space and Astronautical Science) to evaluate the phase coherence among the MHD waves in the earth's foreshock region. The correlation of wave phases does exist, indicating that the nonlinear interactions between the waves is in progress.

Phase Coherence of Foreshock MHD Waves: Wavelet Analysis

The earth's foreshock is a region where particularly large amplitude MHD waves are commonly observed. They exhibit various waveforms, suggesting that nonlinear interaction between the waves is in progress. In a previous paper (Hada et al., 2003) we have introduced a method to quantitatively evaluate the strength of phase coherence among the waves from a given time series data. Here we further develop our method by applying wavelet filtering technique. From the analysis it was found that, although the turbulence is consisted of waves with a wide range of plasma rest frame frequencies, only those frequencies lower than the ion gyrofrequency are responsible for generating the phase coherence.

Small scale solar wind ion flux and IMF quasi-harmonical structures in the earth's foreshock: INTERBALL-1 and MAGION-4 observations

High time resolution data obtained by VDP and FM-31 instruments onboard INTERBALL-1 spacecraft were used to study the small-scale correlation between solar wind ion flux and magnetic field magnitude in the Earth's foreshock. Correlated quasi-harmonic structures were found simultaneously in ion flux and magnetic field data. Statistical analysis of these structures was done and a summary of obtained results is presented. Multipoint observations by INTERBALL-1 and MAGION-4 were used to estimate spatial correlation of small quasi-harmonic structures.

Evidence for Langmuir wave tunneling in the inhomogeneous solar wind

Spacecraft observations of beat‐like Langmuir waveforms on two orthogonal antennas in Earth's foreshock and the solar wind have been interpreted as beating associated with large‐angle reflection of Langmuir waves from density inhomogeneities or nonlinear decay processes. However, the waveforms are often irregular, with uncorrelated waveform envelopes on orthogonal antennas. One interpretation is that irregular waveforms are a manifestation of the electromagnetic nature of Langmuir waves scattered to low wave numbers in the inhomogeneous solar wind. An alternative interpretation, investigated here, is that the shape of the waveform envelopes on orthogonal antennas becomes substantially different as Langmuir waves tunnel through evanescent regions, where the local plasma frequency in the inhomogeneous plasma exceeds the Langmuir wave frequency. We demonstrate that observations of uncorrelated waveform envelopes on orthogonal antennas are consistent with theoretical predictions for Langmuir wave tunneling in evanescent regions in the inhomogeneous solar wind. Incident Langmuir waves which are nearly aligned with the density gradient are also partially converted to transverse electromagnetic waves at the plasma frequency. The characteristic dual‐antenna waveform signature of mode conversion is difficult to detect for typical solar wind parameters.

A quantitative theory for terrestrial foreshock radio emissions

We present the first quantitative theoretical results for the spatial distribution and flux levels of fundamental (fp) and second harmonic (2fp) plasma radiation generated in Earth's foreshock by beam‐driven Langmuir waves. The theory predicts that both the fp and 2fp source regions typically extend over several hundred Earth radii (RE) along the tangent magnetic field line. In the direction perpendicular to the magnetic tangent, however, the source regions are more localized, with the peak emission confined to ≲10RE for 2fp radiation and ≲1RE for fp radiation. The flux levels predicted by our model are in close agreement with the levels measured in situ by various spacecraft, with typical values ∼10−14W m−2 for 2fp radiation. The fp flux densities are typically 2–3 orders of magnitude lower.

Oblique “1‐Hz” whistler mode waves in an electron foreshock: The Cassini near‐Earth encounter

The Cassini spacecraft flew toward the Earth in a trajectory almost along the Sun‐Earth line, giving a unique perspective of low‐frequency plasma waves in the Earth's foreshock. At the time of the fly‐through, the angle between the magnetic field and Sun‐Earth direction was ∼70°. For this orientation, only the most energetic (≥12 keV) ions could reach the upstream region, thus Cassini passed through an almost “pure” electron foreshock. We demonstrate the presence of nonlinear foreshock “1‐Hz” whistler‐mode waves and their properties. Power spectra demonstrate that the waves span a frequency range from ∼0.3 to ∼10 Hz with a center frequency of ∼2 Hz. Close to the bow shock the waves had peak‐to‐peak transverse amplitudes as large as ∼14 nT in a 35‐nT ambient field. The waves were compressive with a maximum value of Δ|B|/B0 ≈ 0.25. The waves were propagating primarily along B0. Of the waves, 82% were right‐hand‐polarized, 9% were linearly polarized, and 9% were left‐hand‐polarized (in the spacecraft frame). The wave amplitudes were largest near the bow shock and decreased with increasing distance in the upstream direction. Further from the shock the waves are determined to be propagating obliquely to B0 (θkB≥20°). There is an equal mix of right‐hand, left‐hand, and linearly polarized (in the spacecraft frame) waves. Left‐hand‐polarized waves propagating parallel to B0 were not detected. Wave power changed dramatically as the interplanetary magnetic field rotated slightly. Arguments are presented for why low‐energy (tens of eV) electrons are responsible for wave generation, rather than cyclotron resonant energetic (>13 keV) electrons.

The dependence of plasma and magnetic field correlations in the solar wind on geomagnetic activity

The solar wind structures measured by four spacecraft (ISEE 1, ISEE 3, IMP 8, and Wind) are correlated and examined in the light of their geoeffectiveness. The average plasma and magnetic field correlations range from about 0.6 to 0.7 during quiet periods and increase substantially during the geomagnetic storms. Using the Ap and Dst indices as a measure for the level of geomagnetic disturbance, we find that correlations of plasma density, |B|, Bz and By are about 0.85 for the most geoeffective events. Earth's foreshock significantly degrades the correlation when one or both spacecraft are within ∼30 RE of Earth during quiet periods, and this degradation extends beyond 50 RE during geoeffective periods. Excluding the foreshock effect, the correlations show little dependence on the spacecraft separation along the Sun‐Earth line, but depend strongly on the spacecraft separation in the direction perpendicular to the Earth‐Sun line, consistent with previous findings. The decrease in correlation in the perpendicular direction is less severe during geoeffective periods, suggesting that geoeffective features have larger scale sizes. The front normals of geoeffective features are predominantly in the propagation direction, consistent with radially outward propagating ejecta.

Theory of type II radio emission from the foreshock of an interplanetary shock

We present an analytical model for type II solar radio bursts and then apply it to an observed type II event. Electron beams are produced in the foreshock of an interplanetary shock via shock drift acceleration. Reflection is treated in the de Hoffman‐Teller frame with efficiencies modeled by a losscone that incorporates the effects of the static cross‐shock potential ϕ. Stochastic growth theory is used to treat electron beam driven Langmuir wave growth in the type II foreshock. Nonlinear wave‐wave interactions are used as the mechanisms for converting Langmuir wave energy into freely propagating radio emission. The electron beams produced in the foreshock have a wide range of speeds and number densities. These electron beams are qualitatively consistent with observations in a type II foreshock as well as earlier theoretical predictions, and observations in Earth's foreshock. Significant levels of Langmuir waves and ƒp and 2ƒp emission are predicted. In particular, the predicted volume emissivities are similar to those predicted for type III bursts. The simple model developed for the source environment of the type II event on August 26, 1998, produces fluxes in reasonable agreement with observation.

Solar wind preconditioning in the flank foreshock: IMP 8 observations

We use IMP 8 plasma, magnetic field, and energetic ion observations within the Earth's foreshock from January through August 1995 to determine the effects of energetic ion bursts on the ambient solar wind for comparison with model predictions. Owing to the spiral interplanetary magnetic field orientation, the events are far more common upstream from the prenoon than postnoon bow shock. Pressures associated with the energetic ions depress foreshock magnetic field strengths and plasma densities. The magnitude of the depression is proportional to the intensity of energetic ions. The excavated plasma and magnetic field sometimes pile up in narrow regions of enhanced plasma densities and magnetic field strengths, but depressed flow velocities, just outside the foreshock cavities. Typical amplitudes of the depressions and enhancements at IMP 8 far upstream from the bow shock are far less (20% and 10%, respectively) than those seen in past case studies of events observed just outside the bow shock. The cavities occur preferentially during high‐speed solar wind streams but show no clear dependence upon other solar wind parameters. The distribution of burst durations resembles those for interarrival times for interplanetary magnetic field discontinuities, magnetopause motion, and flux transfer events, suggesting causal relationships between these phenomena.

Stochastic growth theory of spatially‐averaged distributions of Langmuir Fields in Earth's foreshock

Langmuir‐like waves in the foreshock of Earth are characteristically bursty and irregular, and are the subject of a number of recent studies. Averaged over the foreshock, it is observed that the probability distribution (log E) is power‐law in the wave field E, with the bar denoting this averaging over position. In this paper it is shown that stochastic growth theory (SGT) can explain power‐law spatially‐averaged distributions (log E), when the observed power‐law variations of the mean and standard deviation of log E with position are combined with the log normal statistics predicted by SGT at each location.