Earth's Electron Foreshock Research Articles

Determining the wavelength of Langmuir wave packets at the Earth's bow shock

Abstract. The propagation of Langmuir waves in plasmas is known to be sensitive to density fluctuations. Such fluctuations may lead to the coexistence of wave pairs that have almost opposite wave-numbers in the vicinity of their reflection points. Using high frequency electric field measurements from the WIND satellite, we determine for the first time the wavelength of intense Langmuir wave packets that are generated upstream of the Earth's electron foreshock by energetic electron beams. Surprisingly, the wavelength is found to be 2 to 3 times larger than the value expected from standard theory. These values are consistent with the presence of strong inhomogeneities in the solar wind plasma rather than with the effect of weak beam instabilities.

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.

Plasma waves in the Earth's electron foreshock: 1. Time‐of‐flight electron distributions in a generalized Lorentzian plasma and dispersion solutions

The correlated studies discussed here used high‐quality and frequent in situ measurements provided by the Wind spacecraft to investigate the properties of the foreshock plasma (measured by Wind/3DPlasma) and the enhanced plasma waves (detected by Wind/WAVES). A time‐of‐flight electron distribution model was developed in a generalized Lorentzian plasma using experimental data. The Wind/3DP results show that typical foreshock electron distributions are well approximated by this model, although discernible “bumps” in distributions that may be unstable are not often observed or resolved by the 3DP instrument. We used unstable distributions described by the model to initialize our study. In addition to verifying the interdependence of dispersion, cutoff velocity and beam density that was previously found in a Maxwellian beam‐plasma system, our dispersion solutions demonstrate how the dispersion topology and wave spectral bandwidths evolve as a consequence of wave modifications of time‐of‐flight distributions. By identifying sections of distributions that interact with each of the growing and damping branches, we analyzed the role played by nonthermal electrons in the evolution of the instability. Our results complement those from previous investigations and, more importantly, provide information about the linear behavior of the system that will enable the simulation studies discussed in our companion paper [Yin et al., this issue] to examine possible nonlinear interactions and to address the issue of whether nonlinear wave‐wave interactions in the foreshock nonthermal plasma are a significant factor in producing the observed electromagnetic emissions.

Generation of electromagnetic fpe and 2fpe waves in the Earth's electron foreshock via linear mode conversion

This study examines the mode conversion from electrostatic to electromagnetic waves near the plasma frequency in the Earth's electron foreshock. The conversion and reflection coefficients are obtained by solving coupled differential equations in a weakly magnetized warm plasma with a longitudinal linear density gradient. Results indicate that the foreshock first harmonic electromagnetic emissions and the backward‐propagating Langmuir waves required for the generation of the second harmonic electromagnetic waves may be efficiently produced by the linear conversion process in an inhomogeneous plasma.

Whistler instability enhanced by suprathermal electrons within the Earth's foreshock

The electron temperature‐anisotropy driven whistler instability in the presence of a suprathermal power law tail on the electron population, such as is observed in the Earth's electron foreshock, is investigated. The enhancement in energetic electrons significantly accentuates whistler growth at wavenumbers smaller than those expected for a bi‐Maxwellian electron distribution of similar temperature anisotropy and brings the unstable frequencies and wavelengths closer to those expected for the 1‐Hz (in the spacecraft frame) whistler waves observed in the electron foreshock. The presence of a power law tail, furthermore, causes a rapid increase in growth rate with increasing electron temperature anisotropy. This means that even very modest temperature anisotropies, like those that are frequently present in the magnetically connected foreshock, can strongly destabilize parallel whistlers. This instability could be responsible for the nearly field aligned so‐called “1 Hz” whistlers previously observed in the Earth's foreshock, which are more difficult to account for in models of the oblique whistler instability.

Observations of electron plasma waves upstream of the Jovian bow shock

The Ulysses spacecraft encountered the planet Jupiter in February 1992, on its journey towards high heliospheric latitude. During the approach to the planet, as well as on the outbound pass, while receding from the Jovian bow shock, the Plasma Frequency Receiver that is part of the Unified Radio and Plasma Wave experiment (URAP) recorded bursts of plasma waves in the frequency range of a few kHz. These emissions, first observed by the PWS experiment onboard the Voyager spacecraft, have been identified as upstream electron plasma waves. In this paper, we present the first analysis of the characteristics of these emissions, which are very similar to those found in the Earth's electron foreshock, upstream of the Earth's bow shock. These bursty emissions, with a peak frequency very close to the local electron plasma frequency F pe, have a typical electric field amplitude in the range 0.01–0.1 mV m −1, with some bursts above 1 mV m −1. The frequency bandwidth over which significant power can be found above the instrument background noise ranges from below 0.2 F pc to about 2 F pc. On the basis of our present knowledge of similar emissions observed at Earth, we suggest that the broadband emissions are triggered by suprathermal (a few tens of eV) electrons, streaming back from Jupiter's bow shock.

Electron density in the Martian foreshock as a by‐product of the electron plasma oscillation observations

Electron plasma oscillations have been observed in the solar wind upstream of the Martian bow shock by the plasma wave system (PWS) on the Phobos 2 spacecraft. These waves occurred when the interplanetary magnetic field line through the spacecraft position was connected to the shock, i.e., when the spacecraft went through the electron foreshock region in which suprathermal electrons accelerated at the bow shock were streaming back from it. The PWS observations are compared to the expectations one might have in light of the results obtained in the Earth's electron foreshock, which are briefly reviewed. The spectrum of the electron plasma oscillations peaks at or near the ambient solar wind plasma frequency. We then have an estimate of the solar wind plasma density upstream of the Martian bow shock. The 12‐min averages of the plasma density are shown to vary between less than 0.5 cm−3 and 19 cm−3 from February 1 to March 26, 1989. This corresponds to an electron plasma frequency range from 6.4 to 39 kHz. Moreover, some structures were observed in the electron foreshock region of Mars. They are presented and tentatively interpreted.

Strong plasma turbulence in the Earth's electron foreshock

A quantitative model is developed to account for the distribution in magnitude and location of the intense plasma waves observed in the Earth's electron foreshock given the observed rms levels of waves. In this model, nonlinear strong‐turbulence effects cause solitonlike coherent wave packets to form and decouple from incoherent background beam‐excited weak turbulence, after which they convect downstream with the solar wind while collapsing to scales as short as 100 m and fields as high as 2 V m−1. The existence of waves with energy densities above the strong‐turbulence wave‐collapse threshold is inferred from observations from IMP 6 and ISEE 1 and quantitative agreement is found between the predicted distribution of fields in an ensemble of such wave packets and the actual field distribution observed in situ by IMP 6. Predictions for the polarization of plasma waves and the bandwidth of ion‐sound waves are also consistent with the observations. It is shown that strong‐turbulence effects must be incorporated in any comprehensive theory of the propagation and evolution of electron beams in the foreshock. Previous arguments against the existence of strong turbulence in the foreshock are refuted.

Trapping saturation of the bump‐on‐tail instability and electrostatic harmonic excitation in Earth's foreshock

Trapping saturation of the bump‐on‐tail instability is discussed using electron plasma Vlasov simulation results. The role of electrostatic harmonic excitation is considered in detail and shown to play a decisive role in the saturation of the instability. An extensive discussion of the simulation results is given to show that the results are not significantly limited by the finite number of Fourier modes used nor by the discrete distribution of those modes in wave number. It is argued that in the leading edge of Earth's electron foreshock a narrow wave number band of unstable field modes leads to trapping saturation of the bump‐on‐tail instability while simultaneously exciting electrostatic plasma waves at harmonics of the plasma frequency in similar narrow bands of shorter wavelengths. The argument is based (1) on the observations of Lacombe et al. (1985), who found intense plasma waves at the leading edge of the foreshock with a spectral distribution sufficiently narrow to trap particles in resonance with the waves, and (2) on numerical simulations of the foreshock electron plasma which indicate that trapping saturation of the bump‐on‐tail instability leads to phase space vortex formation with consequent excitation of electrostatic harmonics. Thus it is suggested that observations of electrostatic harmonics in the leading edge of the foreshock would strongly implicate trapping as the saturation mechanism for the bump‐on‐tail instability in that region.

On the persistence of unstable bump‐on‐tail electron velocity distributions in the Earth's foreshock

Further evidence for the persistence of bump‐on‐tail unstable reduced velocity distributions in the Earth's electron foreshock is presented. This persistence contradicts our understanding of quasi‐linear saturation of the bump‐on‐tail instability; the distributions should be stabilized through velocity space diffusion too quickly to allow an observation of their unstable form. A modified theory for the saturation of the bump‐on‐tail instability in the Earth's foreshock is proposed and examined using numerical simulation and quasi‐linear theoretical techniques. It is argued that the mechanism due to Filbert and Kellogg and to Cairns which is responsible for the creation of the bump‐on‐tail velocity distribution in the foreshock is still operative during the evolution of the bump‐on‐tail instability. The saturated state of the plasma must represent a balance between this creation mechanism and velocity space diffusion; the saturated state is not determined by velocity space diffusion alone. Thus the velocity distribution of the saturated state may still appear bump‐on‐tail unstable to standard linear analysis which does not take the creation mechanism into account. The bump‐on‐tail velocity distributions observed in the foreshock would then represent the state of the plasma after saturation of the bump‐on‐tail instability, not before. Numerical simulations of two types are discussed. In the first, the particle distribution function and the field are assumed periodic over a spatial interval of several tens or hundreds of Debye lengths along the local magnetic field. In the second, nonperiodic boundary conditions are imposed on the distribution function to model the spatial gradients which are responsible for the creation of the bump‐on‐tail unstable distribution. This mechanism for creating the unstable distribution continues to drive the particle distribution unstable during the evolution of the bump‐on‐tail instability. The saturated velocity distributions of the periodic and nonperiodic simulated plasmas are compared. At saturation the periodic velocity distribution exhibits plateau formation while the nonperiodic distribution does not. A new quasi‐linear theory for the space‐averaged velocity distribution function is constructed. This theory includes the effects of nonperiodic boundary conditions; it can be used to compare the evolution of periodic and nonperiodic bump‐on‐tail unstable particle distributions. In addition, this theory is based on the filtered Vlasov‐Maxwell system of equations; velocity space filamentation has been removed from the distribution function. It is shown that this theory is applicable on a finite spatial interval within which the field has been expressed in terms of a discrete Fourier mode expansion. Thus direct comparisons between theory and simulation are possible. Some predictions of this new quasi‐linear theory are compared favorably to the results of the bump‐on‐tail simulations.

The downshift of electron plasma oscillations in the electron foreshock region

Electron plasma oscillations in the earth's electron foreshock region are observed to shift above and below the local electron plasma frequency. As plasma oscillations shift downward from the plasma frequency, their bandwidth increases and their wavelength decreases. Observations of plasma oscillations well below the plasma frequency are correlated with times when ISEE 1 is far downstream of the electron foreshock boundary. Although wavelengths of plasma oscillations below the plasma frequency satisfy kλDe ≈ 1, the Doppler shift due to the motion of the solar wind is not sufficient to produce the observed frequency shifts. A beam‐plasma interaction with beam velocities on the order of the electron thermal velocity is suggested as an explanation for plasma oscillations above and below the plasma frequency. Frequency, bandwidth, and wavelength changes predicted from the beam‐plasma interaction are in good agreement with the observed characteristics of plasma oscillations in the foreshock region.

Plasma electron signature of magnetic connection to the Earth's bow shock: ISEE 3

Enhanced fluxes of low‐energy electrons backstreaming from the earth's bow shock have been identified at ISEE 3. When present, these fluxes modify ambient solar wind electron velocity distributions f(υ) in characteristic ways that depends on whether ISEE 3 is near the edge of, or within the interior of the earth's electron foreshock. Near the edge, energy peaks in f(υ) are observed. Such distributions should be locally unstable to electron plasma oscillations. Well within the interior of the foreshock, enhanced fluxes of electrons with energies up to the maximum detected by the Los Alamos electron analyzer (∼1 keV) are observed over the full backward hemisphere. These electrons can be modelled with an asymptotic power law distribution having index in the range 4 ≲ pbs ≲ 6. At intermediate energies (∼20–50 eV), twin angular peaks are observed centered on the magnetic field direction . Also observed at these times are depressions in f(υ) at energies less than ∼20 eV that are centered on . Such distributions having a perpendicular temperature greater than their parallel temperature may be locally unstable to the generation of whistler waves. Analysis of a particularly clean example of connection to the bow shock is consistent with the possibility that the observed electron fluxes emerge from the forward foot of the electron heating region within the bow shock where the electron density and temperature are larger than that of the unperturbed upstream solar wind by a factor of ∼1.2. This analysis also indicates that the electrostatic potential within the forward foot of the shock is between ∼5 and 50 V more positive than that within plasma far upstream at ISEE 3. However, these interpretations depend on the assumption of nearly scatter‐free propagation, which may not hold. Using parameters derived from model fits to measured velocity distributions, we estimate ∼10−4 of the incident solar wind electrons are accelerated by the bow shock back into the upstream region with energies greater than 1 keV.