Electron Acoustic Instability Research Articles

Effects of suprathermal electrons on electron-acoustic instabilities

We study the electron-acoustic instabilities in plasmas with two kappa-distributed electrons and stationary ions. The instabilities are driven by the relative drift between two electron components. The suprathermal effects of different species on growth rates and instability thresholds are analyzed and compared by numerical calculations. The present study reveals that the suprathermal electrons with slow most probable speed play more important roles than the suprathermal ones with fast most probable speed. The former significantly reduces the instabilities and raises the instability thresholds. The parameters used in this study are inspired from the observations in Earth’s magnetopause.

Preacceleration in the Electron Foreshock. I. Electron Acoustic Waves

To undergo diffusive shock acceleration, electrons need to be preaccelerated to increase their energies by several orders of magnitude, else their gyroradii will be smaller than the finite width of the shock. In oblique shocks, where the upstream magnetic field orientation is neither parallel nor perpendicular to the shock normal, electrons can escape to the shock upstream, modifying the shock foot to a region called the electron foreshock. To determine the preacceleration in this region, we undertake particle-in-cell simulations of oblique shocks while varying the obliquity and in-plane angles. We show that while the proportion of reflected electrons is negligible for θ Bn = 74.°3, it increases to R ∼ 5% for θ Bn = 30°, and that, via the electron acoustic instability, these electrons power electrostatic waves upstream with energy density proportional to R 0.6 and a wavelength ≈2λ se, where λ se is the electron skin length. While the initial reflection mechanism is typically a combination of shock-surfing acceleration and magnetic mirroring, we show that once the electrostatic waves have been generated upstream, they themselves can increase the momenta of upstream electrons parallel to the magnetic field. In ≲1% of cases, upstream electrons are prematurely turned away from the shock and never injected downstream. In contrast, a similar fraction is rescattered back toward the shock after reflection, reinteracts with the shock with energies much greater than thermal, and crosses into the downstream.

The electron foreshock at high-Mach-number non-relativistic oblique shocks

In the Universe, matter outside of stars and compact objects is mostly composed of collisionless plasma. The interaction of a supersonic plasma flow with an obstacle results in collisionless shocks that are often associated with intense nonthermal radiation and the production of cosmic ray particles. Motivated by simulations of non-relativistic high-Mach-number shocks in supernova remnants, we investigate the instabilities excited by relativistic electron beams in the extended foreshock of oblique shocks. The phase-space distributions in the inner and outer foreshock regions are derived with a particle-in-cell simulation of the shock and used as initial conditions for simulations with periodic boundary conditions to study their relaxation toward equilibrium. We find that the observed electron-beam instabilities agree very well with the predictions of a linear dispersion analysis: the electrostatic electron-acoustic instability dominates in the outer region of the foreshock, while the denser electron beams in the inner foreshock drive the gyroresonant oblique-whistler instability.

Electron Heat Flux Instabilities in the Inner Heliosphere: Radial Distribution and Implication on the Evolution of the Electron Velocity Distribution Function

Abstract This Letter investigates the electron heat flux instability using the radial models of the magnetic field and plasma parameters in the inner heliosphere. Our results show that both the electron acoustic wave and the oblique whistler wave are unstable in the regime with large relative drift speed (ΔV e ) between electron beam and core populations. Landau-resonant interactions of electron acoustic waves increase the electron parallel temperature that would lead to suppressing the electron acoustic instability and amplifying the growth of oblique whistler waves. Therefore, we propose that the electron heat flux can effectively drive oblique whistler waves in an anisotropic electron velocity distribution function. This study also finds that lower-hybrid waves and oblique Alfvén waves can be triggered in the solar atmosphere, and that the former instability is much stronger than the latter. Moreover, we clarify that the excitation of lower-hybrid waves mainly results from the transit-time interaction of beaming electrons with resonant velocities v ∥ ∼ ω/k ∥, where ω and k ∥ are the wave frequency and parallel wavenumber, respectively. In addition, this study shows that the instability of quasi-parallel whistler waves can dominate the regime with medium ΔV e at the heliocentric distance nearly larger than 10 times of the solar radius.

Electron acoustic instability in four component space plasmas with observed generalized (r,q) distribution function

Electron acoustic instability in magnetized four component plasma has been studied by employing non-Maxwellian generalized (r, q) distribution function. We observed electron velocity distribution function using Cluster data and found that the electron distribution contains three components, cool, hot and warm beam (strahl) all showing flat-top nature. By fitting the observed distribution with the generalized (r, q) distribution, we used the fitting parameters for cool, hot and beam electron components in the numerical results. We have investigated the effect of beam density, beam temperature, beam velocity and propagation angle on the real frequency and growth rate of the electron acoustic waves in strongly magnetized plasma.

Electron acoustic waves and parametric instabilities in a 4-component relativistic quantum plasma with Thomas-Fermi distributed electrons

The interaction of Circularly Polarized Electro-Magnetic (CPEM) waves with a 4-component relativistic quantum plasma is studied. The plasma constituents are: relativistic-degenerate electrons and positrons, dynamic degenerate ions, and Thomas-Fermi distributed electrons in the background. We have employed the Klein-Gordon equations for the electrons as well as for the positrons, while the ions are represented by the Schrodinger equation. The Maxwell and Poisson equations are used for electromagnetic waves. Three modes are observed: one of the modes is associated with the electron acoustic wave, a second mode at frequencies greater than the electron acoustic wave mode could be associated with the positrons, and the third one at the lowest frequencies could be associated with the ions. Furthermore, Stimulated Raman Scattering (SRS), Modulational, and Stimulated Brillouin Scattering (SBS) instabilities are studied. It is observed that the growth rates of both the SRS and SBS instabilities decrease with incre...

Multiple-scale kinetic simulations with the energy conserving semi-implicit particle in cell method

The recently developed energy conserving semi-implicit method (ECsim) for particle-in-cell (PIC) simulation is applied to multiple-scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or ion-scale processes. Unlike hybrid methods, the ECsim is capable of providing kinetic electron information, such as wave–electron interaction (Landau damping or cyclotron resonance) and non-Maxwellian electron velocity distributions. However, like hybrid methods, the ECsim does not need to resolve all electron scales, allowing time steps and grid spacings orders of magnitude larger than in explicit PIC schemes. The additional advantage of the ECsim is that the stability at large scale is obtained while conserving energy exactly. Three examples are presented: ion acoustic waves, electron acoustic instability and reconnection processes.

On the generation of double layers from ion- and electron-acoustic instabilities

A plasma double layer (DL) is a nonlinear electrostatic structure that carries a uni-polar electric field parallel to the background magnetic field due to local charge separation. Past studies showed that DLs observed in space plasmas are mostly associated with the ion acoustic instability. Recent Van Allen Probes observations of parallel electric field structures traveling much faster than the ion acoustic speed have motivated a computational study to test the hypothesis that a new type of DLs—electron acoustic DLs—generated from the electron acoustic instability are responsible for these electric fields. Nonlinear particle-in-cell simulations yield negative results, i.e., the hypothetical electron acoustic DLs cannot be formed in a way similar to ion acoustic DLs. Linear theory analysis and the simulations show that the frequencies of electron acoustic waves are too high for ions to respond and maintain charge separation required by DLs. However, our results do show that local density perturbations in a two-electron-component plasma can result in unipolar-like electric field structures that propagate at the electron thermal speed, suggesting another potential explanation for the observations.

A particle-in-cell approach to obliquely propagating electrostatic waves

The electron-acoustic and beam-driven modes associated with electron beams have previously been identified and studied numerically. These modes are associated with Broadband Electrostatic Noise found in the Earth's auroral and polar cusp regions. Using a 1-D spatial Particle-in-Cell simulation, the electron-acoustic instability is studied for a magnetized plasma, which includes cool ions, cool electrons and a hot, drifting electron beam. Both the weakly and strongly magnetized regimes with varying wave propagation angle, θ, with respect to the magnetic field are studied. The amplitude and frequency of the electron-acoustic mode are found to decrease with increasing θ. The amplitude of the electron-acoustic mode is found to significantly grow at intermediate wavenumber ranges. It reaches a saturation level at the point, where a plateau forms in the hot electron velocity distribution after which the amplitude of the electron-acoustic mode decays.

High and low frequency instabilities driven by counter-streaming electron beams in space plasmas

A four-component plasma composed of a drifting (parallel to ambient magnetic field) population of warm electrons, drifting (anti-parallel to ambient magnetic field) cool electrons, stationary hot electrons, and thermal ions is studied in an attempt to further our understanding of the excitation mechanisms of broadband electrostatic noise (BEN) in the Earth's magnetospheric regions such as the magnetosheath, plasmasphere, and plasma sheet boundary layer (PSBL). Using kinetic theory, beam-driven electrostatic instabilities such as the ion-acoustic, electron-acoustic instabilities are found to be supported in our multi-component model. The dependence of the instability growth rates and real frequencies on various plasma parameters such as beam speed, number density, temperature, and temperature anisotropy of the counter-streaming (relative to ambient magnetic field) cool electron beam are investigated. It is found that the number density of the anti-field aligned cool electron beam and drift speed play a central role in determining which instability is excited. Using plasma parameters which are closely correlated with the measurements made by the Cluster satellites in the PSBL region, we find that the electron-acoustic and ion-acoustic instabilities could account for the generation of BEN in this region.

High and low frequency instabilities driven by a single electron beam in two-electron temperature space plasmas

In an attempt to understand the excitation mechanisms of broadband electrostatic noise, beam-generated electrostatic instabilities are investigated using kinetic theory in a four-component magnetised plasma model composed of beam electrons (magnetic field-aligned), background hot and cool electrons and ions. All species are fully magnetised and considered to be Maxwellian. The dependence of the instability growth rates and real frequencies on various plasma parameters such as beam speed, particle densities and temperatures, magnetic field strength, wave propagation angle, and temperature anisotropy of the beam are examined. In this study we have found that the electron-acoustic, electron beam-resonant and ion-acoustic instabilities are excited. Our studies have focused on three velocity regimes, namely, the low (vdbz<Ch), intermediate (Ch<vdbz<2 Ch), and high velocity (vdbz>2 Ch) regimes, where vdbz (Ch) is the electron beam drift speed (thermal speed of the hot electrons). Plasma parameters from satellite measurements are used where applicable to provide realistic predictions.

The magnetized electron-acoustic instability driven by a warm, field-aligned electron beam

The electron-acoustic instability in a magnetized plasma having three electron components, one of which is a field-aligned beam of intermediate temperature, is investigated. When the plasma frequency of the cool electrons exceeds the electron gyrofrequency, the electron-acoustic instability “bifurcates” at sufficiently large propagation angles with respect to the magnetic field to yield an obliquely propagating, low-frequency electron-acoustic instability and a higher frequency cyclotron-sound instability. Each of these instabilities retains certain wave features of its progenitor, the quasiparallel electron-acoustic instability, but displays also new magnetic qualities through its dependence on the electron gyrofrequency. The obliquely propagating electron-acoustic instability requires a lower threshold beam speed for its excitation than does the cyclotron-sound instability, and for low to intermediate beam speeds has the higher maximum growth rate. When the plasma is sufficiently strongly magnetized that the plasma frequency of the cool electrons is less than the electron gyrofrequency, the only instability in the electron-acoustic frequency range is the strongly magnetized electron-acoustic instability. Its growth rate and real frequency exhibit a monotonic decrease with wave propagation angle and it grows at small to intermediate wave numbers where its parallel phase speed is approximately constant. The relevance of the results to the interpretation of cusp auroral hiss and auroral broadband electrostatic noise is briefly discussed.

Excitation of electron acoustic waves near the electron plasma frequency and at twice the plasma frequency

In this paper we investigate the nonlinear development of the electron acoustic instability that can lead to the transfer of wave energy to frequencies just above the electron plasma frequency (ωpe) and to waves with approximately twice the electron plasma frequency (2ωpe). Using plasma conditions in the upstream electron foreshock region based on data from the AMPTE‐UKS spacecraft, an electron beam is considered in plasma containing a background of hot and cold electrons. This leads to the linear excitation of large‐amplitude electron acoustic waves at frequencies between about 0.8 and 1.0 ωpe. A modified decay instability then excites waves in the spectrum just above ωpe. This is followed by a second nonlinear coalescence process that causes the excitation of waves at frequencies just below 2ωpe. The linear and nonlinear properties of the electron acoustic instability are examined for observed conditions using analytical theory, particle‐in‐cell simulations, and Vlasov simulations. These results have application to observations made inside the electron foreshock region, as well as the polar cap and auroral zone, where plasma oscillations and waves at 2ωpe are observed.

Electron-acoustic instability driven by a crossfield hot electron-beam

On the basis of kinetic theory, the electron-acoustic instability is studied in a three component plasma consisting of a hot electron-beam and stationary cool electrons and ions. The transformation of the instability into the modified two-stream instability for wave propagation oblique to the confining magnetic field is also investigated. In our model both the electrons and ions are magnetized, with the beam drifting across the external magnetic field. The dependence of the growth rate on plasma parameters, such as electron-beam density, electron-beam speed, magnetic field strength and propagation angle, is examined. In addition, we investigate the effect of anisotropies in the velocity distributions of the hot electron-beam and the cool electrons on the instability growth rate.

Electron-acoustic instability driven by a field-aligned hot electron beam

Using kinetic theory, the electron-acoustic instability is investigated in a three-component plasma consisting of a hot electron beam and stationary cool electrons and ions. In the model considered here both the electrons and ions are magnetized, with the beam drift along the external magnetic field. The dependence of the growth rate on plasma parameters, such as electron-beam density, electron-beam speed, magnetic field strength and propagation angle, is studied. In addition, the effects of anisotropies in the velocity distributions of the hot electron beam and the cool electrons on the instability growth rate are examined.

Wave propagation effects of broadband electrostatic noise in the magnetotail

The theory for the generation of broadband electrostatic noise (BEN) by plasma instabilities of energetic ion beams that exist in the plasma sheet boundary layer (PSBL) predicts two characteristic signatures in the wave data for BEN. These signatures are a gradual rise in the upper frequency of BEN as the spacecraft approaches the plasma boundary layer, and a very rapid rise in the upper frequency near the crossing into the plasma sheet boundary layer from the lobe. Wave data from the 1978 ISEE 1 mission are investigated during approaches and crossings for those two signatures. Several examples of crossings are presented that exhibit both signatures similar to that predicted by the theory. A case of crossings is shown in which the gradual frequency rise signature is absent but the rapid rise is present. This exhibits BEN in the range expected for the low‐frequency ion‐ion two‐stream and the high‐frequency Buneman instability. The intermediate frequencies are less intense, which may arise because the intermediate frequency beam‐acoustic instability is close to stability (a warm beam temperature can quench it), as is the electron acoustic instability that can occur for warmer ion beams. An example is also given that was detected in a 1980 entry into the PSBL.

Broadband electrostatic noise due to field‐aligned currents

There are observations of broadband electrostatic noise in the plasma sheet boundary layer that are associated with field‐aligned currents (electron beams), which often have an upper cutoff frequency above the electron plasma frequency. In this paper, using linear theory and numerical simulations we present results from a study of instabilities caused by an electron beam in a thermally mixed plasma. It is shown that two instabilities, the electron acoustic and electronion instabilities can combine to form a broadbanded wave spectrum that rapidly destroys the electron beam.

Simulation of the electron acoustic instability for a finite‐size electron beam system

Satellite observations at midaltitudes (≈ 20,000 km) near the earth's dayside polar cusp boundary layer indicate that the upward electron beams have a narrow latitudinal width up to 0.1°. In the cusp boundary layer where the electron population consists of a finite‐size electron beam in a background of uniform cold and hot electrons, the electron acoustic mode is unstable inside the electron beam but damped outside the electron beam. Simulations of the electron acoustic instability for a finite‐size beam system are carried out with a particle‐in‐cell code to investigate the heating phenomena associated with the instability and the width of the heating region. The simulations show that the finite‐size electron beam radiates electrostatic electron acoustic waves. The decay length of the electron acoustic waves outside the beam in the simulation agrees with the spatial decay length derived from the linear dispersion equation. The ambient cold electrons in a diffusion region surrounding the beam are heated to a higher temperature by absorbing the radiated electron acoustic waves, with the heating occurring mainly in the parallel direction. In the heat diffusion region, the temperature of the cold electrons decreases with the distance from the beam with a temperature gradient length smaller than the decay length of the wave energy. This feature of electron heating is modeled by using a heat diffusion equation derived from the second‐order theory. In solving the heat diffusion equation, the wave energy inside the beam is assumed to be saturated by trapping the beam and the cold electrons. The dominant wave number is determined by assuming that the wave frequency outside the beam is equal to the frequency corresponding to the maximum growth rate inside the beam. These results are discussed with respect to the DE 1 plasma and wave observations in the polar cusp region. Using the typical parameters in the cusp boundary layer, the spatial decay length of the electron acoustic waves is estimated to be in the range of 1–10 km and the heat diffusion region is about 5 km. The results suggest that the electron acoustic waves generated by cusp upward electron beams are probably confined in a small region surrounding the beams.

Generation of high‐frequency broadband electrostatic noise: The role of cold electrons

Broadband electrostatic noise (BEN) is commonly observed in the plasma sheet boundary layer in association with ion beams. Here we investigate the generation of these waves in a plasma consisting of an ion beam and a background of hot ions, hot electrons, and cold electrons. The cold electrons are of ionospheric origin. A complete, systematic study of electrostatic ion beam instabilities, including cold electrons, has been done, and it is shown that for the plasma configuration described, four instabilities can be excited. These are the (1) ion acoustic, (2) Buneman, (3) beam resonant, and (4) electron acoustic instabilities. A low and high beam temperature division is shown to exist that separates when different instabilities can be excited. For typically observed parameters in the plasma sheet boundary layer, the ion beams lie in the high‐temperature regime. In this regime, the beam resonant and electron acoustic instabilities are excited, and these instabilities can account for the high‐frequency (> 500 Hz), low‐power portion of the BEN spectrum. In the absence of cold electrons, no such wave growth occurs.

Electron acoustic instabilities in the geomagnetic tail

Electron acoustic waves present in a two temperature electron plasma can be driven unstable when ion beams propagate along the magnetic field. Both linear theory and numerical simulations indicate that this instability contributes to the generation of broadband electrostatic noise (BEN) in the geomagnetic tail.