Electron Acoustic Waves Research Articles

Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-perpendicular Shocks

Collisionless low-Mach-number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave–particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (v sh ≈ (5500–22000) km s−1) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that the EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (v sh ≈ 300 km s−1), the ESW wavelength is reduced to one-tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.

Electron-acoustic solitary waves via suprathermal populations in Saturn's magnetosphere: Bifurcation, sensitivity, and stability analysis

Cassini and Voyager space missions observed non-thermal electron populations (with varying characteristics) in Saturn's magnetosphere, which can be correctly described using kappa distributions. Based on these observations, our objective is to inspect the evolution of electron-acoustic solitary waves (EASWs) within Saturn's magnetosphere. The propagation of weakly nonlinear (EASWs) in a collisional plasma system comprising a cold electron fluid, hot electrons following a kappa distribution, and stationary ions is investigated. By employing the reductive perturbation technique, the Korteweg–de Vries Burgers (KdV–B) equation is derived. An exact solution of the KdV–B equation, with a conformable time-derivative, is found using the unified method. It is observed that plasma current-induced collision between electrons and ions leads to remarkable dissipation, generating EASWs. Furthermore, when studying the sensitivity of the system, the appearance of a positive potential is depicted as external forces vanish, which may be due to stationary ions. Additionally, bifurcation, stability, and significant influence of plasma characteristics are considered.

Soliton interaction in a two-temperature electron plasma with trapping and superthermality effects

Head-on collision of the two small-amplitude electron-acoustic (EA) solitons is studied in an unmagnetized collisionless plasma in the presence of superthermal (hot) trapped electrons. For this purpose, using a well-known extended Poincare–Lighthill–Kuo (PLK) method, a pair of the trapped Korteweg–de Vries (tKdV) equations is derived to investigate the soliton trajectories and phase shifts. The latter are found dependent on amplitudes of the interacting solitons, effectively altering with hot-electron superthermality and plasma parameters. Typical parameters for the electron diffusion region (EDR) and day-side auroral zone have been selected to examine the impact of hot-electron superthermality, trapping parameter, hot-to-cold electron number density ratio, and cold-to-hot electron temperature ratio on the profiles of potential excitations and phase shifts of interacting solitons. It is found that phase speed of the EA waves becomes altered by varying the κ–parameter, strongly modifying the nonlinearity and dispersive coefficients in a superthermal trapped plasma. However, particle trapping phenomenon does not affect the linear phase speed but introduces a fractional nonlinearity in the tKdV equations of two interacting solitons. The impact of the adiabatic and isothermal pressures is also highlighted to show new modifications in the propagation characteristics of two interacting solitons.

Electron acoustic solitary waves in relativistically quantum magnetoplasmas with electron exchange correlation effects

The propagating of electron acoustic solitary waves (EASWs) in relativistically magnetized quantum plasmas which consists inertial cold electrons, inertialess hot electrons and stationary background ions have been theoretically investigated. The modified Zakharov-Kuznetsov (ZK) equation is derived by adopting the standard reductive perturbation method to describe the nonlinear evolution of the EASWs. After discussing the effects of various parameter values on the solitary structures, it is shown that the solitary structures are very sensitive to the relativistic degeneracy effect, the cold to hot electrons number density ratio and the electron exchange correlation effects. The numerical analysis can be well described by the existing analytical theory. Our results may be useful in explaining the physics behind the formation of the EASWs in both astrophysical and laboratory plasmas.

Influences of densities and thermal temperatures of electron and beam fluids on the characteristics of the electron acoustic electrostatic fields and fluid energies

A model of nonlinear electron acoustic electrostatic plasma waves having electron beams has been investigated. The structure of Korteweg–de Vries soliton energy and the corresponding electrostatic field have been discussed. The parametric regimes for wave existence of compressive and rarefactive structures have been examined via auroral zone data. The effects of densities and thermal temperature of electrons and beams on the nature of the electrostatic field and fluid energies have been taken into account.

Beam‐Driven Electron Cyclotron Harmonic and Electron Acoustic Waves as Seen in Particle‐In‐Cell Simulations

AbstractRecent study has demonstrated that electron cyclotron harmonic (ECH) waves can be excited by a low energy electron beam. Such waves propagate at moderately oblique wave normal angles (∼70°). The potential effects of beam‐driven ECH waves on electron dynamics in Earth's plasma sheet is not known. Using two‐dimensional Darwin particle‐in‐cell simulations with initial electron distributions that represent typical plasma conditions in the plasma sheet, we explore the excitation and saturation of such beam‐driven ECH waves. Both ECH and electron acoustic waves are excited in the simulation and propagate at oblique wave normal angles. Compared with the electron acoustic waves, ECH waves grow much faster and have more intense saturation amplitudes. Cold, stationary electrons are first accelerated by ECH waves through cyclotron resonance and then accelerated in the parallel direction by both the ECH and electron acoustic waves through Landau resonance. Beam electrons, on the other hand, are decelerated in the parallel direction and scattered to larger pitch angles. The relaxation of the electron beam and the continuous heating of the cold electrons contribute to ECH wave saturation and suppress the excitation of electron acoustic waves. When the ratio of plasma to electron cyclotron frequency ωpe/ωce increases, the ECH wave amplitude increases while the electron acoustic wave amplitude decreases. Our work reveals the importance of ECH and electron acoustic waves in reshaping sub‐thermal electron distributions and improves our understanding on the potential effects of wave‐particle interactions in trapping ionospheric electron outflows and forming anisotropic (field‐aligned) electron distributions in the plasma sheet.

Bifurcation analysis of electron-acoustic waves in electron beam-plasma with suprathermal electrons

It has investigated the properties of nonlinear electron-acoustic waves propagating in a four-component collisionless, unmagnetized plasma. The system consists of cool inertial background electrons of temperature T c , the cool inertial electron beam of temperature T b , hot inertialess suprathermal electrons modeled by a κ-distribution of temperature T h , and ions. The nonlinear modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation that characterizes the electron acoustic waves in such a plasma model is derived. The wave solutions of the resultant mKdV-Burgers equation are investigated using planar dynamical system bifurcation theory. The unperturbed hot, cool, and beam electron densities and the superthermal electron parameter are revealed to have a considerable influence on the nonlinear electron-acoustic traveling waves and the associated electric fields. The system evolves also monotonic shock waves when the dissipation term dominates over the dispersion term. The current model might be useful for understanding the generation of nonlinear electron-acoustic waves in a variety of astrophysical plasma settings, including the Earth's magnetosphere.

Nonlinear electron-acoustic waves in non-Maxwellian plasma: application in terrestrial magnetosphere

Nonlinear electron-acoustic waves in non-Maxwellian plasma: application in terrestrial magnetosphere

Small amplitude solitary electron acoustic wave for hot electrons taking regularized kappa distribution

AbstractThe properties of small‐amplitude solitary electron acoustic waves in a plasma where the hot electrons take regularized kappa distribution are investigated via the reductive perturbation method. It is found there only exists the sup‐electron‐acoustic rarefactive soliton, the electron acoustic velocity is modified by the regularized kappa distribution. The amplitude and width of the electron acoustic soliton decrease monotonously with the increase of the exponential cutoff parameter of hot electrons. But they vary with respect to the spectral index non‐monotonously. As to the observed parameters in the Earth's inner magnetosphere, the speed, electric field strength, and the width of solitary electron acoustic wave are comparable with the observations.

Intermittency, bursty turbulence, and ion and electron phase-space holes formation in collisionless current-carrying plasmas

In the previous studies of nonlinear saturation of the Buneman instability caused by high electron drift velocity relative to ions, the phase-space holes and the plateau on the electron velocity distribution function were identified as features of the saturation stage of instability [notably in the paper by Omura et al., J. Geophys. Res. 108, 1197 (2003)]. We have performed a much longer simulation of the Buneman instability and observed a secondary instability. This secondary instability generates fast electron-acoustic waves. By analyzing the phase-space plot of ions and electrons, we show that the fast electron heating and the formation of the plateau of electron velocity distribution function are not due to the quasi-linear diffusion but due to the nonlinear interaction of ion- and electron-acoustic solitary waves (phase-space holes) by exchange of trapped electrons in each wave. We also report the details on the intermittent and bursty nature of turbulence driven by this instability.

Numerical Simulation for Solitary Waves of the Generalized Zakharov Equation Based on the Lattice Boltzmann Method

The generalized Zakharov equation is a widely used and crucial model in plasma physics, which helps to understand wave particle interactions and nonlinear wave propagation in plasma. The solitary wave solution of this equation provides insights into phenomena such as electron and ion acoustic waves, as well as magnetic field disturbances in plasma. The numerical simulation of solitary wave solutions to the generalized Zakharov equation is an interesting problem worth studying. This is crucial for plasma-based technology, as well as for understanding nonlinear wave propagation in plasma physics and other fields. In this study, a numerical investigation of the generalized Zakharov equation using the lattice Boltzmann method has been conducted. The lattice Boltzmann method is a new modeling and simulating method at the mesoscale. A lattice Boltzmann model was constructed by performing Taylor expansion, Chapman–Enskog expansion, and time multiscale expansion on the lattice Boltzmann equation. By defining the moments of the equilibrium distribution function appropriately, the macroscopic equation can be restored. Furthermore, the numerical experiments for the equation are carried out with the parameter lattice size m=100, time step Δt=0.001, and space step size Δx=0.4. The solitary wave solution of the equation is numerically simulated. Numerical results under different parameter values are compared, and the convergence and effectiveness of the model are numerically verified. It is obtained that the model is convergent in time and space, and the convergence orders are all 2.24881. The effectiveness of our model was also verified by comparing the numerical results of different numerical methods. The lattice Boltzmann method demonstrates advantages in both accuracy and CPU time. The results indicate that the lattice Boltzmann method is a good tool for computing the generalized Zakharov equation.

Nonlinear Landau resonant interaction between whistler waves and electrons: Excitation of electron-acoustic waves

Electron-acoustic waves (EAWs) as well as electron-acoustic solitary structures play a crucial role in thermalization and acceleration of electron populations in Earth's magnetosphere. These waves are often observed in association with whistler-mode waves, but the detailed mechanism of EAW and whistler wave coupling is not yet revealed. We investigate the excitation mechanism of EAWs and their potential relation to whistler waves using particle-in-cell simulations. Whistler waves are first excited by electrons with a temperature anisotropy perpendicular to the background magnetic field. Electrons trapped by these whistler waves through nonlinear Landau resonance form localized field-aligned beams, which subsequently excite EAWs. By comparing the growth rate of EAWs and the phase mixing rate of trapped electron beams, we obtain the critical condition for EAW excitation, which is consistent with our simulation results across a wide region in parameter space. These results are expected to be useful in the interpretation of concurrent observations of whistler-mode waves and nonlinear solitary structures and may also have important implications for investigation of cross-scale energy transfer in the near-Earth space environment.

A two-dimensional numerical study of ion-acoustic turbulence

We investigate the linear and nonlinear evolution of the current-driven ion-acoustic instability in a collisionless plasma via two-dimensional (2-D) Vlasov–Poisson numerical simulations. We initialise the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding physically unrealisable super-critical initial conditions. A comprehensive analysis of the nonlinear evolution of ion-acoustic turbulence (IAT) is presented, including the detailed characteristics of the evolution of the particles’ distribution functions, (2-D) wave spectrum and the resulting anomalous resistivity. Our findings reveal the dominance of 2-D quasi-linear effects around saturation, with nonlinear effects, such as particle trapping and nonlinear frequency shifts, becoming pronounced during the later stages of the system's nonlinear evolution. Remarkably, the Kadomtsev–Petviashvili (KP) spectrum is observed immediately after the saturation of the instability. Another crucial and noteworthy result is that no steady saturated nonlinear state is ever reached: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived, challenging earlier theoretical results. Towards the conclusion of the simulation, electron-acoustic waves are triggered by the formation of a double layer and strong modifications to the particle distribution induced by IAT.

The Dynamics of Electron Acoustic Solitary Waves in a Nonmagnetized Quantum Plasma with Two Temperature Electrons

In this article we have studied the linear and nonlinear properties of plasma waves using a one-dimensional quantum hydrodynamic (QHD) model specifically designed for quantum plasma with electron acoustic waves (EAWs). In particular, we use the standard reductive perturbation method to investigate the solitary structures resulting from nonlinearity. We use this method to derive and numerically analyze the Kortewegde Vries (KdV) equation relevant to the plasma system as well as the dispersion relation. Furthermore, in order to shed light on the dynamics of plasma waves under external influences, we investigate the temporal evolution of a forced KdV equation. PACS-52.20.j; 52.25.b; 52.30.d; 52.35.Mw; 52.65.Vv.

The impact of electron beams on the arbitrary amplitude electron–acoustic solitons in a nonthermal plasma

This study examines the nonlinear dynamics of high-frequency electron–acoustic waves (EAWs) in a collisionless, unmagnetized plasma consisting of several components, including inertial cold electrons, an inertial electron beam, and inertialess Cairns-distributed hot electrons in addition to background stationary ions. We use a nonlinear pseudopotential (Sagadeev potential) method to investigate the possibility of stationary-profile electron–acoustic solitons (EASs). In this study, the nonthermal parameter, the temperature ratio between hot and cold electrons, density ratios, and electron beam parameters are carefully examined to see how they change the features of EASs. As the nonthermality of hot electrons rises, the beam speed decreases, the density ratio of the beam to the cold electron increases, and the existence domain for EASs gets bigger. The current theoretical model shows a link between the wideband noise seen in Geotail satellites and the plasma sheet boundary layer in Earth's magnetosphere.

Shock electrostatic electron acoustic wave features in four-component electron–positron plasma

The linear (nonlinear) wave properties of dissipative electron acoustic plasma have been studied. The impacts of temperatures and densities on the properties of linear real and imaginary (growth rate) plasma frequencies have been examined. The effects of viscosities in the linear growth rate are also studied. Accordingly, the significant shock-like electrostatic field in auroral plasmas has been discussed. Furthermore, the electrostatic dissipative fields have been studied to explain experimental observations. A comparison between the obtained electrostatic dissipative fields and satellite observations in auroral plasmas is briefly discussed.

Nonlinear interaction of electromagnetic wave with electron acoustic wave in plasma

An analysis on the nonlinear interaction of electromagnetic waves with electron acoustic waves is performed in plasma with two different temperature electron fluids in the presence of a neutralizing static ion background. A newly structured Zakharov’s equations are derived employing two fluid two-time scale theory. These coupled Zakharov’s equations describe the weakly nonlinear interaction of em wave perturbation with electron acoustic waves while propagating through plasma. In the low frequency or adiabatic limit, these Zakharov’s equations may be unified to produce a modified NLSE. A solution of the equation, novel in the literature, is derived following the method shown by Kudryashov. In a resonant regime, the modified NLSE reduces to NLSE. Though a stable solution exists for both cases, instability analysis shows caviton instability may arise. The threshold value of the electric field, at which instability sets in, is virtually zero for the resonant region whereas, apart from that region there is a threshold value of the electric field, determined by the frequency difference of em wave and electron plasma wave. Experimental observations support these results. This study is relevant for laser-plasma interaction and astrophysical and space plasma.

Effect of κ-deformed Kaniadakis distribution on the modulational instability of electron-acoustic waves in a non-Maxwellian plasma

In this paper, the modulational instability (MI) of the high-frequency electron-acoustic waves (EAWs) is reported in a non-Maxwellian plasma composed of two distinct types of electrons and stationary ions. One type of electrons is treated as a cold inertial fluid, whereas the other type is considered as inertialess species following κ-deformed Kaniadakis distribution. The fluid equations to the current model are reduced via a reductive perturbation technique to a nonlinear Schrödinger equation, which is then used to compute the MI and the growth rate of the EAWs. It is instructive to note that the deformation parameter (which develops the Kaniadakis entropy) and the hot-to-cold electron density ratio (hot electron concentration) significantly affect the conditions for MI. The modulated envelope black (dark and gray) solitons are investigated. The current results are beneficial in analyzing the spectrum of the cosmic rays, which violates manifestly the Boltzmann–Gibbs statistics. Moreover, the obtained results can be used to understand the mystery of many observations in stars where the presence of non-Maxwellian particles dominates.

Large‐Amplitude Shocklets With Trapped Hot‐Electrons in Space Plasmas

AbstractLarge‐amplitude stationary electron‐acoustic (EA) waves are studied, which are developed into the shocklets with the passage of time in an unmagnetized non‐isothermal plasma. The latter comprises two groups of electrons; namely the hot and cool electrons that are distinctly characterized by different electron densities and temperatures. On an EA timescale, the cool electrons behave as fluid, while non‐isothermal hot electrons obey the vortex‐like trapped distribution in the background of immobile ions. The nonlinear fluid equations are solved together both analytically and numerically within the framework of diagonalization matrix technique. Various parameters such as the free hot‐to‐trapped hot electron temperature ratio (β), the cool electron density ratio (α), and the cool‐to‐hot electron temperature ratio (σ) are numerically analyzed for dayside auroral zone plasma, showing a significant modification of solitary and shocklet structures. The plasma model is also applied to the electron diffusion region at the earth magnetopause, revealing the potential excitations depending significantly on the trapping parameter. These findings are important for understanding the nonlinear properties and steepening effects of the EA waves, especially in auroral zone and electron diffusion regions of earth's magnetosphere, where different types of electron populations are observed.

Electron-Acoustic Waves and Parametric Instabilities in 3-Component Relativistic Quantum Plasma with a Beam of Non-relativistic Quantum Electrons

Electron-Acoustic Waves and Parametric Instabilities in 3-Component Relativistic Quantum Plasma with a Beam of Non-relativistic Quantum Electrons