Electron-acoustic Double Layers Research Articles

Head-on collision between two-counter-propagating electron acoustic soliton and double layer in an unmagnetized plasma

The head-on collision between two-counter-propagating electron acoustic solitons and double layers (DLs) in an unmagnetized collisionless multi-species plasma consisting of inertial cold electron fluid and (α, q)-distributed hot electrons and positrons has been analyzed with the stationary background of massive positive ions. For nonlinear analysis of colliding wave phenomena, the coupled Korteweg–de Vries equation (KdVE), modified KdVE (mKdVE), and standard Gardner equation have been derived by adopting the extended Poincaré–Lighthill–Kuo technique. The effect of non-dimensional parameters on the collisional KdV, mKdV, and Gardner solitons (GSs) and DLs has been examined in detail by considering the limiting cases of (α, q)-distributions. It is found that the plasma model supports (i) the compressive and rarefactive collisional KdV solitons and GSs, (ii) only compressive mKdV solitons, and (iii) only rarefactive collisional DLs. The rarefactive collisional solitons are more affected by nonextensivity and the increase of the temperature of electrons than their compressive counterpart, whereas the rarefactive collisional DLs only existed in the presence of nonthermality.

Electron-acoustic solitons and double layers in a non-uniform plasma with field-aligned shear flow

Electron-acoustic solitary waves (EASWs) are investigated in a non-uniform electron plasma with field-aligned shear flow and two electron populations: hot and cold. Hot electrons are assumed to follow kappa distribution and temperature of cold electrons is considered to be less than those of hot electrons , whereas ions provide a stationary background of positive charge. Intermediate frequency drift wave couples with electron-acoustic wave (EAW) due to plasma density inhomogeneity. It is pointed out that the linear phase speed of the waves weakly depend upon the superthermality and temperature ratio of hot to cold electrons. Set of two fluid partial differential equations is reduced to an ordinary differential equation in a co-moving frame which has soliton solution in one limit. This ordinary differential equation can also be expressed in the form of an energy integral equation which admits double layer (DL) solution in another limit under appropriate boundary conditions. The results are applied to broadband electrostatic noise (BEN) in the dayside auroral zone of ionosphere.

Large-amplitude electrostatic fluctuations at the Earth’s magnetopause with a vortex-like distribution of hot electrons

Large-amplitude electrostatic solitary waves (ESWs) associated with asymmetric magnetic reconnection at the Earth’s magnetopause are studied in a four-component plasma composed of a mixture of the magnetosheath and magnetosphere plasma of a cold, warm and hot electron populations, and background ions. The species are modeled as adiabatic fluids except for the hot electrons which have a kinetic vortex-like velocity distribution. The hybrid model uses the Sagdeev pseudopotential technique to study the arbitrary amplitude ion- and electron-acoustic solitons and double layers. The numerical computations reveal that for the parameters corresponding to magnetosphere side of the ion diffusion region, only slow electron-acoustic solitons and double layer can exist. On the magnetosheath side of the ion diffusion region, only the electron-acoustic/beam solitons can exist. The electric field amplitude of the electrostatic solitary waves (ESWs) predicted by our model are consistent with the Magnetospheric Multiscale (MMS) observations.

Electrostatic Solitary Structures in Space Plasmas: Soliton Perspective

Occurrence of electrostatic solitary waves (ESWs) is ubiquitous in space plasmas, e.g., solar wind, Lunar wake and the planetary magnetospheres. Several theoretical models have been proposed to interpret the observed characteristics of the ESWs. These models can broadly be put into two main categories, namely, Bernstein–Green–Kruskal (BGK) modes/phase space holes models, and ion- and electron- acoustic solitons models. There has been a tendency in the space community to favor the models based on BGK modes/phase space holes. Only recently, the potential of soliton models to explain the characteristics of ESWs is being realized. The idea of this review is to present current understanding of the ion- and electron-acoustic solitons and double layers models in multi-component space plasmas. In these models, all the plasma species are considered fluids except the energetic electron component, which is governed by either a kappa distribution or a Maxwellian distribution. Further, these models consider the nonlinear electrostatic waves propagating parallel to the ambient magnetic field. The relationship between the space observations of ESWs and theoretical models is highlighted. Some specific applications of ion- and electron-acoustic solitons/double layers will be discussed by comparing the theoretical predictions with the observations of ESWs in space plasmas. It is shown that the ion- and electron-acoustic solitons/double layers models provide a plausible interpretation for the ESWs observed in space plasmas.

Quantum Electron Acoustic Solitons and Double Layers with κ-deformed Kaniadakis Distributed Electrons

The present investigation is dedicated to the study of propagation characteristics of electron acoustic (EA) waves and double layers in the quantum plasma system containing inertialess hot electrons and inertial cold electrons with stationary ions forming the charge neutralizing background. It is assumed that hot electrons follow κ-deformed Kaniadakis distribution as governed by the parameter κ. Using the appropriate stretched coordinates and reductive perturbation method (RPM) the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations have been derived. For the sake of analysis, a limit of range of deformation parameter (κ) has been set as -0.4≤κ≤0.4. For the defined range, it has been observed that plasma system supports rarefactive solitary structures. The amplitude and width of KdV soliton have been significantly affected by the quantum effects and remains unaffected by the deformation parameter (κ). The analysis was further extended to the derivation of mKdV equation to investigate the existence of small amplitude double layers (DLs). Only negative potential DLs are found to exist whose dynamics significantly depends on deformation parameter (κ), quantum effects (H) and hot to cold electron density ratio (α). The outcome of the present discourse may be helpful to understand the use of generalized entropies in the environment of plasma physics.

Arbitrary amplitude electron-acoustic solitons and double layers with Cairns–Tsallis-distributed hot electrons

In the present research paper, propagation attributes of nonlinear electron-acoustic (EA) waves have been investigated in an unmagnetised plasma system consisting of cool fluid electrons and hot electrons observing the hybrid Cairns–Tsallis distribution. Sagdeev pseudopotential method has been used to explore the occurrence of large-amplitude solitons and double layers, focussing on how their characteristics depend upon different parameters. The analysis is further extended to examine the dynamics of large- and small-amplitude double layers. It is revealed that the present plasma system supports the existence of negative potential solitons and double layers in certain region of parameter space. The numerical results show that the Cairns–Tsallis-distributed hot electrons may affect the spatial profiles of EA waves and double layers. The present investigation may be relevant to the observation from Viking satellite in the dayside auroral zone.

Formation of Asymmetric Electron Acoustic Double Layers in the Earth's Inner Magnetosphere

AbstractThe Van Allen Probes have observed both symmetric and asymmetric bipolar electric field structures in the Earth's inner magnetosphere. In general, the symmetric bipolar structures are identified as electron‐phase space holes, whereas the asymmetric structures are interpreted as electron acoustic double layers (EADLs). The generation mechanism of these EADLs is not entirely understood yet. We have modeled the EADLs observed on 13 November 2012 by Van Allen Probe‐B. We performed a fluid simulation of the EADLs and tracked their formation and evolution in the simulation. We found that the localized depletion and enhancement in the electron populations act as a perturbation to excite the symmetric bipolar electron acoustic solitary waves, which later evolve into the EADLs. The Ponderomotive force is found to be the main driver behind transformation of the symmetric electron acoustic solitary waves to EADLs via formation of the electron acoustic shocks.

Electron acoustic double layers in a magnetized plasma in the presence of superthermal particles

An analytical study of the small amplitude electron acoustic double layers in a magnetized plasma consisting of superthermal electrons and ions along with cold fluid electrons is discussed. The dispersion relation allows electron acoustic waves with the frequency within electron and ion gyro-frequency in the modelled plasma. In the process of study of the nonlinear structures, the Sagdeev pseudo-potential method for small amplitude regions is employed. The existence domains for the double layers are investigated in terms of the Mach numbers of the structures and the temperature ratios of the species for different ratios of their concentration. The effects of the compositional parameters on the nature and size of the double layers are also explored and it is observed that the plasma can support both compressive and rarefactive double layers depending on the values of those parameters and the Mach numbers.

A review of nonlinear fluid models for ion-and electron-acoustic solitons and double layers: Application to weak double layers and electrostatic solitary waves in the solar wind and the lunar wake

Electrostatic solitary waves (ESWs) have been observed in the Earth's magnetosphere, solar wind, lunar wake, and also in other planetary magnetospheres. The observed characteristics of the ESWs have been interpreted in terms of models based either on Bernstein-Green-Kruskal (BGK) modes/phase space holes or ion- and electron-acoustic solitons. However, the space community has favored the models based on BGK modes/phase space holes. In this review, current understanding of the fluid models for ion-and electron-acoustic solitons and double layers in multi-component plasmas is presented. The relationship between the theoretical models and space observations of ESWs is emphasized. Two specific applications of ion- and electron-acoustic solitons to the occurrence of weak double layers and coherent electrostatic waves in the solar wind and the lunar wake are discussed by comparing the observations and theoretical predictions. It is concluded that models based on ion- and electron-acoustic solitons/double layers provide a plausible interpretation for the ESWs observed in space plasmas.

Slow electron acoustic double layer (SEADL) structures in bi-ion plasma with trapped electrons

The properties of ion acoustic double layer (IADL) structures in bi-ion plasma with electron trapping are investigated by using the quasi-potential analysis. The κ-distributed trapped electrons number density expression is truncated to some finite order of the electrostatic potential. By utilizing the reductive perturbation method, a modified Schamel equation which describes the evolution of the slow electron acoustic double layer (SEADL) with the modified speed due to the presence of bi-ion species is investigated. The Sagdeev-like potential has been derived which accounts for the effect of the electron trapping and superthermality in a bi-ion plasma. It is found that the superthermality index, the trapping efficiency of electrons, and ion to electron temperature ratio are the inhibiting parameters for the amplitude of the slow electron acoustic double layers (SEADLs). However, the enhanced population of the cold ions is found to play a supportive role for the low frequency DLs in bi-ion plasmas. The illustrations have been presented with the help of the bi-ion plasma parameters in the Earth's ionosphere F-region.

Arbitrary amplitude fast electron-acoustic solitons in three-electron component space plasmas

We examine the characteristics of fast electron-acoustic solitons in a four-component unmagnetised plasma model consisting of cool, warm, and hot electrons, and cool ions. We retain the inertia and pressure for all the plasma species by assuming adiabatic fluid behaviour for all the species. By using the Sagdeev pseudo-potential technique, the allowable Mach number ranges for fast electron-acoustic solitary waves are explored and discussed. It is found that the cool and warm electron number densities determine the polarity switch of the fast electron-acoustic solitons which are limited by either the occurrence of fast electron-acoustic double layers or warm and hot electron number density becoming unreal. For the first time in the study of solitons, we report on the coexistence of fast electron-acoustic solitons, in addition to the regular fast electron-acoustic solitons and double layers in our multi-species plasma model. Our results are applied to the generation of broadband electrostatic noise in the dayside auroral region.

Electron-acoustic waves in a plasma with a κ-deformed Kaniadakis electron distribution

We examine the effects of the κ-deformed Kaniadakis electron distribution on small amplitude electron-acoustic double-layers (EADLs). The deformed mean kinetic energy of the electrons is computed to narrow the values of the deformation parameter κ that underpins Kaniadakis entropy. It is shown that the Kaniadakis entropy effect is to higher the critical Mach number beyond which EADLs are admitted. An increase of |κ| leads to a decrease of the critical value of the density ratio beyond which the EADLs cease to exist. This alternative generalization may contribute to the ongoing investigations involving generalized entropies in the context of plasma physics. One can also devise an experimental approach to constrain what κ is in a given experiment or natural phenomenon.

Effects of hot electron inertia on electron-acoustic solitons and double layers

The propagation of arbitrary amplitude electron-acoustic solitons and double layers is investigated in a plasma containing cold positive ions, cool adiabatic and hot isothermal electrons, with the retention of full inertial effects for all species. For analytical tractability, the resulting Sagdeev pseudopotential is expressed in terms of the hot electron density, rather than the electrostatic potential. The existence domains for Mach numbers and hot electron densities clearly show that both rarefactive and compressive solitons can exist. Soliton limitations come from the cool electron sonic point, followed by the hot electron sonic point, until a range of rarefactive double layers occurs. Increasing the relative cool electron density further yields a switch to compressive double layers, which ends when the model assumptions break down. These qualitative results are but little influenced by variations in compositional parameters. A comparison with a Boltzmann distribution for the hot electrons shows that only the cool electron sonic point limit remains, giving higher maximum Mach numbers but similar densities, and a restricted range in relative hot electron density before the model assumptions are exceeded. The Boltzmann distribution can reproduce neither the double layer solutions nor the switch in rarefactive/compressive character or negative/positive polarity.

Higher-order nonlinear equations for the electron-acoustic waves in a nonextensive electron-positron-ion plasma

A precise theoretical investigation has been made on electron-acoustic (EA) Gardner solitons (GSs) and double layers (DLs) in a four-component plasma system consisting of nonextensive hot electrons and positrons, inertial cold electrons, and immobile positive ions. The well-known reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations along with their solitary wave as well as double layer solutions. It has been found that depending on the plasma parameters, the K-dV solitons and GSs are either compressive or rarefactive, whereas the mK-dV solitons are only compressive, and Gardner DLs are only rarefactive. The analytical comparison among the K-dV solitons, mK-dV solitons, and GSs are also investigated. It has been identified that the basic properties of such EA solitons and EA DLs are significantly modified due to the effects of nonextensivity and other plasma parameters related to plasma particle number densities and to temperature of different plasma species. The results of our present investigation can be helpful for understanding the nonlinear electrostatic structures associated with EA waves in various interstellar space plasma environments and cosmological scenarios (viz. quark-gluon plasma, protoneutron stars, stellar polytropes, hadronic matter, dark-matter halos, etc.)

Cylindrical and spherical electron-acoustic Gardner solitons and double layers in a two-electron-temperature plasma with nonthermal ions

Cylindrical and spherical Gardner solitons (GSs) and double layers (DLs) in a two-electron-temperature plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the electron-acoustic (EA) waves is derived, and its nonplanar GS and DL solutions are numerically analyzed. The parametric regimes for the existence of GSs, which are associated with both positive and negative potential, and DLs which are associated with positive potential, are obtained. The basic features of nonplanar EA GSs, and DLs, which are found to be different from planar ones, are also identified. The implications of our results in space and laboratory plasmas are briefly discussed.

Planar electron-acoustic solitary waves and double layers in a two-electron-temperature plasma with nonthermal ions

A rigorous theoretical investigation of nonlinear electron-acoustic (EA) waves in a plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) is studied by the reductive perturbation method. The modified Gardner (MG) equation is derived and numerically solved. It has been found that the basic characteristics of the EA Gardner solitons (GSs), which are shown to exist for α around its critical value α c [where α is the nonthermal parameter, α c is the value of α corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (K-dV) equation, e.g. α c ≃0.31 for μ=n h0/n i0=0.5, σ=T h /T i =10, n h0, n i0 are, respectively, hot electron and nonthermal ion number densities at equilibrium, T h (T i ) is the hot electron (ion) temperature], are different from those of the K-dV solitons, which do not exist for α around α c , and mixed K-dV solitons, which are valid around α∼α c , but do not have any corresponding double layers (DLs) solution. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential, are obtained. The present investigations can be observed in various space plasma environments (viz. the geomagnetic tail, the auroral regions, the cusp of the terrestrial magnetosphere, etc.).

Generation of electrostatic solitary waves in the plasma sheet boundary layer

[1] Generation of electrostatic solitary waves (ESWs) in the plasma sheet boundary layer in terms of electron-acoustic solitons and double layers is proposed. The plasma sheet boundary layer is treated as a multicomponent magnetized plasma consisting of background electrons, counter-streaming electron beams and ions. The model is based on the multifluid equations and the Poisson equation, and uses the Sagdeev pseudo-potential technique. For the plasma parameters at the time of broadband electrostatic noise in the plasma sheet boundary layer observed by Cluster on 22 September 2004, the model predicts solitons/double layer with electric field ∼(0.01–30) mV/m with time durations ∼(0.1–4.5) ms. Such short electric field pulses, when Fourier transformed to the frequency domain, can appear as broadband electrostatic noise in the frequency range of ∼220 Hz to 10 kHz. It is proposed that the model can be a good candidate for explaining the generation of broadband electrostatic noise in the plasma sheet boundary layer.

Electron acoustic double layers in a plasma with a q-nonextensive electron velocity distribution

Electron acoustic double layers in a plasma with a q-nonextensive electron velocity distribution

Ion- and electron-acoustic solitons and double layers in multi-component space plasmas

A general model for the ion- and electron-acoustic solitons and double layers in a multi-component unmagnetized plasma consisting of background electrons, counter-streaming electron beams and ions is discussed. The model is based on the multi-fluid equations and the Poisson equation, and uses the Sagdeev pseudo-potential techniques. For identical counter-streaming electron beams and depending upon the plasma parameters, three types of solutions, namely, ion-acoustic, slow and fast electron-acoustic soliton/double layer, are possible. Generally, the ion acoustic solitons have positive potentials, slow-electron acoustic solitons have negative potentials and fast electron-acoustic solitons and double layers can have either positive or negative potentials depending on the core electron density. As beam speed is increased, first ion-acoustic and then slow electron-acoustic solitons disappear. At large beam speed, only fast electron-acoustic solitons/double layers survive. The results may be relevant to the observations of the electrostatic solitary waves (ESWs) observed in the Earth’s magnetosphere.

Electron acoustic solitary waves and double layers with superthermal hot electrons

The problem of arbitrary amplitude electron acoustic solitary waves (EASWs) are discussed using Sagdeev’s pseudopotential technique for a plasma comprising cold electrons, superthermal hot electrons, and stationary ions. The standard normal-mode analysis is used to study the dispersion relation for linear waves. It is found that the present plasma model supports EASWs having negative potential. The influence of superthermal hot electrons on the present plasma model is investigated for the existence of solitary waves. The investigation shows that the solitary structure ceases to exist when the parameter κ crosses a certain limit. It is also found that the small amplitude double layer solution can exist in such a plasma system in some parametric regions. It is shown that solitary structures and double layers are affected by superthermality, as well as by relevant plasma parameters.