Electron-acoustic Solitons Research Articles

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.

Excitation of nonlinear longitudinal structures in spin‐1/2 quantum plasma in the presence of ion beam

AbstractThe formation of longitudinal, nonlinear structures in an interacting ion beam, spin‐1/2 quantum, electron‐ion plasma is reported by employing a separate spin evolution quantum hydrodynamic model (SSE‐QHD). The reductive perturbation method is followed to develop the KdV equations. In the presence of an ion beam and keeping the finite electron inertial effects, ion acoustic (IA) soliton and spin electron acoustic (SEA) soliton are found. The critical values of beam speed and spin polarization, required for the existence of solitary structures, are highlighted. It is prescribed that the present model supports rarefactive and compressive SEA soliton and compressive IA soliton. It is shown that the ion beam is essential for the existence of a compressive SEA solitary structure. We have also calculated and compared the energy densities of both solitons. Furthermore, the dependence of the nonlinear structures on the beam parameters and spin polarization are also examined. Our findings would be useful to understand the new spin‐dependent nonlinear structures as well as the features of nonlinear IA waves in ion beam–plasma interactions.

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.

Overtaking interaction of electron-acoustic solitons in Saturn’s magnetosphere

The progression of nonlinear electron-acoustic waves (EAWs) in a magnetized and collision-free plasma made up of cold inertial electrons, inertialess superthermal electrons, and stationary background ions with special reference to Saturn’s magnetosphere (SMS) is explored. The method of reductive perturbation (MRP) is employed to obtain the evolution equation (i.e., Zakharov– Kuznetsov equation (ZKE)) that governs the propagation of electron acoustic solitons (EASs). Using the elegant and efficient Hirota bilinear method (HBM), multi-soliton solutions (MSSs) of the ZKE are determined. The impact of the effects of hot-to-cold electron density ratio, magnetic field (MF) strength, and superthermality on single as well as the interaction of EASs is examined. Estimates of the values of the electric field at several radii of SMS (i.e., 12 R s − 17.8 R s, where R s is the radius of Saturn) are presented, which are found in μV/ m to mV/ m range and are in perfect agreement with the data from Cassini radio and plasma wave science wideband receiver. Moreover, the influence of the relevant plasma parameters on the interaction time and spatial extent of the interacting EASs is also explored.

A Mechanism for Large-Amplitude Parallel Electrostatic Waves Observed at the Magnetopause

Large-amplitude electrostatic waves propagating parallel to the background magnetic field have been observed at the Earth’s magnetopause by the Magnetospheric Multiscale (MMS) spacecraft. These waves are observed in the region where there is an intermixing of magnetosheath and magnetospheric plasmas. The plasma in the intermixing region is modeled as a five-component plasma consisting of three types of electrons, namely, two counterstreaming hot electron beams and cold electrons, and two types of ions, namely, cold background protons and a hot proton beam. Sagdeev pseudo-potential technique is used to study the parallel propagating nonlinear electrostatic solitary structures. The model predicts four types of modes, namely, slow ion-acoustic mode, fast ion-acoustic mode, slow electron-acoustic mode and fast electron-acoustic modes. Except the fast ion-acoustic mode, all other modes support solitons. Whereas slow ion-acoustic solitons have positive potentials, both slow and fast electron-acoustic solitons have negative potentials. For the case of 4% cold electron density, the slow ion-acoustic solitons have electric field ∼(40–120) mV m−1. The fast Fourier transforms (FFT) of slow ion-acoustic solitons produce broadband frequency spectra having peaks between ∼100 Hz to 1000 Hz. These theoretical predictions are in good agreement with the observations. The slow and fast electron-acoustic solitons could be relevant in explaining the low-intensity high (>1 kHz) frequency waves which are also observed at the same time.

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.

INVESTIGATION OF THE ELABORATE DYNAMICS OF WEAKLY NONLINEAR FRACTIONAL ION-ACOUSTIC WAVES IN MAGNETIZED ELECTRON–POSITRON PLASMA

This study employs three advanced computational and numerical techniques to solve the nonlinear fractional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV–ZK) equation in magnetized plasma. The reductive perturbation approach is utilized to investigate the dynamics of various components, namely isothermal species, immobile background species, and warm adiabatic fluid, in magnetized plasma. Emphasis is placed on unraveling the asymmetrical propagation characteristics of nonlinear electrostatic waves. The model’s solutions encompass diverse types of solitons, including ion-acoustic, dust acoustic, and electron acoustic solitons. Analytical solutions are obtained using a variety of mathematical functions, such as exponents, trigonometry, and hyperbolas. Two- and three-dimensional density graphs illustrate the practical behavior of a single soliton. The primary objective of employing numerical schemes is to assess the accuracy of the derived solutions, and the outcomes demonstrate the efficacy of the analytical method in solving nonlinear mathematical and physical problems. Several techniques are employed to validate the consistency between calculated and estimated results, ensuring the study’s accuracy and reliability. Overall, this investigation underscores the effectiveness of numerical and analytical techniques in tackling complex mathematical models, offering a promising avenue for future research in the field. The findings carry significant implications for comprehending nonlinear phenomena in magnetized plasma and contribute to advancing the field.

Solitons in a cold electron beam plasma

Necessary and sufficient conditions for the existence of dissipative electron-acoustic solitons in a cold electron beam plasma with superthermal trapped electrons described by the Schamel equation are derived in this paper. Soliton solutions to the Schamel equation are constructed using formal analytical techniques which yield counter-intuitive conditions for the existence of these solutions. The existence conditions are derived in terms of system parameters and initial conditions. Computational experiments are used to validate the obtained results.

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.

Electron-acoustic solitary potential in nonextensive streaming plasma

The linear/nonlinear propagation characteristics of electron-acoustic (EA) solitons are examined in an electron-ion (EI) plasma that contains negative superthermal (dynamical) electrons as well as positively charged ions. By employing the magnetic hydrodynamic (MHD) equations and with the aid of the reductive perturbation technique, a Korteweg-de-Vries (KdV) equation is deduced. The latter admits soliton solution suffering from the superthermal electrons and the streaming flow. The utility of the modified double Laplace decomposition method (MDLDM) leads to approximate wave solutions associated with higher-order perturbation. By imposing finite perturbation on the stationary solution, and with the aid of MDLDM, we have deduced series solution for the electron-acoustic excitations. The latter admits instability and subsequent deformation of the wave profile and can’t be noticed in the KdV theory. Numerical analysis reveals that thermal correction due to superthermal electrons reduces the dimensionless phase speed (bar{U}_{ph}) for EA wave. Moreover, a random motion spread out the dynamical electron fluid and therefore, gives rise to bar{U}_{ph}. A degree enhancement in temperature of superthermal (dynamical) electrons tappers of (increase) the wave steeping and the wave dispersion, enhancing (reducing) the pulse amplitude and the spatial extension of the EA solitons. Interestingly, the approximate wave solution suffers oscillation that grows in time. Our results are important for understanding the coherent EA excitation, associated with the streaming effect of electrons in the EI plasma being relevant to the earth’s magnetosphere, the ionosphere, the laboratory facilities, etc.

Interaction of electron acoustic solitons in auroral region for an electron beam plasma system

The propagation of linear and nonlinear electron acoustic waves (EAWs) in an unmagnetized plasma, comprising dynamical inertial electrons, hot (r, q) distributed electrons, warm electron beam, and immobile ions is studied. The linear dispersion relation is investigated for varying beam velocity. The Korteweg-de Vries (KdV) equation for EAWs is derived in the small amplitude limit. Depending on the beam density, temperature and velocity, we get a critical condition for which the quadratic nonlinearity vanishes from the plasma system. For such a condition, the modified Korteweg de Vries (mKdV) equation, with cubic nonlinearity, is derived, which admits both negative and positive potential solitary structures. It is noted that the spectral indices r and q of the generalized (r, q) distribution, the concentration of the cold, hot and the beam electrons, and the temperature ratios, significantly affect the fundamental properties of the propagation and interaction of electron acoustic solitary waves (EASWs). The types of possible overtaking interaction of two mKdV solitons are investigated. The spatial regime for the two soliton interaction is found to vary in accordance with the variation of single soliton for various plasma parameters. The results of present study may be beneficial to comprehend the interaction between two EASWs in laboratory, space and astrophysical plasmas.

The envelope soliton for the nonlinear interaction of Langmuir waves with electron acoustic waves in the Earth's inner magnetosphere

The nonlinear coupling of Langmuir waves with electron-acoustic waves is investigated using the kinetic theory, where the hot electron component is modeled by the kappa distribution with an exponential cutoff at high energy tail, i.e., the cutoff kappa distribution. The one dimensional structure of envelope Langmuir solitons is analyzed by the numerical calculation with parameters typical of the Earth's inner magnetosphere. In the case of hot electrons with a cutoff kappa distribution, envelope Langmuir solitons have larger width and slower speed than that in the case of hot electrons with a Maxwellian distribution. The envelop Langmuir soliton with density depletion obtained in the Earth's inner magnetosphere propagates at a speed lower than the electron-acoustic velocity. At a given amplitude of electrostatic field, the envelope Langmuir soltions have a speed comparable with the ones of electron-acoustic wave solitons, but a wider scale in the case of hot electrons with a cutoff kappa distribution.

Electron-acoustic solitons in dense electron–positron–ion plasma: Degenerate relativistic enthalpy function

An enthalpy function Hj∝1+ηj2 is deduced from the density of states for degenerate relativistic charged particulate. Here ηj=pj/mjc2 stands for the relativistic factor, pjmj is the Fermi momentum (mass) for the jth degenerate relativistic species and c designates the vacuum speed of light. The enthalpy function reduces the results Weinberg (1972), Lee and Cheong (2007) obtained for the nondegenerate nonrelativistic (NR) and ultrarelativistic (UR) fluids. The linear and nonlinear propagation characteristics of the electron-acoustic (EA) solitons are examined for dense electron–positron–ion (EPI) plasma that comprises degenerate relativistic electrons/positrons and non-degenerate ions. By using Hj and with the aid of the relativistic hydrodynamic equations, a linear dispersion relation for the EA waves is derived that admits the evolution of the fast and slow electron-acoustic (FEA/SEA) excitations. For the nonlinear EA waves, a Korteweg–de Vries (KdV) equation is obtained; numerical analysis reveals that the FEA mode may ensue in the solitary potential. The propagation of the SEA solitons is forbidden as it suffers from a negative phase dispersion effect. At a relatively low concentration of positrons, the EPI plasma may admit the evolution of electron–holes and therefore, give rise to the compressive FEA solitons. This investigation is important for understanding localized excitations in degenerate relativistic plasmas, as that are relevant in white dwarfs, neutron stars, and high-energy density facilities.

Electron acoustic dressed solitons in an electron-beam plasma with higher-order contributions

In this investigation, the evolution of electron acoustic solitons (EASs) and electron acoustic dressed solitons formed due to the contribution of higher-order effects in a superthermal plasma in the presence of an electron beam has been examined. The reductive perturbation method is employed to derive the nonlinear Korteweg–de Vries (KdV) and KdV-type inhomogeneous equations with contribution of higher-order effects of nonlinearity and dispersion. From the solutions of these nonlinear equations, the characteristics of EASs and dressed EASs are analysed under the influence of superthermality of electrons, parameters of an electron beam and other plasma parameters. The findings of present work may be useful to explore and understand the evolution of nonlinear structures in the space and laboratory plasmas especially in Earth’s magnetospheres.

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.

A mechanism for spin electron acoustic soliton observed in a spin-polarized nanosized electron-hole plasma

The formation and the characteristics of spin electron acoustic (SEA) soliton in a beam interacting spin-polarized electron-hole plasma are investigated. These wavepackets are supposed to be the source of heating during the excitation process. We have used the separate spin evolution-quantum hydrodynamic (SSE-QHD) model along with Maxwell equations and derived the Korteweg–de Vries (KdV) equation by using the reductive perturbation method (RPM). We note that the larger values of beam density and spin polarization can change the soliton nature from rarefactive to compressive. Our findings may be important to understand the characteristics of localized spin-dependent nonlinear waves in nanosized semiconductor devices.

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.

KBM approach to electron acoustic envelope soliton in viscous astrophysical plasma

Modulation instability (MI) of envelope soliton is studied in an unmagnetized viscous plasma. Using Krylov-Bogoliubov Mitropolsky (KBM) method, the nonlinear Schrödinger equation (NLSE) is obtained, and the growth rate of modulationally unstable electron acoustic wave in such plasma is discussed. The solution of the electron-acoustic envelope-solitons is obtained from the Nonlinear Schrödinger equation. The hypothetical outcomes have been examined mathematically for various parameters of plasma, and the outcomes are introduced graphically. This theoretical investigation can be experienced experimentally with certain modification of the experiment had been performed by Ikezawa and Nakamura []. Our outcomes might be material for the investigation of nonlinear wave measures in relativistic thick plasmas of astrophysical articles, to be specific, in dwarfs and neutron stars.

Finite amplitude electron-acoustic waves in the electron diffusion region

The electron-acoustic solitons are studied with two temperature electrons (a hot trapped having vortex-like velocity distribution and a warm adiabatic fluid) and stationary ions. The theoretical model is based on the observations of a mixture of the hot, tenuous magnetospheric and warm, dense magnetosheath plasma particles associated with the asymmetric magnetic reconnection at the Earth’s magnetopause by Magnetospheric Multiscale (MMS). Using the reductive perturbation technique, the model supports the existence of nonlinear electron-acoustic structures derived from the mKdV-like equation. The electron-acoustic waves propagate at supersonic speeds above the electron sound speed. The results are applied to observations of electric field structures in the electron diffusion region (EDR).