Electron-acoustic Solitary Waves Research Articles

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.

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.

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.

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.

Arbitrary amplitude electron acoustic solitary excitations with Cairns–Tsallis distributed hot electrons and positrons in magnetized space plasmas

A rigorous theoretical study is performed to understand the characteristics of nonlinear electron acoustic (EA) solitary waves propagating in collisionless magnetized plasma system comprising cold inertial electrons, nonthermal–nonextensive hot electrons and positrons and stationary ions. The propagation and evolution of two potential modes (fast and slow) are studied in the linear regime. By employing magnetic hydrodynamic equations and with the aid of travelling wave approximation, the nonlinear wave dynamics is demonstrated by the first integral of motion in the form of a pseudo-energy balance equation. In exploring the EA soliton characteristics, numerical results reveal that only negative polarity EA solitons exist in a restricted range of the physical parametric space of the plasma system. It is revealed that the effects of nonthermal and nonextensive parameters, hot to cold electron density ratio, Mach number and magnetic strength considerably modify the basic properties of solitary waves. The present results may be important in space plasmas as well as laboratory plasmas with non-Maxwellian particle population.

Analysis of solitons structure of the damped KdV equation arising in superthermal plasmas: Application of homotopy analysis method

AbstractThe aim of the proposed work is to analyze the soliton structures of dust‐ion acoustic waves obtained in the framework of the Korteg‐de Vries (KdV) equation with the presence of a damping term. The concept of electron acoustic solitary wave in an unmagnetized plasma consisting of superthermal electrons has been taken into consideration. The KdV equation with the presence of a damping term has been derived with the help of the reductive perturbation technique and solved by using the well‐known homotopy analysis method. The considered method approximates all problems in a straightforward and simplified manner. The method computes the series solution efficiently and provides a simple way to ensure its convergence. The approximate analytical solution obtained from the present analysis is compared with available results in the literature for a different choice of pertinent parameters. The upshots specified that the amplitude of solitary waves increases for increasing values of the damping parameter. This study would in a way to demonstrate the potential and effectiveness of the homotopy analysis method to evaluate the various kinds of nonlinear equations arising in the soliton theory.

Obliquely overtaking Collisions of electron-acoustic solitary waves of inertial cold and beam electrons in the presence of superthermal electrons

Overtaking collision of the electron-acoustic solitary waves in the four-component collisionless, magnetized plasma has been investigated. The system consists of cool inertial background electrons of temperature Tc, cool inertial electron beam of temperature Tb, hot inertialess superthermal electrons modeled by a κ-distribution of temperature Th and ions. Nonlinear Korteweg–de Vries (KdV) equation that characterizing the EASWs in such a plasma model is derived. The system admits both compressive and rarefactive solitary waves. The overtaking collision of two and three-soliton solutions is investigated using Hirota’s bilinear technique. Physical parameters influence the interchange of energy caused by overtaking collisions. These parameters comprise the magnetic field, obliquity angle, the beam, cool and hot electrons number densities and temperatures, and this causes the solitons behavior to be alternated. The amplitude, and width increase as the superthermal electrons temperature increases or magnetic field decreases. The system parameters have an effect on the phase shifts as well. The current research is an attempt to shed light on the characteristics of N-soliton in the four-component collisionless, magnetized plasma that are applicable in several astrophysical plasma environments such as the Earth’s magnetosphere.

Evidence of oblique electron acoustic solitary waves triggered by magnetic reconnection in Earth’s magnetosphere

Motivated by the recent Magnetospheric Multiscale (MMS) observations of oblique electron acoustic waves, we addressed the generation mechanism of the observed waves by utilizing the reductive perturbation technique. A nonlinear Zakharov-Kuznetsov (ZK) equation is derived for a collisionless, magnetised plasma composed of cool inertial background electrons, cool inertial electron beam, hot inertialess suprathermal electrons; represented by a κ-distribution, and stationary ions. Moreover, the instability growth rate is derived by using the small-k perturbation expansion method. Our findings revealed that the structure of the electrostatic wave profile is significantly influenced by the external magnetic field, the unperturbed hot, cool, and electron beam densities, the obliquity angle, and the rate of superthermality. Such parameters also have an effect on the instability growth rate. This study clarifies the characteristics of the oblique electron solitary waves that may be responsible for changing the electron and ion distribution functions, which alter the magnetic reconnection process. Moreover, the increase of the growth rate with the plasma parameters could be a source of anomalous resistivity that enhances the rate of magnetic reconnection.

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.

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.

Electron acoustic singular solitons interaction in the Earth’s magnetotail region

Electron acoustic potential structures are generated in the presence of a large-amplitude electric field in Earth’s magnetotail region, Earth’s magnetosphere according to the numerous space observations by satellites. In this article, we study the electron-acoustic solitary waves (EASWs) in an unmagnetized electron–ion plasma consisting of cold electrons and isothermal ions with two different temperatures. Nonlinear evolution equations are derived from the hydrodynamic model of collisionless, unmagnetized electron–ion plasma. Exact analytic solutions are obtained from derived Korteweg-de Vries (KdV) equations and modified Korteweg-de Vries (MKdV) equations separately with the aid of the Hirota Bilinear method. Two singular soliton solutions of both KdV and MKdV equations are obtained separately. The efficiency and interactive approach of the heuristic Hirota Bilinear method leads to multiple singular soliton solutions for its beautiful algebraic technique which generates solitons solutions as well as singular solitons explicitly. Then the significant multi singular soliton interaction has been studied for KdV singular solitons and MKdV singular solitons in the critical parameter set.

The overtaking interaction of electron acoustic solitary waves in a plasma with hot non-extensive electrons

In the present work, we investigate the propagation and overtaking interaction of electron-acoustic solitary waves (EASWs) in a plasma comprising cold electron fluid, hot nonextensive electrons and immobile ions. For this purpose, the Korteweg–de Vries (KdV) equation is derived for this model. Then Hirota’s direct method is used to the KdV equation to obtain multisoliton solution for studying the interaction process. Our one-dimensional plasma model supports rarefactive EASWs. For both single soliton and multisoliton solutions, the amplitude and velocity of the solitons increase with the increase of nonextensivity or superthermality of hot electrons. It is found that the temporal scale of collision between two solitons decreases with the decrease of nonextensive parameter . The choice of propagation vectors on the interaction of the solitons is also significant. The present analysis may be helpful for further study of the modified bipolar or tripolar electric field signatures observed in the auroral zone.

Electron-Acoustic Solitons in Magnetized Collisional Nonthermal Plasmas

The properties of obliquely propagating dissipative electron-acoustic solitary waves (OPdEASWs) have been investigated in a magnetized collisional superthermal plasma consisting of inertial cold electrons, inertialess hot electrons featuring κ-distribution, and static ions via the fluid dynamical approach. Using the reductive perturbation technique, a nonlinear Schamel equation that governs the nonlinear features of OPdEASWs is obtained. The solitary wave solution of the Schamel equation is used to examine the basic features of small but finite amplitude OPdEASWs in such a magnetized collisional superthermal plasma. The basic features (width, amplitude, speed, and so on) of OPdEASWs are found to be modified by the different plasma configuration parameters, such as the superthermality index, obliquity angle, collisional parameter, trapping parameter, and external magnetic field. The nature of electrostatic disturbances, that may propagate in different realistic space and laboratory plasma systems (e.g., in Saturn ring), is briefly discussed.

Analysis of electron acoustic waves interaction in the presence of homogeneous unmagnetized collision-free plasma

In this research, the transmission and interaction of nonlinear electron acoustic waves (EAWs) in such an unmagnetized, homogeneous, collision-free plasma composed of hot and cold electrons together with stationary ions throughout in the background have been analyzed. For the small-amplitude limit, the Korteweg–de Vries (KdV) equation for (EAWs) have been extracted. For electron acoustic solitary waves (EASWs), using the new extended direct algebraic approach, soliton solutions have also documented. The parametric analysis demonstrated that the hot to cold electron ratio and hot electron superthermal play a key role in changing the (EASWs) amplitude. The family of semi-bright solitons, dark singular solitons, Type 1 as well as 2 single solitons, trigonometric, intermingled hyperbolic and rational solitons was constructed and tested with the assistance of the innovative package software of numerical computations. The results show that the method is clear and efficient, produces analytical results in a generalized form, and these findings can also help resolve the difficulties and predicaments in the relevant disciplines of plasma physics and may be useful for studying the relationship between two (EASWs) in astrophysical and laboratory plasma. The solutions presented in this prototype are the latest in a literature review. For physical interpretation, some randomly selected solutions are shown graphically. Conclusions are held at the end.

Electron acoustic solitary waves in unmagnetized nonthermal plasmas

Electron acoustic (EA) solitary waves (SWs) are studied in an unmagnetized plasma consisting of hot electrons (following Cairns-Tsalli distribution), inertial cold electrons, and stationary ions. By employing a reductive perturbation technique (RPT), the nonlinear Korteweg–de Vries (KdV) equation is derived and its SW solution is analyzed. Here, the effects of plasma parameters such as the nonextensivity parameter (q), the nonthermality of electrons (α), and the cold-to-hot electron density ratio (β) are investigated.

Determination of maximum electric field amplitude sustained by electron acoustic solitary waves in an unmagnetized plasma with kappa-distributed electrons

This manuscript investigates the maximum electric field amplitude sustained by nonlinear electron acoustic waves, without losing their initial structure, and propagating in an unmagnetized homogeneous plasma comprising cold inertial electrons, hot kappa-distributed electrons, and stationary ions. Using nonlinear fluid Maxwell’s equations in one dimension, traveling wave solutions have been derived in the wave frame, and negative potential solitary structures have been observed. Furthermore, a pseudo-potential method has been employed to determine the maximum electric field amplitude as a function of the dimensionless Mach number (M), initial density ratio of hot to cold electron species (Rn=nh0nc0), and spectral index (κ) of the hot electron species velocity distribution function. We find that at this maximum electric amplitude, the density of the cold electron fluid becomes singular and thus can be called the wave breaking limit [J. M. Dawson, Phys. Rev. 113, 383 (1959)]. Density singularity is an artifact of the cold fluid plasma model and actually diminishes if one introduces a nonzero temperature to the cold inertial electrons. In that case, we find that the maximum electric field amplitude gets modified and follows the same scaling as the ratio of cold to hot electron species temperature (σ=TecTeh), as obtained by Coffey [Phys. Fluids 14, 1402 (1971)], with electron thermal velocity derived for the wave breaking limit of electron plasma waves in a warm plasma.

Phase plane analysis of small amplitude electron-acoustic supernonlinear and nonlinear waves in magnetized plasmas

Phase plane analysis of small amplitude electron-acoustic supernonlinear and nonlinear waves in a magnetized nonextensive electron-ion plasma is examined. These electron-acoustic waves (EAWs) are studied based on the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations. The dynamical systems for both the KdV and mKdV equations are formed using the propagating wave transfiguration. Phase plane analyses of EAWs corresponding to the KdV and mKdV equations are shown. Analytical solution corresponding to the electron-acoustic solitary wave for the KdV equation is derived. Analytical forms of kink, anti-kink and periodic wave solutions in ranges −1 < q < 0 and 0 < q < 1 are obtained for the mKdV equation. Superperiodic EAWs under the mKdV equation in the range q > 1 are shown numerically. Existence of small amplitude superperiodic EAWs under the mKdV equation is shown for the first time in a magnetized nonextensive electron-ion plasma using the concept of planar dynamical systems. Effects of system parameters on different traveling wave solutions of EAWs are displayed. Outcome of the study can be implemented to understand nonlinear and supernonlinear EAWs in space and atmosphere, such as, auroral zones and magnetosphere.

Planar and Nonplanar Electron-Acoustic Solitary Waves in the Presence of Positrons

The propagation of planar and nonplanar electron-acoustic waves composed of stationary ions, cold electrons, superthermal hot electrons, and positrons is studied by using Korteweg–de Vries (KdV) equation in the planar and nonplanar coordinates. The analytical and numerical solutions of KdV equation reveal that the nonplanar electron-acoustic solitons are modified significantly with positron concentration and behave differently in different geometries. It is found that the positron concentration β and positron temperature σ have a negative effect on the wave potential and width of the wave, there is a decrease in the amplitude as well as width of the wave. Thus, it is noticed that the strength of the wave decreases with the growing values of β and σ. From the examination, it is discovered that this increase in height and steepness is more articulated in the spherical geometry than in the cylindrical one. The strength of the wave grows with increment of superthermal particles (low value of κ). There is also an increase in the width of the solitary wave with decreasing the value of κ, which is in agreement with the results of [1]. Further, it is noticed that the spherical wave moves faster than cylindrical waves. This difference arises due to the presence of the geometry term $$m{\text{/}}2\tau $$ , whose value becomes zero in the planar case ( $$m = 0$$ ), $$1{\text{/}}(2\tau )$$ in the cylindrical and $$2{\text{/}}2\tau $$ in the spherical case. Results of our work may be helpful in analyses of the physical behaviour of solitary waves features in different astrophysical and space environments like the supernovas, polar regions and in the vicinity of black holes.

Interaction of electron acoustic waves in the presence of superthermal electrons in terrestrial magnetosphere

We have investigated the propagation and interaction of nonlinear electron acoustic waves (EAWs) in a plasma comprising hot (superthermal) and cold electrons and immobile ions. We have derived the Korteweg-de Vries equation for EAWs in the small amplitude limit. Employing the Hirota's Direct method, we have investigated the multisoliton solutions for electron acoustic solitary waves (EASWs). It has been found that the system under consideration admits only rarefactive electrostatic solitary structures. As the observable data are available in terms of electric field rather than electric potential, therefore, we have discussed our results in terms of bipolar electric field structures. The numerical analysis has revealed that the ratio of hot to cold electrons and superthermality of hot electrons play a crucial role in changing the amplitude of EASWs. The interaction of the two solitons and its dependence on the choice of propagation vectors, superthermality, and density ratio have also been elaborated. The results of the present study may be beneficial to comprehend the interaction between two EASWs in astrophysical and laboratory plasmas.

Formation of solitary structures and envelope solitons in electron acoustic wave in inner magnetosphere plasma with suprathermal ions

AbstractThe propagation of electron acoustic solitary waves is investigated in magnetized two‐temperature electron plasma with supra‐thermal ion. By using the reductive perturbation technique, the Korteweg de‐Vries (KdV) equation is derived. Later solving this equation, a solitary wave solution has been derived. These are mainly in astrophysical plasmas where changes of local charge density, temperature, and energy of particles produce considerable effects on the plasma system. The effects of supra‐thermality, density, and Mach number on solitary structures are studied in detail. The results show that the supra‐thermal index (κ) and ion to electron temperature ratio (σ) alters the regime where solitary waves may exist. While studying the solitary profile for different parametric variation some interesting conclusion can be drawn; it is shown that the solitary profile becomes flatter. This can be due to the thermal energy associated with the hot electrons. However, with the increase in ion density with respect to the cold electrons' density, the solitary waves become steeper and sharper. This is due to the comparatively heavier mass of ions. The density of cold electron also increases the solitary structures in a similar manner. The higher the density of cold electrons, sharper will be the profile. The above findings will be helpful in understanding many astrophysical phenomena and data obtained by space missions. For a further study, we keep the investigation of the formation of other kinds of stationary structures like shocks, double layers, etc.