Interaction phenomena of ion‐acoustic quasi‐solitons and classical‐solitons in three component plasma

The space–time evolution of the cnoidal‐soliton solution, characteristics of the quasi‐soliton solution of Korteweg‐de‐Vries (KdV) equation, and the interaction phenomena of ion‐acoustic waves (IAWs) are investigated in a plasma system consisting of positive and negative ions with superthermal electrons. To do this, and (Ar⁺, F^?) plasmas are considered and two‐sided KdV equations (KdVEs) are derived applying the extended Poincaré‐Lighthill‐Kuo (ePLK) method. The effects on wave structures, potential profiles, and propagation characteristics with plasma parameters of the cnoidal‐wave, quasi‐soliton solution, and head‐on collision phenomena of IAWs are presented graphically. It was found that the superthermality parameter and the mass ratio of ions play a significant role in the head‐on collision between soliton and standing cnoidal wave and reveal that the collision is elastic and both waves change their phase shifts due to collision. Moreover, the superthermality parameters are also responsible for the production of compressive and rarefactive phase shifts in overtaking collision processes between right travelling classical soliton (CS) and cnoidal wave (CW) and reduced the amplitudes of IAWs. It was also found that a new wave is created with a high amplitude in the interacting region during collision depending on the plasma parameters.     

Interaction phenomena and effect of higher order dispersion on electron acoustic solitary waves in weakly relativistic regimes

The interaction phenomena of electron acoustic solitary waves (EASWs) and the higher order correction of Korteweg‐de Vries (KdV) equations (KdVEs) have investigated in unmagnetized collisionless plasma system consisting of relativistic cold electrons and electron beams, non‐relativistic Maxwellian hot electrons and stationary ions. To understand the physical issues concerned, the two‐sided KdVEs using extended Poincaré‐Lighthill‐Kue (ePLK) method are derived taking the higher order correction into consideration. The analyses reveal that the widths and amplitudes of EASWs (as obtain from KdVEs) are decreasing with plasma parameters. The plasma parameters are responsible for the modification of KdV‐soliton structure. It is found that the narrowness of width and the steepness of dip of the solitons become more pronounced and the electric field behaves like semi‐kink solitons due to the higher order correction of KdVEs. Dip shape rarefactive soliton becomes pronounced by plasma parameters. The phase shifts of EASWs are also enhanced due to the effects of plasma species temperatures and density ratios.     

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

Two‐dimensional (2D) magnetosonic wave propagation in magnetized quantum dissipative plasmas is studied. The plasma system is comprised of inertial ions, inertia‐less electrons, and positrons. The multi‐fluid quantum hydrodynamic model is used, in which quantum statistical and quantum tunnelling effects of electrons and positrons are included. Reductive perturbation analysis is performed to derive the Zabolotskaya–Khokhlov equation for the 2D propagation of a magnetosonic shock wave in a magnetized qauntum plasma. The effects of varying the different plasma parameters such as positron density and magnetic field intensity on the propagation characteristics of magnetosonic shock waves are discussed with non‐relativistic degenerate plasma parameters in astrophysical plasma situations.     

Ion‐ and positron‐acoustic solitons in magnetized dusty plasma with q‐non‐extensive electron and positron velocity distribution

In this study, the properties of ion‐ and positron‐acoustic solitons are investigated in a magnetized multi‐component plasma system consisting of warm fluid ions, warm fluid positrons, q‐non‐extensive distributed positrons, q‐non‐extensive distributed electrons, and immobile dust particles. To drive the Korteweg–de Vries (KdV) equation, the reductive perturbation method is used. The effects of the ratio of the density of positrons to ions, the temperature of the positrons, and ions to electrons, the non‐extensivity parameters q_e and q_p , and the angle of the propagation of the wave with the magnetic field on the potential of ion‐ and positron‐acoustic solitons are also studied. The present investigation is applicable to solitons in fusion plasmas in the edge of tokamak.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

Head-on collision of quantum ion-acoustic solitary waves in a dense electron-positron-ion plasma

The characteristics of the head-on collision between two-quantum ion-acoustic solitary waves (QIASWs) in a dense electron-positron-ion plasma are investigated. Using the extended Poincaré-Lighthill-Kuo (PLK) method, the Korteweg-de Vries (KdV) equations and the analytical phase shifts, after two QIASWs collision occurs, are derived. This study is a first attempt to illustrate the effects of both of the quantum diffraction corrections and the Fermi temperature ratio of positrons to electrons on the phase shifts. It is found that the electron-positron-ion plasma parameters modify significantly the phase shifts of the two colliding solitary waves.     

Dust‐acoustic envelope solitons in super‐thermal plasmas

The modulational instability (MI) of the dust‐acoustic waves (DAWs) in an electron‐positron‐ion‐dust plasma (containing super‐thermal electrons, positrons, and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the non‐linear Schrödinger equation (NLSE). To derive the NLSE, the reductive perturbation method was employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super‐thermal electrons, positrons, and ions significantly modifies both the stable and unstable regions. The critical wave number k_c (at which MI sets in) depends on the super‐thermal electron, positron, and ion, and adiabatic dust concentrations.     

A New Scheme for High‐Intensity Laser‐Driven Electron Acceleration in a Plasma

We propose a new approach to high‐intensity relativistic laser‐driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward‐scattering of an incident laser pulse can be in the longest acceleration phase with injected relativistic beam electrons. This is why the plasma wave has the maximum amplification coefficient which is determined by the acceleration time and the breakdown (overturn) electric field in which the acceleration of the injected beam electrons occurs. We must note that for the longest acceleration phase the relativity of the injected beam electrons plays a crucial role in our scheme. We estimate qualitatively the acceleration parameters of relativistic electrons in the field of a plasma wave generated at the stimulated forward‐scattering of a high‐intensity laser pulse in a plasma. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dissipative ion acoustic solitary waves in collisional,magneto‐rotating,non‐thermal electron–positron–ion plasma

The linear and non‐linear dynamics of ion acoustic waves are investigated in three‐component magnetized plasma consisting of cold inertial ions and non‐thermal electrons and positrons. The non‐thermal components are modelled by the hybrid distribution, representing the combination of two (kappa and Cairn's) non‐thermal distributions. The relevant processes, including the slow rotation of plasma along the magnetic field axis and collision between ions and neutrals, are taken into consideration. It is shown that the non‐linear dynamics of the considered system are governed by the Zakharov–Kuznetsov equation in modified form. In the general dissipation regime, the effects of the two non‐thermal distributions on the solitary waves are compared. The effects of other plasma parameters, such as collisional and rotational frequency, are also discussed in detail.     

The (3+1)‐dimensional dust‐acoustic waves in multi‐components magneto‐plasmas

A three‐dimensional four components magneto‐plasma system consists of super‐thermal κ‐distributed electrons and positrons, Maxwellian ions, and inertial massive negatively charged dust grains is considered to examine the modulational instability (MI) of the dust‐acoustic waves (DAWs), which propagates in such a magneto‐plasma system. The reductive perturbation method, which is valid for small but finite amplitude DAWs, is employed to derive the (3 + 1)‐dimensional non‐linear Schrödinger equation (NLSE). The NLSE leads to the MI of DAWs as well as the formation of dust‐acoustic rogue waves (DARWs) which are formed due to the effects of non‐linearity in the propagation of the DAWs. It is found that the basic features (viz. amplitude and width) of the DAWs and DARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as κ‐distributed electrons and positrons, temperatures, and number densities of plasma species, and so on. The application of the results in both space and laboratory magneto‐plasma systems is briefly discussed.     

Interactions of ion acoustic multi-soliton and rogue wave with Bohm quantum potential in degenerate plasma

This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo(PLK) method is employed to derive the two-sided Korteweg–de Vries(Kd V) equations with their corresponding phase shifts. The nonlinear Schr o¨dinger equation(NLSE) is obtained from the modified Kd V(m Kd V) equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.     

Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma

This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries (KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influence of plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequency waves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.     

Theoretical analysis of planar and non‐planar electron ‐ acoustic shock waves in electron‐positron‐ion plasma

The propagation properties of planar and non‐planar electron acoustic shock waves composed of stationary ions, cold electrons, and q‐non‐extensive hot electrons and positrons are studied in unmagnetized electron‐positron‐ion plasma. In this model, the Korteweg‐de Vries Burgers equation is obtained in the planar and non‐planar coordinates. We have investigated the combined action of the dissipation, non‐extensivity, density ratio of hot to cold electrons, concentration of positrons, and temperature difference of cold electrons, hot electrons, and positrons. It was found that the amplitude of shock wave in e‐p‐i plasma increases when the positron concentration and temperature increase. The same effect is observed in the case of kinematic viscosity η. Furthermore, it is noticed that spherical wave moves faster in comparison to the shock waves in cylindrical geometry. This difference arises due to the presence of the geometry term m/2τ. It should be noted that the contribution of the geometry factor comes through the continuity equation. Results of our work may be helpful to illustrate the different properties of shock wave features in different astrophysical and space environments like supernova, polar regions, and in the vicinity of black holes.     

Nonplanar ion-acoustic shocks in electron–positron–ion plasmas: Effect of superthermal electrons

Ion-acoustic shock waves (IASWs) in a homogeneous unmagnetized plasma, comprising superthermal electrons, positrons, and singly charged adiabatically hot positive ions are investigated via two-dimensional nonplanar Kadomstev–Petviashvili–Burgers (KPB) equation. It is found that the profiles of the nonlinear shock structures depend on the superthermality of electrons. The influence of other plasma parameters such as, ion kinematic viscosity and ion temperature, is discussed in the presence of superthermal electrons in nonplanar geometry. It is also seen that the IASWs propagating in cylindrical/spherical geometry with transverse perturbation will be deformed as time goes on.     

Weakly dissipative dust acoustic solitons in the presence of superthermal particles

An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated.     

Pressure anisotropy effects on nonlinear electrostatic excitations in magnetized electron-positron-ion plasmas

The propagation of linear and nonlinear electrostatic waves is investigated in a magnetized anisotropic electron-positron-ion (e-p-i) plasma with superthermal electrons and positrons. A two-dimensional plasma geometry is assumed. The ions are assumed to be warm and anisotropic due to an external magnetic field. The anisotropic ion pressure is defined using the double adiabatic Chew-Golberger-Low (CGL) theory. In the linear regime, two normal modes are predicted, whose characteristics are investigated parametrically, focusing on the effect of superthermality of electrons and positrons, ion pressure anisotropy, positron concentration and magnetic field strength. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential (disturbance) via a reductive perturbation method. The parametric role of superthermality, positron content, ion pressure anisotropy and magnetic field strength on the characteristics of solitary wave structures is investigated. Following Allen and Rowlands [J. Plasma Phys. 53, 63 (1995)], we have shown that the pulse soliton solution of the ZK equation is unstable to oblique perturbations, and have analytically traced the dependence of the instability growth rate on superthermality and ion pressure anisotropy.     

Ion-acoustic shock waves and their head-on collision in a dense electron-positron-ion quantum plasma

Ion-acoustic shock waves and their head-on collision in a dense quantum plasma comprised of electrons, positrons, and ions are studied. The extended Poincaré-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries-Burgers equations for shock waves in this plasma. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. The effects of the ratio of positrons to ions unperturbation number density μ, the normalized kinematic viscosity ηi0, and the quantum Bohm potential H on the interaction and structure of the shock waves are investigated. It is found that there are integrally vertical downward movements for both the colliding shocks after their head-on collision, but there are no shifts of the postcollision trajectories (phase shifts). It is also found that these plasma parameters can significantly influence the collision and properties of the colliding shocks. The results may have relevance in dense astrophysical plasmas (such as neutron stars or white dwarfs) as well as in intense laser-solid density plasma experiments.     

Dissipative ion‐acoustic waves in collisional electron‐positron‐ion plasmas with Kappa distribution

In this work, linear and non‐linear structures of ion‐acoustic waves (IAWs) are investigated in a collisional plasma consisting of warm ions, superthermal electrons, and positrons. A dissipative effect is assumed due to ion‐neutral collisions. The linear properties of IAWs are investigated. It is shown that the dynamics of the IAWs is governed by the damped Korteweg‐de Vries (K‐dV) equation. It is seen that the ion‐neutral collisions modify the basic features of ion‐acoustic solitary waves significantly. Also, the effect of the plasma parameters on the dissipative IAWs is discussed in detail.     

Head-on collision of ion-acoustic solitary waves in a Thomas-Fermi plasma containing degenerate electrons and positrons

Head-on collision between two ion acoustic solitary waves in a Thomas-Fermi plasma containing degenerate electrons and positrons is investigated using the extended Poincaré-Lighthill-Kuo (PLK) method. The results show that the phase shifts due to the collision are strongly dependent on the positron-to-electron number density ratio, the electron-to-positron Fermi temperature ratio and the ion-to-electron Fermi temperature ratio. The present study might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs.     

Nonlinear Propagation of Positron-Acoustic Periodic Travelling Waves in a Magnetoplasma with Superthermal Electrons and Positrons

The nonlinear propagation of positron acoustic periodic(PAP) travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ions is examined. The reductive perturbation technique is employed to derive a nonlinear Zakharov-Kuznetsov equation that governs the essential features of nonlinear PAP travelling waves. Moreover, the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions. It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves. It is observed that the superthermality of hot positrons, the concentrations of superthermal electrons and positrons, the positron cyclotron frequency, the direction cosines of wave vector k along the z-axis,and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves. The present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons.