Kadomtsev–Petviashvili equation for solitary waves in warm dense astrophysical electron-positron-ion plasmas (original) (raw)
Related papers
Electrostatic Solitary Waves in Relativistic Degenerate Electron–Positron–Ion Plasma
IEEE Transactions on Plasma Science, 2015
The linear and nonlinear properties of ion acoustic excitations propagating in warm dense electron-positron-ion plasma are investigated. Electrons and positrons are assumed relativistic and degenerate, following the Fermi-Dirac statistics, whereas the warm ions are described by a set of classical fluid equations. A linear dispersion relation is derived in the linear approximation. Adopting a reductive perturbation method, the Korteweg-de Vries equation is derived, which admits a localized wave solution in the form of a small-amplitude weakly super-acoustic pulse-shaped soliton. The analysis is extended to account for arbitrary amplitude solitary waves, by deriving a pseudoenergy-balance like equation, involving a Sagdeev-type pseudopotential. It is shown that the two approaches agree exactly in the small-amplitude weakly super-acoustic limit. The range of allowed values of the pulse soliton speed (Mach number), wherein solitary waves may exist, is determined. The effects of the key plasma configuration parameters, namely, the electron relativistic degeneracy parameter, the ion (thermal)-to-the electron (Fermi) temperature ratio, and the positron-to-electron density ratio, on the soliton characteristics and existence domain, are studied in detail. Our results aim at elucidating the characteristics of ion acoustic excitations in relativistic degenerate plasmas, e.g., in dense astrophysical objects, where degenerate electrons and positrons may occur. Index Terms-Plasma oscillations, plasma waves. I. INTRODUCTION R ECENTLY there has been a great deal of interest in elucidating the dynamics of collective processes in degenerate dense plasmas, commonly found in dense astrophysical objects (e.g., white and brown dwarfs, neutron stars, and magnetars), in the core of giant planets (e.g., Jovian planets), which can Manuscript
Journal of Plasma Physics, 2012
Arbitrary amplitude and small amplitude ion-acoustic solitary waves (IASWs) have been investigated in a relativistic, collisionless, unmagnetized, and degenerate dense electron–positron–ion plasma. The arbitrary amplitude IASWs have been studied by using the Sagdeev-type pseudo-potential approach. Along with approximate solution, the exact amplitude solitary structure has also been studied numerically. The electrons and positrons are assumed to follow the corresponding Fermi distribution function and the ions are described by the hydrodynamic equations. A new dispersion relation for the ion-acoustic wave has been derived for the relativistic Thomas–Fermi plasma. An energy balance-like equation involving the Sagdeev-type pseudo-potential has been investigated and it has been shown that the concentration of plasma particles has significant effect on the permitted Mach number range of IASWs. Also, it has been pointed out that the only compressional supersonic IASWs can propagate in the...
Czechoslovak Journal of Physics, 2004
A rigorous theoretical investigation has been made of arbitrary amplitude compressive and rarefactive ion acoustic solitary waves in three component plasmas, consisting of ions, positrons and non-thermally distributed electrons. The pseudo-potential approach, which is valid for large amplitude solitary waves and the reductive perturbation technique for small amplitude solitary waves, have been employed. It is shown from both weakly and highly nonlinear analyses that the presence of the fast or non-thermal electrons may allow compressive and rarefactive solitary waves to coexist. It is found that the effect of the positron density changes the minimum value of α (a parameter determining the number of fast electrons present in our model) and M (the Mach number) for which the compressive and rarefactive solitary waves can coexist. The present theory is applicable to analyse arbitrary amplitude ion acoustic waves associated with positrons which may occur in space plasmas.
Advances in Astrophysics
Analytical and numerical studies are presented for electron acoustic solitary wave structure in relativistic degenerate two-component unmagnetized astrophysical plasma. The existence of a wave mode of pure quantum origin is predicted. The effect of various plasma parameters on the conditions of existence and properties of solitary wave is investigated. It is shown that depending on the values of plasma parameters both rarefactive and compressive type of solitons can exist. It is observed that the amplitude and width of the solitons are significantly affected by the quantum and relativistic effects. The relativistic effects arising out of streaming motion is treated by Eulerean formulation whereas the relativistic degeneracy effects is investigated by making use of Chandrasekhar formula.
Nonplanar Electrostatic Solitary Waves in a Relativistic Degenerate Dense Plasma
By employing the reductive perturbation technique, the propagation of cylindrical and spherical ion acoustic solitary waves is studied in an unmagnetized dense relativistic plasma, consisting of relativistically degenerate electrons and cold fluid ions. A modified Korteweg-de-Vries equation is derived and its numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate Fermi plasma. Different degrees of relativistic electron degeneracy are discussed and compared. It is found that increasing number density leads to decrease the amplitude the width of the ion acoustic solitary wave in both the cylindrical and spherical geometries. The relevance of the work to the compact astrophysical objects, particularly white dwarfs is pointed out.
Solitary and rogue waves in Fermi-Dirac plasmas: relativistic degeneracy effects
Ion acoustic (IA) solitary and rogue waves are studied in an unmagnetized plasma consisting of nondegenerate warm ions, relativistically degenerate electrons and positrons. By using the reductive perturbation technique, the evolution of IA solitary waves is described by the Korteweg-de Vries (KdV) equation. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency then the KdV equation is also used to study the nonlinear evolution of modulationally unstable modified IA wavepackets through the derivation of nonlinear Schrödinger equation. It is found that the characteristics of the IA solitary and rogue waves are substantially influenced by the intrinsic plasma parameters. The relevance of the present investigation involving IA solitary and rogue waves in astrophysical plasma environments is also highlighted.
International Journal of Applied and Computational Mathematics, 2019
Based on reductive perturbation theory, the nonlinear structure of non-extensive multispecies plasma containing hot electrons, adiabatic cold electrons, cold positrons and ions has been investigated via different nonlinear KdV, mKdV and Gardner's equations. It is shown that the formation and properties of electron acoustic solitary waves and double-layer can exist in such plasma system depending on some relevant physical parameters such as electron and positron density ratios, electrons temperatures ratio and non-extensive parameter. The existence conditions of these types of waves are extensively discussed. The obtained results may be useful in improving and understanding the propagation of the nonlinear electron waves in space plasma, Earth's magnetosphere and solar wind.
Applied Mathematics and Computation, 2012
In this paper, the Zakharov-Kuznetsov equation which describes the propagation of the electrostatic excitations in the electron-positron-ion (e-p-i) plasmas are investigated. New exact solitary wave solutions are obtained using Hirota's bilinear method and generalized three-wave type of ansatz approach. These new exact solutions will enrich previous results and help us further understand the physical structures and analyze the dynamics of the electrostatic solitons in the e-p-i plasmas. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by phase velocity, ion-to-electron density ratio, rotation frequency and cyclotron frequency.
Ion-acoustic solitary waves in a partially degenerate plasma
2022
The propagation of arbitrary amplitude ion-acoustic (IA) solitary waves (SWs) is studied in unmagnetized, collisionless, homogeneous electron-positron-ion (e-p-i) plasmas with finite temperature degeneracy of both electrons and positrons. Starting from a set of fluid equations for classical ions and Fermi-Dirac distribution for degenerate electrons and positrons, a linear dispersion relation for IA waves is derived. It is seen that the wave dispersion is significantly modified due to the presence of positron species and the effects of finite temperature degeneracy of electrons and positrons. In the nonlinear regime, the Sagdeev's pseudopotential approach is employed to study the existence domain and the evolution of nonlinear IA-SWs in terms of the parameters that are associated with the finite temperature degeneracy, the background number densities, and the thermal energies of electrons and positrons. It is found that in contrast to classical electron-ion plasmas both the subso...