Small amplitude electron-acoustic double layers and solitons in fully relativistic plasmas of two-temperature electrons

Abstract

A Korteweg–de Vries (KdV) equation for fully relativistic one dimensional plasmas of arbitrarily large streaming speed and temperature is derived by using the reductive perturbation method. For plasmas with more than two species of particles, the coefficient representing quadratic nonlinearity in KdV can vanish at critical values of certain parameters. To describe the nonlinear evolution at this critical parameter, a modified KdV (mKdV) equation that contains a cubic nonlinear term is obtained. Furthermore, a mixed mKdV equation pertaining to parameters in the vicinity of the critical values is also derived, in which the quadratic and cubic nonlinearities are both present. As an illustration of the results, the mixed mKdV equation is applied to a plasma comprised of cold ions and electrons having cold (T=0) and finite temperature components. For warm temperature T⪡mec2, it is found that electron-acoustic nonlinear waves in the shape of double layer (kink) and solitary waves can exist, which have phase speed 3T/(4+α)me in the rest frame of plasma, where α is the polytropic index of the equation of state of the warm electrons. The thickness of the transitional layer of the kink structure is of the order of Debye length λD. For extremely high temperature T⪢mec2, it is also found that double layer and soliton-type solutions can exist with phase speed α−1c, which is equal to the well known relativistic sound speed c/3 for α=4/3. The thickness of the transition layer scales as δ∼T−1/4, which is different from the T⪡mec2 case.

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

“…6 Equation (33) is known as SG equation. It is also called mixed mK-dV equation (Lee 2009). It supports both the SWs and DLs solutions since it contains both ψ-term of K-dV and ψ 2 -term of mK-dV equation.…”

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

“…From the third order calculation, which utilizes another set of stretched coordinate, a mK-dV equation is obtained to describe the nonlinear evolution near this critical parameter. The stretched coordinates (Lee 2009) for mK-dV equation is:…”

“…This means that to study the finite EA-SWs and EA-DLs beyond this K-dV limit, one must resort the other type of nonlinear dynamical equation which can be valid for α ∼ α c . Therefore, in our present work, we derive a higher order nonlinear equation [known as Gardner equation (Lee 2009;Mannan and Mamun 2011;, and study the nonlinear features of the finite amplitude planar EA-SWs and EA-DLs in such a realistic non-thermal plasma system (consisting of cold electrons, hot electrons obeying a Boltzmann distribution, and nonthermal ions following nonthermal distribution). We show here how the electron-acoustic Gardner solitons (EA-GSs) differ from K-dV solitons and modified K-dV (mK-dV) solitons.…”

Multi-component Dust-ion-acoustic Solitary and Shock Waves in an Unmagnetized Dusty Plasma with Kappa Distributed Superthermal Electrons

“…To analyze the nonlinear evolution near the critical parameter µ e µ c , mK-dV equation is obtained from the third order calculation of , which utilizes another set of stretched coordinates. The stretched co-ordinates [42,43] for mK-dV equation is:…”