Derivation of electrostatic Korteweg–deVries equation in fully relativistic two-fluid plasmas

Abstract

A second order Korteweg–deVries (KdV) equation that describes the evolution of nonlinear electrostatic waves in fully relativistic two-fluid plasmas is derived without any assumptions restricting the magnitudes of the flow velocity and the temperatures of each species. In the derivation, the positive and negative species of plasmas are treated with equal footings, not making any species specific assumptions. Thus, the resulting equation, which is expressed in transparent form symmetric in particle species, can be applied to any two-fluid plasmas having arbitrarily large flow velocity and ultrarelativistically high temperatures. The phase velocity of the nonlinear electrostatic waves found in this paper is shown to be related to the flow velocity and the acoustic wave velocity through the Lorentz addition law of velocities, revealing the relativistic nature of the formulation in the present study. The derived KdV equation is applied to some limiting cases, and it is shown that it can be reduced to existing results in nonrelativistic plasmas, while there are some discrepancies from the results in the weak relativistic approximations.

Envelope solitary waves exist and collide head-on without phase shift in a dusty plasma

“…The rarefactive nonlinear waves in a dusty plasma have been extensively studied analytically during the past years by using the traditional reductive perturbation method 16 and verified by the experiments 13 14 15 . Recently, the application scope of the reductive perturbation method in a dusty plasma has been given by using the PIC numerical method 17 .…”

Nonlinear positron-acoustic waves in fully relativistic degenerate plasmas

“…Our theory is valid for arbitrary values of flow velocity and temperature of each plasma species. The relativistic nature of the present formulation was revealed by the equations (41) and (42), which show the relation of phase velocity, (ν) and the flow velocity, ( s0 b ) through the Lorentz addition law of velocities [42].…”

Electron trapping in the electrosound solitary wave for propagation of high intensity laser in a relativistic plasma

“…We employ the longitudinal components of 1D continuity and momentum equations for ions and electrons in the relativistic two-fluid plasma [21][22][23][24][25][26]:…”

“…We have adopted the fully relativistic continuity and force balance equations [19][20][21][22][23] to formulate the proposed problem with appropriate assumptions. Lee and Choi [24] and Lee [25,26] employed these equations for the first time in order to investigate the electrostatic ion-acoustic solitary waves in a relativistic plasma. These basic equations, derived directly from the conservation of the particle number and the energy-momentum tensor, are more general than their previous counterparts [27][28][29].…”