Nonlinear electrostatic waves in an electron–positron plasma

S J Yang,Y Chen,C Z Xiao

doi:10.1063/1.5130013

Abstract

This paper presents a theoretical and numerical study of all possible nonlinear electrostatic waves in an unmagnetized and collisionless electron–positron plasma. From a two-component plasma with an arbitrary ion/positron-to-electron mass ratio β and a temperature ratio TR, four possible waves are discussed: Langmuir waves (LWs), electron acoustic waves, ion acoustic waves, and ion-bulk (IBk) waves. Although LWs are ubiquitous, the existence of the other three acoustic waves depends on the values of β and TR. In an electron–positron plasma, only LWs and IBk waves are allowed. The dispersion relation of these waves varies from a “thumb” curve to a “thumb–teardrop” curve when TR &lt; 1. Vlasov simulations are used to verify predicted waves and reveal several characteristics of excited waves, such as sideband instability, harmonic effect, and nonlinear shifts in frequency and wave number. The present results for an electron–positron plasma can be easily applied to plasmas with arbitrary β and TR, especially when the dispersion relations of these waves are close to each other.

Highlights

The electron–positron plasma, or the so-called pair plasma, is an important part of the early universe1 and appears in many astrophysical environments such as near quasars,2 pulsars,3,4 and black holes.5,6 Such a plasma can be produced by laboratory experiments7–11 and provides the basis and opportunity for exploring many astrophysical and antimatter phenomena
Langmuir waves (LWs) are nearly undamped because their phase velocity is much greater than the electron thermal velocity, ion acoustic waves (IAWs) are strongly damped by Landau damping because the electron and positron temperatures are nearly the same, which leads to cs ≈ vthp, where cs is the sound velocity, and vthp is the thermal velocity of positrons
In deriving the nonlinear dispersion relations of undamped electrostatic waves, we find that the LW is ubiquitous, whereas the existence of the three acoustic waves (EAWs, IAWs, and IBk waves) depends on the mass and temperature ratios

Summary

INTRODUCTION

The electron–positron plasma, or the so-called pair plasma, is an important part of the early universe and appears in many astrophysical environments such as near quasars, pulsars, and black holes. Such a plasma can be produced by laboratory experiments and provides the basis and opportunity for exploring many astrophysical and antimatter phenomena. Linear Langmuir waves (LWs) and ion acoustic waves (IAWs) in an unmagnetized electron–positron plasma have been studied well. In an electron–ion plasma, these curves are completely separated in frequency space The excitation of these nonlinear waves via a resonant three-wave process has been studied, along with their properties.. In deriving the nonlinear dispersion relations of undamped electrostatic waves, we find that the LW is ubiquitous, whereas the existence of the three acoustic waves (EAWs, IAWs, and IBk waves) depends on the mass and temperature ratios. The general dispersion relation is a “thumb–teardrop” curve These nonlinear waves can be excited via an external ponderomotive force induced by two electromagnetic waves. Theoretical and simulated dispersion relations are clearly consistent, and the nonlinear shift in frequency, the harmonic effect, and the sideband effect are all observed.

THEORETICAL DISPERSION RELATION OF WAVES

VLASOV SIMULATION

CONCLUSION AND SUMMARY