Ion-Acoustic Envelope Modes in a Degenerate Relativistic Electron-Ion Plasma

TL;DR

This paper develops a relativistic two-fluid model for electron-ion plasmas, deriving a nonlinear Schrödinger equation to study ion-acoustic envelope modes and the impact of relativistic effects on wave stability and solitons.

Contribution

It introduces a self-consistent relativistic model and derives an NLSE for plasma wave envelopes, highlighting relativistic effects on modulational instability and soliton solutions.

Findings

Relativistic effects modify the density dependence in the NLSE.

Relativistic plasma dispersion laws differ from non-relativistic cases.

Envelope soliton properties are influenced by relativistic factors.

Abstract

A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schr\"odinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case - in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.