Phase Mixing of Relativistically Intense Longitudinal Wave Packets in a Cold Plasma

TL;DR

This paper investigates the evolution and breaking of relativistically intense longitudinal wave packets in a cold plasma, deriving a phase mixing time scale formula and validating it through analytical and numerical methods.

Contribution

It introduces a general expression for phase mixing time scale based on wave amplitude and spectral width, validated with numerical simulations.

Findings

Phase mixing time scale depends on wave amplitude and spectral width.

Derived a new analytical formula for phase mixing time.

Numerical simulations confirm the theoretical predictions.

Abstract

The spatio-temporal evolution and breaking of relativistically intense wave packets in a cold homogeneous unmagnetized plasma has been studied analytically and numerically. A general expression for phase mixing time scale as a function of amplitude of the wave packet and width of the spectrum has been derived. Results have been compared with the existing formulae in literature. It is shown that phase mixing time scale crucially depends on the relative magnitude of the amplitude and dimensionless spectral width of the wave packet. Finally we have verified our results with respect to both the amplitude of the wave packet and width of the spectral using numerical simulations based on Dawson Sheet Model.