Longitudinal wave-breaking limits in a unified geometric model of relativistic warm plasmas

TL;DR

This paper develops a unified geometric model for relativistic warm plasmas to analyze wave-breaking limits, showing that certain waterbag geometries yield finite maximum electric field amplitudes as wave velocity approaches the speed of light.

Contribution

It introduces a geometric formulation of the waterbag paradigm that generalizes previous models and demonstrates finite wave-breaking limits in relativistic regimes.

Findings

Finite maximum electric field amplitude for specific waterbag geometries

Unified geometric framework encompassing prior relativistic plasma models

Wave-breaking limit behavior as phase velocity approaches light speed

Abstract

The covariant Vlasov-Maxwell system is used to study breaking of relativistic warm plasma waves. The well-known theory of relativistic warm plasmas due to Katsouleas and Mori (KM) is subsumed within a unified geometric formulation of the `waterbag' paradigm over spacetime. We calculate the maximum amplitude $E_\text{max}$ of non-linear longitudinal electric waves for a particular class of waterbags whose geometry is a simple 3-dimensional generalization (in velocity) of the 1-dimensional KM waterbag (in velocity). It is well known that the value of $\lim_{v\to c}E_\text{max}$ (with the effective temperature of the plasma electrons held fixed) diverges for the KM model; however, we show that a certain class of simple 3-dimensional waterbags yields a finite value for $\lim_{v\to c}E_\text{max}$, where $v$ is the phase velocity of the wave and $c$ is the speed of light.