The nonlinear development of the relativistic two-stream instability

TL;DR

This paper presents the first nonlinear simulations of the relativistic two-stream instability, showing initial agreement with linear theory and highlighting nonlinear effects that prevent saturation in ideal hydrodynamics.

Contribution

It provides the first nonlinear numerical analysis of relativistic two-stream instability, extending understanding beyond linear theory.

Findings

Initial growth matches linear predictions

Nonlinear effects prevent saturation in ideal hydrodynamics

Instability remains active without saturation

Abstract

The two-stream instability has been mooted as an explanation for a range of astrophysical applications from GRBs and pulsar glitches to cosmology. Using the first nonlinear numerical simulations of relativistic multi-species hydrodynamics we show that the onset and initial growth of the instability is very well described by linear perturbation theory. In the later stages the linear and nonlinear description match only qualitatively, and the instability does not saturate even in the nonlinear case by purely ideal hydrodynamic effects.