Non-resonant magnetohydrodynamics streaming instability near magnetized relativistic shocks

TL;DR

This paper combines linear analysis and numerical simulations to study the non-resonant streaming instability near relativistic shocks, revealing its growth characteristics and magnetic amplification effects relevant for understanding turbulence.

Contribution

It provides a comprehensive analysis valid for all shock velocities and confirms the instability's behavior through simulations, highlighting magnetic amplification near relativistic shocks.

Findings

Maximum growth rate at ultra-relativistic shocks

Magnetic amplification up to 10 times the initial field

Wavenumber dependence of growth rate as k_x^{1/2}

Abstract

We present in this paper both a linear study and numerical relativistic MHD simulations of the non-resonant streaming instability occurring in the precursor of relativistic shocks. In the shock front restframe, we perform a linear analysis of this instability in a likely configuration for ultra-relativistic shock precursors. This considers magneto-acoustic waves having a wave vector perpendicular to the shock front and the large scale magnetic field. Our linear analysis is achieved without any assumption on the shock velocity and is thus valid for all velocity regimes. In order to check our calculation, we also perform relativistic MHD simulations describing the propagation of the aforementioned magneto-acoustic waves through the shock precursor. The numerical calculations confirm our linear analysis, which predicts that the growth rate of the instability is maximal for ultra-relativistic shocks and exhibits a wavenumber dependence $\propto k_x^{1/2}$. Our numerical simulations also depict the saturation regime of the instability where we show that the magnetic amplification is moderate but nevertheless significant ($\delta B/B\leq 10$). This latter fact may explain the presence of strong turbulence in the vicinity of relativistic magnetized shocks. Our numerical approach also introduces a convenient means to handle isothermal (ultra-)relativistic MHD conditions.