Turbulence and particle acceleration in a relativistic plasma

TL;DR

This paper investigates how turbulence in relativistic collisionless plasmas influences particle energy distributions, revealing that magnetic turbulence compressibility affects the power-law tail exponent, supported by phenomenological and numerical analysis.

Contribution

It introduces a new understanding of how magnetic turbulence compressibility determines the power-law index in relativistic plasma particle energy distributions.

Findings

The power-law index $oldsymbol{\alpha}$ depends on magnetic compressibility.

Analytic predictions agree with numerical simulations.

Turbulence evolves into a state with ultra-relativistic temperature and mildly relativistic fluctuations.

Abstract

In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a non-thermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter $\sigma \gg 1$) quickly evolves into a state with ultra-relativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent $\alpha$ in the power-law particle energy distribution function, $f(\gamma)d\gamma\propto \gamma^{-\alpha}d\gamma$, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent $\alpha$ is in good agreement with the numerical results.