Non-linear collisionless damping of Weibel turbulence in relativistic blast waves

TL;DR

This paper investigates the non-linear collisionless damping of Weibel turbulence downstream of relativistic shock waves, revealing that non-linear effects increase damping rates and impact astrophysical shock physics.

Contribution

It provides the first explicit calculation of non-linear damping terms for Weibel turbulence in relativistic shocks, highlighting their significance in astrophysical contexts.

Findings

Non-linear effects increase damping rates of Weibel turbulence.

Damping is significant when scattering length exceeds magnetic coherence length.

Implications for gamma-ray burst shock physics.

Abstract

The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order non-linear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic shock wave of a gamma-ray burst.