On Fermi acceleration and MHD-instabilities at ultra-relativistic magnetized shock waves

TL;DR

This paper investigates the conditions for Fermi acceleration at ultra-relativistic magnetized shock waves, focusing on magnetic field amplification mechanisms and the limitations of MHD instabilities.

Contribution

It analyzes magnetic field amplification via MHD instabilities and explores the potential for other instabilities to enable Fermi acceleration at relativistic shocks.

Findings

MHD instabilities saturate at deltaB/B ~ 1, insufficient for Fermi acceleration

Short-scale magnetic turbulence can facilitate Fermi acceleration under certain conditions

Other non-MHD instabilities may provide the necessary magnetic amplification

Abstract

Fermi acceleration can take place at ultra-relativistic shock waves if the upstream or downstream magnetic field has been remodeled so that most of the magnetic power lies on short spatial scales. The relevant conditions under which Fermi acceleration become efficient in the presence of both a coherent and a short scale turbulent magnetic field are addressed. Within the MHD approximation, this paper then studies the amplification of a pre-existing magnetic field through the streaming of cosmic rays upstream of a relativistic shock wave. The magnetic field is assumed to be perpendicular in the shock front frame, as generally expected in the limit of large shock Lorentz factor. In the MHD regime, compressive instabilities seeded by the net cosmic-ray charge in the shock precursor (as seen in the shock front frame) develop on the shortest spatial scales but saturate at a moderate level deltaB/B ~ 1, which is not sufficient for Fermi acceleration. As we argue, it is possible that other instabilities outside the MHD range provide enough amplification to allow successful Fermi acceleration.