Kinetic approaches to particle acceleration at cosmic ray modified shocks

TL;DR

This paper reviews kinetic models of particle acceleration at cosmic ray modified shocks, emphasizing their ability to incorporate non-linear effects like magnetic field amplification and shock dynamics.

Contribution

It provides a technical comparison of two kinetic approaches, demonstrating their consistent conclusions on shock modification effects.

Findings

Shock modification alters particle spectral shape

Maximum particle momentum is affected by magnetic field amplification

The approaches agree on the impact of non-linear effects on acceleration

Abstract

Kinetic approaches provide an effective description of the process of particle acceleration at shock fronts and allow to take into account the dynamical reaction of the accelerated particles as well as the amplification of the turbulent magnetic field as due to streaming instability. The latter does in turn affect the maximum achievable momentum and thereby the acceleration process itself, in a chain of causality which is typical of non-linear systems. Here we provide a technical description of two of these kinetic approaches and show that they basically lead to the same conclusions. In particular we discuss the effects of shock modification on the spectral shape of the accelerated particles, on the maximum momentum, on the thermodynamic properties of the background fluid and on the escaping and advected fluxes of accelerated particles.