Simulations of Ion Acceleration at Non-relativistic Shocks. III. Particle Diffusion

TL;DR

This paper uses hybrid simulations to study how energetic particles diffuse around non-relativistic shocks, revealing how magnetic field amplification influences particle scattering and maximum energy in cosmic ray acceleration.

Contribution

It provides a detailed measurement of particle diffusion in self-generated turbulence, distinguishing between quasi-linear and non-linear magnetic field amplification regimes.

Findings

Mean free path is comparable to particle gyroradius.

Diffusion follows self-generated turbulence in moderate shocks.

Bohm-like diffusion occurs in strongly amplified fields.

Abstract

We use large hybrid (kinetic protons-fluid electrons) simulations to investigate the transport of energetic particles in self-consistent electromagnetic configurations of collisionless shocks. In previous papers of this series, we showed that ion acceleration may be very efficient (up to $10-20\%$ in energy), and outlined how the streaming of energetic particles amplifies the upstream magnetic field. Here, we measure particle diffusion around shocks with different strengths, finding that the mean free path for pitch-angle scattering of energetic ions is comparable with their gyroradii calculated in the self-generated turbulence. For moderately-strong shocks, magnetic field amplification proceeds in the quasi-linear regime, and particles diffuse according to the self-generated diffusion coefficient, i.e., the scattering rate depends only on the amount of energy in modes with wavelengths comparable with the particle gyroradius. For very strong shocks, instead, the magnetic field is amplified up to non-linear levels, with most of the energy in modes with wavelengths comparable to the gyroradii of highest-energy ions, and energetic particles experience Bohm-like diffusion in the amplified field. We also show how enhanced diffusion facilitates the return of energetic particles to the shock, thereby determining the maximum energy that can be achieved in a given time via diffusive shock acceleration. The parametrization of the diffusion coefficient that we derive can be used to introduce self-consistent microphysics into large-scale models of cosmic ray acceleration in astrophysical sources, such as supernova remnants and clusters of galaxies.