Monte Carlo simulations of a diffusive shock with multiple scattering angular distributions

TL;DR

This paper develops a Monte Carlo simulation for diffusive shock acceleration, extending it to include anisotropic scattering laws, revealing how scattering angular distributions affect shock structures and particle energy spectra.

Contribution

The paper introduces an extended Monte Carlo simulation incorporating anisotropic scattering laws, advancing the modeling of collisionless shock acceleration.

Findings

Energy spectral index increases with scattering angular distribution standard deviation.

Subshock's energy spectral index decreases as scattering angular distribution standard deviation increases.

Different shock structures and evolutions are observed with varying Gaussian scattering angles.

Abstract

We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained. Since the same results test the validity of the dynamical Monte Carlo method for simulating a collisionless shock, we extend the simulation toward including an anisotropic scattering law for further developing this dynamical Monte Carlo simulation. Under this extended anisotropic scattering law, a Gaussian distribution function is used to describe the variation of scattering angles in the particle's local frame. As a result, we obtain a series of different shock structures and evolutions in terms of the standard deviation values of the given Gaussian scattering angular distributions. We find that the total energy spectral index increases as the standard deviation value of the scattering angular distribution increases, but the subshock's energy spectral index decreases as the standard deviation value of the scattering angular distribution increases.