A New Time-Dependent Finite Difference Method for Relativistic Shock Acceleration

TL;DR

This paper introduces a new finite difference method for modeling relativistic shock acceleration, accurately capturing particle distributions and synchrotron losses in high-speed plasma flows.

Contribution

It develops a novel time-dependent finite difference approach using the method of lines to simulate relativistic shock acceleration including synchrotron losses.

Findings

Accurately reproduces power law behavior in particle momentum distributions.

Successfully models synchrotron cutoff shapes in non-relativistic shocks.

Efficiently scales on high-performance computing clusters.

Abstract

We present a new approach to calculate the particle distribution function about relativistic shocks including synchrotron losses using the method of lines with an explicit finite difference scheme. A steady, continuous, one dimensional plasma flow is considered to model thick (modified) shocks, leading to a calculation in three dimensions plus time, the former three being momentum, pitch angle and position. The method accurately reproduces the expected power law behaviour in momentum at the shock for upstream flow speeds ranging from 0.1c to 0.995c (1 < \Gamma < 10). It also reproduces approximate analytical results for the synchrotron cutoff shape for a non-relativistic shock, demonstrating that the loss process is accurately represented. The algorithm has been implemented as a hybrid OpenMP--MPI parallel algorithm to make efficient use of SMP cluster architectures and scales well up to many hundreds of CPUs.