Journal Article

A new time-dependent finite-difference method for relativistic shock acceleration

S. Delaney, P. Dempsey, P. Duffy and T. P. Downes

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 420, issue 4, pages 3360-3367
Published in print March 2012 | ISSN: 0035-8711
Published online March 2012 | e-ISSN: 1365-2966 | DOI:
A new time-dependent finite-difference method for relativistic shock acceleration

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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 (Γ∈ (1, 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.

Keywords: acceleration of particles; relativistic processes; shock waves; methods: numerical

Journal Article.  6159 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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