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

Authors

  • S. Delaney,

    Corresponding author
    1. School of Cosmic Physics, Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
    2. School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
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  • P. Dempsey,

    1. School of Cosmic Physics, Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
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  • P. Duffy,

    1. School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
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  • T. P. Downes

    1. School of Cosmic Physics, Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
    2. School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
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E-mail: sdelaney@cp.dias.ie

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 (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.

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