Journal Article

A more accurate numerical scheme for diffusive shock acceleration

A. Achterberg and K. M. Schure

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 411, issue 4, pages 2628-2636
Published in print March 2011 | ISSN: 0035-8711
Published online March 2011 | e-ISSN: 1365-2966 | DOI:
A more accurate numerical scheme for diffusive shock acceleration

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We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using stochastic differential equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that contains a shock of finite width and a varying diffusivity of the cosmic rays, where the diffusivity decreases across the shock. We compare the results for the slope of the momentum distribution with those obtained from a perturbation analysis valid for finite but small shock width. These calculations show that this scheme, although computationally more expensive, provides a significantly better performance than the Cauchy–Euler type schemes that were proposed earlier in the case where steep gradients in the cosmic ray diffusivity occur. For constant diffusivity, the proposed scheme gives similar results as the Cauchy–Euler scheme.

Keywords: acceleration of particles; diffusion; shock waves; methods: numerical

Journal Article.  6342 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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