A more accurate numerical scheme for diffusive shock acceleration

Details A more accurate numerical scheme for diffusive shock acceleration A more accurate numerical scheme for diffusive shock acceleration

2011-03-15

arxiv.org/abs/1103.3049v1

2011MNRAS.411.2628A

Astronomy and Astrophysics

Astrophysics

High Energy Astrophysical Phenomena

9 pages, 2 figures. Published in MNRAS

Scientific paper

10.1111/j.1365-2966.2010.17868.x

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.

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