A more accurate numerical scheme for diffusive shock acceleration

Abstract

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.

9 pages, 2 figures. Published in MNRAS

References in corpus (4)

• Particle acceleration by ultra-relativistic shocks: theory and simulations
• Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves
• Postshock turbulence and diffusive shock acceleration in young supernova remnants
• Time-dependent particle acceleration in supernova remnants in different environments

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• The Relation Between Escape and Scattering Times of Energetic Particles in a Turbulent Magnetized Plasma: Application to Solar Flares
• Superdiffusion of energetic particles at shocks: A Lévy Flight model for acceleration
• Sapphire++: A particle transport code combining a spherical harmonic expansion and the discontinuous Galerkin method
• Cosmic ray transport and acceleration in an evolving shock landscape