Cosmic ray transport and acceleration near an oblique, spherical shock

Abstract

A suitable Fokker-Planck transport equation has been developed to describe the behavior of charged particles for an Archimedean spiral magnetic configuration and spherically symmetric fluid flow. Simulations of the pitch angle transport and acceleration of cosmic rays nearby an oblique, spherical shock have been performed. As part of this study, we have developed a generalized total variation diminishing (TVD) method based on one of the well-known numerical techniques to handle the advection problems. By using our developed spatial transport technique, the program running speed can be improved to be 1-2 orders of magnitude faster than a prototype that was developed by Ruffolo (1995), with an acceptable numerical error. The spatial step size can be fully adjusted to a desired general, Courant number (γ = u∆t/∆z), which is restricted not to exceed unity in the standard TVD scheme.