Diffusive Shock Acceleration of Cosmic Rays and Their Stochastic Differential Equations

Abstract:

Diffusive Shock Acceleration is believed to be the mechanism responsible for the acceleration of charged particles at very high energies, which is a phenomenon observed in a wide variety of astrophysical environments. Standard DSA theory is based on solutions of the Parker transport equation (a type of  Fokker-Planck, or Kolmogorov forward equation) where the advection speeds and/or diffusion coefficients are discontinuous functions of position. 

The presence of these discontinuities creates problems with Monte-Carlo simulations of shock acceleration by significantly slowing down run times. In this talk, I discuss how one can efficiently model shock acceleration by simulating an equivalent stochastic process, called Skew Brownian Motion, and present a numerical algorithm that allows one to correctly treat particle behavior at a shock in a physically relevant way.