Stochastic models of particle transport and acceleration

Abstract: Understanding the complex transport of particles in turbulent plasmas is of great relevance in various fields. In astrophysics, the diffusive transport of high-energy particles is often described in an ensemble-averaged way, employing a transport equation that describes the time evolution of the particles distribution function in space and momentum. The standard transport equation can also be re-written into a set of stochastic differential equation. This allows for a Monte-Carlo approach of solving for the particles distribution function, which has been successfully applied to particle transport in the heliosphere, diffusive shock acceleration and recently to shear acceleration. Furthermore, the stochastic model allows for an extension to Levy flights, modeling non-Gaussian diffusion. Particle transport with such underlying power-law jump length distributions cannot be represented by a normal transport equation, but by those including fractional derivatives. While solving fractional differential equations is difficult, stochastic models provide an elegant way to solve for the particles distribution function.In this talk, I will discuss the connection between Fokker-Planck equations and stochastic differential equations, show applications to particle transport and acceleration and give a brief outlook to Levy flights.