A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics

Abstract

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via "toy models". Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.

51 pages, 17 figures, to be published in SSR

References in corpus (10)

• A Cosmic Ray Positron Anisotropy due to Two Middle-Aged, Nearby Pulsars?
• Low energy cosmic ray positron fraction explained by charge-sign dependent solar modulation
• The Diffusion Approximation vs. the Telegraph Equation for Modeling Solar Energetic Particle Transport with Adiabatic Focusing. I. Isotropic Pitch-angle Scattering
• On the variation of solar flare coronal x-ray source sizes with energy
• Spiral Arms as Cosmic Ray Source Distributions
• Propagation in 3D spiral-arm cosmic-ray source distribution models and secondary particle production using PICARD
• A more accurate numerical scheme for diffusive shock acceleration
• Cosmic rays in astrospheres
• A stochastic simulation of the propagation of Galactic cosmic rays reflecting the discreteness of cosmic ray sources. Age and path length distribution
• Effects of the tilted and wavy current sheet on the solar modulation of galactic cosmic rays