A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics
arXiv:1703.06192 · doi:10.1007/s11214-017-0351-y
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
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Cited by in corpus (27)
- Modelling three-dimensional transport of solar energetic protons in a corotating interaction region generated with EUHFORIA
- Large-scale Compression Acceleration during Magnetic Reconnection in a Low- Plasma
- Numerical modeling of cosmic rays in the heliosphere: Analysis of proton data from AMS-02 and PAMELA
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- From Sun to interplanetary space: What is the pathlength of Solar Energetic Particles?
- On the Diversity of M-Star Astrospheres and the Role of Galactic Cosmic Rays Within
- On the applicability of -distributions
- Numerical Modeling of Energetic Electron Acceleration, Transport, and Emission in Solar Flares: Connecting Loop-top and Footpoint Hard X-Ray Sources
- Perpendicular Diffusion of Energetic Particles: A Complete Analytical Theory
- Time and Charge-Sign Dependence of the Heliospheric Modulation of Cosmic Rays
- The Role of Energy Diffusion in the Deposition of Energetic Electron Energy in Solar and Stellar Flares
- Numerically modeling stochastic inflation in slow-roll and beyond
- Particle transport in hybrid PIC shock simulations: A comparison of diagnostics
- Acceleration of solar wind particles by traveling interplanetary shocks
- The Relation Between Escape and Scattering Times of Energetic Particles in a Turbulent Magnetized Plasma: Application to Solar Flares
- Probing solar flare accelerated electron distributions with prospective X-ray polarimetry missions
- On the residence-time of Jovian electrons in the inner heliosphere
- Two Numerical Methods for the 3D Anisotropic Propagation of Galactic Cosmic Rays
- Numerical and experimental evidence for a new interpretation of residence times in space
- Spectral and Imaging Diagnostics of Spatially-Extended Turbulent Electron Acceleration and Transport in Solar Flares
- Superdiffusion of energetic particles at shocks: A Lévy Flight model for acceleration
- Cross-Field Diffusion Effects on Particle Transport in a Solar Coronal Flux Rope
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- Energetic particle acceleration and transport with the novel IcarusPARADISE model
- Propagation Times and Energy Losses of Cosmic Protons and Antiprotons in Interplanetary Space
- Modelling cosmic-ray transport: magnetised versus unmagnetised motion in astrophysical magnetic turbulence
- Data driven analysis of Galactic cosmic rays in the heliosphere: diffusion of cosmic protons and nuclei