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| Paper: |
Energetic Particle Transport with Stochastic Differential Equations: General Methods and the Extension to Anomalous Diffusion Regimes |
| Volume: |
488, 8th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2013) |
| Page: |
201 |
| Authors: |
Effenberger, F. |
| Abstract: |
Numerical solution methods for Stochastic Differential Equations (SDEs) have become an important tool to study charged particle transport, due to their simplicity and conformance with modern computer architecture. Their field of application ranges from the detailed calculation of solar energetic particle events to the cosmic ray transport in the outer heliosphere and in the Galaxy. At the heart of the applicability of SDEs to kinetic equations is the fundamental equivalence between the Fokker-Planck diffusion equation of parabolic type and an SDE involving a Wiener process to represent the stochastic Brownian motion of (pseudo-)particles. This equivalence has recently been extended to anomalous diffusion involving a Fokker-Planck equation of fractional order and generalized Lévy distributions. Numerical tests and applications of this approach to anomalous diffusion and future prospects of the SDE approach in the space physics context are outlined. |
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