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 diffusion in momentum.
In recent years, interest in non-Gaussian, so-called anomalous diffusion has been growing. Evidence comes from observations of power-laws in particle distributions at interplanetary shocks or from MHD simulations. Particle transport with such underlying power-law jump length distributions cannot be represented by a normal transport equation, but to those with 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 and show applications to particle transport and diffusive shock acceleration. The stochastic model will be extended to Levy flights, corresponding to a space-fractional transport equation and applied to superdiffusive shock acceleration.
Dates:
Mardi, 16 septembre, 2025 - 14:00 to 15:00
Localisation / Location:
APC
Salle / Local:
483A-Malevitch
- Séminaire
Nom/Prénom // Last name/First name:
Aerdker / Sophie
Affiliation:
Ruhr U. Bochum
Equipe(s) organisatrice(s) / Organizing team(s):
- Théorie
Pays / Country:
Allemagne