Speaker
Description
In the heliosphere, power laws in space and time profiles of energetic particles are observed. It has been proposed that they result from superdiffusive transport. Such anomalous, non-Gaussian, transport regimes may arise as consequence of intermittent magnetic field structures.
Superdiffusive particle transport can be described by a space-fractional Fokker-Planck equation. Numerical solutions can be obtained by solving the corresponding Stochastic Differential Equation (SDE). In case of Gaussian diffusion, the SDE is driven by a normal distribution, for superdiffusion it is driven by a symmetric stable Lévy distribution.
We solve the fractional diffusion-advection equation with a modified version of CRPropa3.2 and obtain the time-dependent solution of the cosmic-ray density. Our simulations lead to results that are compatible with the expected power law particle distribution upstream of a shock. Furthermore, we compare the SDE approach to a Fourier series approximation of the solution to the space-fractional Fokker-Planck equation.
