Time-dependent transport and subdiffusion of cosmic rays

In this paper, time-dependent diffusion coefficients are calculated by applying linear and nonlinear theories. Such a study can demonstrate whether perpendicular transport of cosmic rays behaves diffusively or not. Whereas transport perpendicular to the magnetic background field in a composite slab/two-dimensional model can be described by recently proposed nonlinear diffusion theories, the subdiffusive behavior for slab geometry cannot be explained by them. By starting with the equations of motion I present a theoretical description of cosmic ray subdiffusion in the magnetostatic slab model. The time dependence obtained from these theoretical considerations agrees with the model of compound diffusion and recently proposed test particle simulations.