A note on the theory of transverse diffusion in shock particle   acceleration
  We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock population in quasi-perpendicualr high-Mach number collisionless shocks to which we apply the theory, we demonstrate that the inferred diffusion coefficients are in excellent agreement with the requirements of the theory and its predictions. Diffusion in the collisionless regime turns out to be non-classical Gibbsian (L\'evy flight), time-dependent though weak. 
R. A. Treumann