Scattering models at super-luminal shocks – a numerical study

We present Monte Carlo calculations of the cosmic ray spectral shapes and cosmic ray energy gains for diffusive shock acceleration at highly oblique relativistic shocks, namely super-luminal shocks, with high upstream flow Lorentz gamma factors, from 10 up to 1000, which could be relevant to models of relativistic astrophysical environments like Active Galactic Nuclei jets and Gamma Ray Burst sites. Both large angle and pitch angle diffusion of the accelerated cosmic rays is considered, applying to the relevant astrophysical models. Our physical/numerical approach allows that the particle's trajectory is followed along the magnetic field lines during shock crossings where the equivalent of a guiding centre approximation is inappropriate, measuring its phase space co-ordinates in the fluid frames, where E=0. We find striking differences in the cosmic ray energy spectral shapes comparing large angle scattering versus pitch angle diffusion methods; showing that the cosmic ray case of diffusion in superluminal shocks could be the 'key' of the problem of the universality of the diffusive shock acceleration (Fermi acceleration).