Shocks and non-thermal particles in clusters of galaxies

Galaxy clusters grow by gas accretion, mostly from mergers of substructures, which release powerful shock waves into cosmic plasmas and convert a fraction of kinetic energy into thermal energy, amplification of magnetic fields and into the acceleration of energetic particles. The modeling of the radio signature of cosmic shocks, combined with the lack of detected gamma-rays from cosmic ray (CR) protons, poses challenges to our understanding of how cosmic rays get accelerated and stored in the intracluster medium. Here we review the injection of CRs by cosmic shocks of different strengths, combining the detailed "microscopic" view of collisionless processes governing the creation of non-thermal distributions of electrons and protons in cluster shocks (based on analytic theory and particle-in-cell simulations), with the "macroscopic" view of the large-scale distribution of cosmic rays, suggested by modern cosmological simulations. We discuss time dependent non-linear kinetic models of particle acceleration by multiple internal shocks with large scale compressible motions of plasma. The models produce soft CR spectra containing a noticeable energy density in the super-thermal protons of energies below a few GeV which are difficult to constrain by Fermi observations. We consider the effect of plasma composition on CR injection and super-thermal particle population in the hot intracluster matter which can be constrained by fine high resolution X-ray spectroscopy of Fe ions.