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It is well accepted today that diffusive acceleration in shocks results to the cosmic ray spectrum formation. This is in principle true for non-relativistic shocks, since there is a detailed theory covering a large range of their properties and the resulting power-law spectrum, which is nevertheless not as efficient to reach the very high energies observed in the cosmic ray spectrum. On the other hand, the cosmic ray maximum energy and the resulting spectra from relativistic shocks, are still under investigation and debate concerning their contribution to the features of the cosmic ray spectrum and the measured, or implied, cosmic ray radiation from candidate astrophysical sources. Here, we discuss the efficiency of the first order Fermi (diffusive) acceleration mechanism up to relativistic shock speeds, presenting Monte Carlo simulations.
We calculate the temporal evolution of distributions of relativistic electrons subject to synchrotron and adiabatic processes and Fermi-like acceleration in shocks. The shocks result from Kelvin-Helmholtz instabilities in the jet. Shock formation and
Radio, X-ray, and gamma-ray observations provide us with strong evidence of particle acceleration to multi-TeV energies in various astrophysical sources. Diffusive shock acceleration is one of the most successful models explaining the presence of suc
Radio relics in galaxy clusters are giant diffuse synchrotron sources powered in cluster outskirts by merger shocks. Although the relic-shock connection has been consolidated in recent years by a number of observations, the details of the mechanisms
We present a theory for the generation of mesoscale ($kr_{g}ll 1$, where $r_{g}$ is the cosmic ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfven waves scattering of
We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using Stochastic Differential Equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that contains a