Cosmic Ray Acceleration at Relativistic Shocks

Theoretical studies of cosmic ray particle acceleration in the first-order Fermi process at relativistic shocks are reviewed. At the beginning we discuss the acceleration processes acting at mildly relativistic shock waves. An essential role of oblique field configurations and field perturbations in forming the particle energy spectrum and changing the acceleration time scale is discussed. Then, we report on attempts to consider particle acceleration at ultra-relativistic shocks, often yielding an asymptotic spectral index sigma = 2.2 at large shock Lorentz factors. We explain why this result is limited to the cases of highly turbulent conditions near shocks. We conclude that our present knowledge of the acceleration processes acting at relativistic shocks is insufficient to allow for realistic modelling of the real shocks. The present review is a modified, extended and updated version of Ostrowski (1999).