Peculiarities of particle acceleration by relativistic shock waves

As Niemiec and Ostrowski (2003a) note, at a relativistic shock wave the bulk velocity of the flow is comparable to the particle velocity. This leads to anisotropy of particle angular distribution, which can substantially influence the process of particle acceleration. In contrast to the non-relativistic case the particle power-law spectral indices depend on the conditions at the shock, including the spectrum and amplitude of magnetic field perturbations and the mean field inclination to the shock's normal (Kirk and Schneider, 1987a,b; Heavens and Drury, 1988; Kirk and Heavens 1989; Ballard and Heavens, 1992; Ostrowski 1991, 1993; Bednarz and Ostrowski, 1996, 1998). In the case of a weakly perturbed magnetic field the acceleration process can be investigated via analytical methods (Kirk and Schneider, 1987a; Heavens and Drury, 1988; Kirk and Heavens, 1989). However, if finite-amplitude MHD waves are present in the medium these approaches are no longer valid and numerical methods have to be used. The particle acceleration studies so far have applied very simple models for numerical modeling of the perturbed magnetic field structure (Ostrowski, 1991, 1993; Ballard and Heavens, 1992; Bednarz and Ostrowski, 1996, 1998).

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