Relativistic Fermi acceleration with shock compressed turbulence

This paper presents numerical simulations of test particle Fermi acceleration at relativistic shocks of Lorentz factor Gamma_sh = 2-60, using a realistic downstream magnetic structure obtained from the shock jump conditions. The upstream magnetic field is described as pure Kolmogorov turbulence; the corresponding downstream magnetic field lies predominantly in the plane tangential to the shock surface and the coherence length is smaller along the shock normal than in the tangential plane. Acceleration is nonetheless efficient and leads to powerlaw spectra with index s = 2.6-2.7 at large shock Lorentz factor Gamma_sh >> 1, markedly steeper than for isotropic scattering downstream. The acceleration timescale t_acc in the upstream rest frame becomes a fraction of Larmor time t_L in the ultra-relativistic limit, t_acc ~ 10 t_L/Gamma_sh. Astrophysical applications are discussed, in particular the acceleration in gamma-ray bursts internal and external shocks.