Relativistic Fermi acceleration with shock compressed turbulence

In this paper we present numerical simulations of test particle Fermi acceleration at relativistic shocks of the 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 none the less efficient and leads to powerlaw spectra with index similar or equal to 2.6 - 2.7 at a large shock Lorentz factor Gamma(sh) >> 1, markedly steeper than for isotropic scattering downstream. The acceleration time-scale t(acc) in the upstream rest frame becomes a fraction of Larmor time t(L) in the ultrarelativistic limit, tacc approximate to 10 t(L)/Gamma(sh). Astrophysical applications are discussed, in particular the acceleration in. - ray bursts internal and external shocks.