  We include a general form for the scattering mean free path in a nonlinear
Monte Carlo model of relativistic shock formation and Fermi acceleration.
Particle-in-cell (PIC) simulations, as well as analytic work, suggest that
relativistic shocks tend to produce short-scale, self-generated magnetic
turbulence that leads to a scattering mean free path (mfp) with a stronger
momentum dependence than the mfp ~ p dependence for Bohm diffusion. In
unmagnetized shocks, this turbulence is strong enough to dominate the
background magnetic field so the shock can be treated as parallel regardless of
the initial magnetic field orientation, making application to gamma-ray bursts
(GRBs), pulsar winds, Type Ibc supernovae, and extra-galactic radio sources
more straightforward and realistic. In addition to changing the scale of the
shock precursor, we show that, when nonlinear effects from efficient Fermi
acceleration are taken into account, the momentum dependence of the mfp has an
important influence on the efficiency of cosmic-ray production as well as the
accelerated particle spectral shape. These effects are absent in
nonrelativistic shocks and do not appear in relativistic shock models unless
nonlinear effects are self-consistently described. We show, for limited
examples, how the changes in Fermi acceleration translate to changes in the
intensity and spectral shape of gamma-ray emission from proton-proton
interactions and pion-decay radiation.
