  Using an eigenfunction expansion to solve the transport equation,
complemented by Monte-Carlo simulations, we show that ultrarelativistic shocks
can be effective particle accelerators even when they fail to produce large
amplitude turbulence in the downstream plasma. This finding contradicts the
widely held belief that a uniform downstream magnetic field perpendicular to
the shock normal inhibits acceleration by the first order Fermi process. In the
ultrarelativistic limit, we find a stationary power-law particle spectrum of
index s=4.17 for these shocks, close to that predicted for a strictly parallel
shock.
