  We study the acceleration of charged particles by ultra-relativistic shocks
using test-particle Monte-Carlo simulations. Two field configurations are
considered: (i) shocks with uniform upstream magnetic field in the plane of the
shock, and (ii) shocks in which the upstream magnetic field has a cylindrical
geometry. Particles are assumed to diffuse in angle due to frequent
non-resonant scattering on small-scale fields. The steady-state distribution of
particles' Lorentz factors is shown to approximately satisfy $dN/d\gamma
\propto \gamma^{-2.2}$ provided the particle motion is scattering dominated on
at least one side of the shock. For scattering dominated transport, the
acceleration rate scales as $t_{\rm acc}\propto t^{1/2}$, though recovers Bohm
scaling $t_{\rm acc}\propto t$ if particles become magnetised on one side of
the shock. For uniform field configurations, a limiting energy is reached when
particles are magnetised on both sides of the shock. For the cylindrical field
configuration, this limit does not apply, and particles of one sign of charge
will experience a curvature drift that redirects particles upstream. For the
non-resonant scattering model considered, these particles preferentially escape
only when they reach the confinement limit determined by the finite system
size, and the distribution approaches the escapeless limit $dN/d\gamma \propto
\gamma^{-1}$. The cylindrical field configuration resembles that expected for
jets launched by the Blandford $\&$ Znajek mechanism, the luminous jets of AGN
and GRBs thus provide favourable sites for the production of ultra-high energy
cosmic rays.
