  We consider the interaction between radiation, matter and a magnetic field in
a compact, relativistic jet. The entrained matter accelerates outward as the
jet breaks out of a star or other confining medium. In some circumstances, such
as gamma-ray bursts (GRBs), the magnetization of the jet is greatly reduced by
an advected radiation field while the jet is optically thick to scattering.
Where magnetic flux surfaces diverge rapidly, a strong outward Lorentz force
develops and radiation and matter begin to decouple. The increase in
magnetization is coupled to a rapid growth in Lorentz factor. We take two
approaches to this problem. The first examines the flow outside the fast
magnetosonic critical surface, and calculates the flow speed and the angular
distribution of the radiation field over a range of scattering depths. The
second considers the flow structure on both sides of the critical surface in
the optically thin regime, using a relaxation method. In both approaches, we
find how the terminal Lorentz factor, and radial profile of the outflow, depend
on the radiation intensity and optical depth at breakout. The effect of bulk
Compton scattering on the radiation spectrum is calculated by a Monte Carlo
method, while neglecting the effects of internal dissipation. The peak of the
scattered spectrum sits near the seed peak if radiation pressure dominates the
acceleration, but is pushed to a higher frequency if the Lorentz force
dominates, and especially if the seed photon cone is broadened by interaction
with a slower component of the outflow.
