  We study a planar bubble wall that is traveling at an ultrarelativistic speed
through a thermal plasma. This situation may arise during a first order
electroweak phase transition in the early universe. As particles cross the
wall, it is assumed that their mass grows from $m_a$ to $m_b$, and they are
decelerated causing them to emit massless radiation. We are interested in the
momentum transfer to the wall, the thermal pressure felt by the wall, and the
resultant terminal velocity of the wall. We employ the semiclassical current
radiation (SCR) formalism to perform these calculations. An incident charged
particle is treated as a point-like classical electromagnetic current, and the
spectrum of quantum electromagnetic radiation (photons) is derived by
calculating appropriate matrix elements. To understand how the spectrum depends
on the thickness of the wall, we explore simplified models for the current
corresponding to an abrupt and a gradual deceleration. For the model of abrupt
deceleration, we find that the SCR formalism can reproduce the
$P_\mathrm{therm} \propto \gamma_w^0$ scaling found in earlier work by assuming
that the emission is soft, but if the emission is not soft the SCR formalism
can be used to obtain $P_\mathrm{therm} \propto \gamma_w^2$ instead. For the
model of gradual deceleration, we find that the wall thickness $L_w$ enters to
cutoff the otherwise log-flat radiation spectrum above a momentum of $\sim
\gamma_w^2 / L_w$, and we discuss the connections with classical
electromagnetic bremsstrahlung.
