  We discuss a mechanism for intense electromagnetic wave emission at an
astrophysical relativistic shock in a magnetized collisionless plasma. At the
magnetized shock, the particle reflection by a compressed magnetic field of the
shock produces a ring-like distribution in momentum, which gives rise to plasma
instabilities. Intense and coherent high-frequency electromagnetic waves will
be emitted if the synchrotron maser instability (SMI) is excited, whereas
non-propagating magnetic fluctuations will be generated when the Weibel
instability (WI) is the dominant mode. The problem is of great astrophysical
interest because if intense radiation is emitted, the interaction with the
upstream medium induces a large-amplitude electrostatic field (or Wakefield),
which may play a role for the acceleration of ultra-high-energy cosmic rays. We
review our recent effort to measure the efficiency of the electromagnetic wave
emission using fully self-consistent, two-dimensional (2D) particle-in-cell
(PIC) simulations for pair plasmas. We found that the emission efficiency in 2D
was systematically lower than one dimensional (1D) PIC simulation results.
However, the power remains finite even when the WI is active to generate
large-amplitude magnetic fluctuations. Astrophysical implications of the
present results are briefly discussed.
