  Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas.
Plasma waves and their associated instabilities (e.g.,Buneman, Weibel and other
two-stream instabilities) created in collisionless shocks are responsible for
particle (electron, positron, and ion) acceleration. Using a 3-D relativistic
electromagnetic particle (REMP) code, we have investigated particle
acceleration associated with a relativistic jet front propagating into an
ambient plasma with and without initial magnetic fields. Simulations show that
the Weibel instability created in the collisionless shock front accelerates jet
and ambient particles both perpendicular and parallel to the jet propagation
direction. The non-linear fluctuation amplitudes of densities, currents,
electric, and magnetic fields in the electron-positron shock are larger than
those found in the electron-ion shock at the same simulation time. This comes
from the fact that both electrons and positrons contribute to generation of the
Weibel instability. The simulation results show that the Weibel instability is
responsible for generating and amplifying nonuniform, small-scale (mainly
transverse) magnetic fields which contribute to the electron's (positron's)
transverse deflection behind the jet head. This small scale magnetic field
structure is appropriate to the generation of ``jitter'' radiation from
deflected electrons (positrons) as opposed to synchrotron radiation.
