  We have investigated particle acceleration and shock structure associated
with an unmagnetized relativistic jet propagating into an unmagnetized plasma.
Strong magnetic fields generated in the trailing jet shock lead to transverse
deflection and acceleration of the electrons. We have self-consistently
calculated the radiation from the electrons accelerated in the turbulent
magnetic fields. We find that the synthetic spectra depend on the bulk Lorentz
factor of the jet, the jet temperature, and the strength of the magnetic fields
generated in the shock. We have also begun study of electron acceleration in
the strong magnetic fields generated by kinetic shear (Kelvin-Helmholtz)
instabilities. Our calculated spectra should lead to a better understanding of
the complex time evolution and/or spectral structure from gamma-ray bursts,
relativistic jets, and supernova remnants.
