  Nonthermal radiation observed from astrophysical systems containing
relativistic jets and shocks, e.g., gamma-ray bursts (GRBs), active galactic
nuclei (AGNs), and microquasars commonly exhibit power-law emission spectra.
Recent PIC simulations of relativistic electron-ion (or electron-positron) jets
injected into a stationary medium show that particle acceleration occurs within
the downstream jet. In collisionless, relativistic shocks, particle (electron,
positron, and ion) acceleration is due to plasma waves and their associated
instabilities (e.g., the Weibel (filamentation) instability) created in the
shock region. The simulations show that the Weibel instability is responsible
for generating and amplifying highly non-uniform, small-scale magnetic fields.
These fields contribute to the electron's transverse deflection behind the jet
head. The resulting "jitter" radiation from deflected electrons has different
properties compared to synchrotron radiation, which assumes a uniform magnetic
field. Jitter radiation may be important for understanding the complex time
evolution and/or spectra in gamma-ray bursts, relativistic jets in general, and
supernova remnants.
