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Nonthermal radiation observed from astrophysical systems containingrelativistic jets and shocks, e.g., active galactic nuclei (AGNs), gamma-raybursts (GRBs), and Galactic microquasar systems usually have power-law emissionspectra. Recent PIC simulations using injected relativistic electron-ion(electro-positron) jets show that acceleration occurs within the downstreamjet. Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas.Plasma waves and their associated instabilities (e.g., the Buneman instability,other two-streaming instability, and the Weibel instability) created in theshocks are responsible for particle (electron, positron, and ion) acceleration.The simulation results show that the Weibel instability is responsible forgenerating and amplifying highly nonuniform, small-scale magnetic fields. Thesemagnetic fields contribute to the electron's transverse deflection behind thejet head. The ``jitter'' radiation from deflected electrons has differentproperties than synchrotron radiation which assumes a uniform magnetic field.This jitter radiation may be important to understanding the complex timeevolution and/or spectral structure in gamma-ray bursts, relativistic jets, andsupernova remnants.

Particle Acceleration, Magnetic Field Generation, and Associated Emission in Collisionless Relativistic Jets