Simulation of relativistic shocks and associated radiation from turbulent magnetic fields

Recent PIC simulations of relativistic electron-positron (electron-ion) jets injected into a stationary medium show that particle acceleration occurs in the shocked regions. Simulations show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields and for particle acceleration. These magnetic fields contribute to the electron's transverse deflection behind the shock. The ``jitter'' radiation from deflected electrons in turbulent magnetic fields has different properties from synchrotron radiation calculated in a uniform magnetic field. This jitter radiation may be important for understanding the complex time evolution and/or spectral structure of gamma-ray bursts, relativistic jets in general, and supernova remnants. In order to calculate radiation from first principles and go beyond the standard synchrotron model, we have used PIC simulations. We will present detailed spectra for conditions relevant to various astrophysical sites of collisionless shock formation. In particular we will discuss application to GRBs and SNRs.