Using our new 3-D relativistic electromagnetic particle (REMP) code parallelized with MPI, we have investigated long-term particle acceleration associated with an relativistic electron-positron jet propagating in an unmagnetized ambient electron-positron plasma. The simulations have been performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. The acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value. Behind the bow shock in the jet shock strong electromagnetic fields are generated. These fields may lead to the afterglow emission. We have calculated the time evolution of the spectrum from two electrons propagating in a uniform parallel magnetic field to verify the technique.
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