Radiation from GRBs in the prompt phase, flares and an afterglow is thought to be produced by accelerated electrons in magnetic fields. Such emission may be produced at collisionless shocks of baryonic outflows or at reconnection sites (at least for the prompt and flares) of the magnetically dominated (Poynting flux driven) outflows, where no shocks presumably form at all. An astonishing recent discovery is that during reconnection strong small-scale magnetic fields are produced via the Weibel instability, very much like they are produced at relativistic shocks. The relevant physics has been successfully and extensively studied with the PIC simulations in 2D and, to some extent, in 3D for the past few years. We discuss how these simulations predict the existence of MeV-range synchrotron/jitter emission in some GRBs, which can be observed with Fermi. Recent results on modeling of the spectral variability and spectral correlations of the GRB prompt emission in the Weibel-jitter paradigm applicable to both baryonic and magnetic-dominated outflows is reviewed with the emphasis on observational predictions.
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