Radiation from many astrophysical sources, e.g. gamma-ray bursts and active galactic nuclei, is believed to arise from relativistically shocked collisionless plasmas. Such sources often exhibit highly transient spectra evolving rapidly, compared with source lifetimes. Radiation emitted from these sources is typically associated with non-linear plasma physics, complex field topologies and non-thermal particle distributions. In such circumstances a standard synchrotron paradigm may fail to produce accurate conclusions regarding the underlying physics. Simulating spectral emission and spectral evolution numerically in various relativistic shock scenarios is then the only viable method to determine the detailed physical origin of the emitted spectra. In this Letter we present synthetic radiation spectra representing the early stage development of the filamentation (streaming) instability of an initially unmagnetized plasma, which is relevant for both collisionless shock formation and reconnection dynamics in relativistic astrophysical outflows, as well as for laboratory astrophysics experiments. Results were obtained using a highly efficient in situ diagnostics method, based on detailed particle-in-cell modeling of collisionless plasmas. The synthetic spectra obtained here are compared with those predicted by a semi-analytical model for jitter radiation from the filamentation instability, the latter including self-consistent generated field topologies and particle distributions obtained from the simulations reported upon here. Spectra exhibit dependence on the presence - or absence - of an inert plasma constituent, when comparing baryonic plasmas (i.e. containing protons) with pair plasmas. The results also illustrate that considerable care should be taken when using lower-dimensional models to obtain information about the astrophysical phenomena generating observed spectra.
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