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Plasma outflows from gamma-ray bursts, supernovae, and relativistic jets, ingeneral, interact with the surrounding medium through collisionless shocks. Themicrophysics of such shocks are still poorly understood, which, potentially,can introduce uncertainties in the interpretation of observations. It is nowwell established that the Weibel two-stream instability is capable ofgenerating strong electromagnetic fields in the transition region between thejet and the ambient plasma. However, the parameter space of collisionlessshocks is vast and still remains unexplored. In this Letter, we focus on how anambient magnetic field affects the evolution of the electron Weibel instabilityand the associated shock. Using a particle-in-cell code, we have performedthree-dimensional numerical experiments on such shocks. We compare simulationsin which a jet is injected into an unmagnetized plasma with simulations inwhich the jet is injected into a plasma with an ambient magnetic field bothparallel and perpendicular to the jet flow. We find that there exists athreshold of the magnetic field strength below which the Weibel two-streaminstability dominates, and we note that the interstellar medium magnetic fieldstrength lies well below this value. In the case of a strong magnetic fieldparallel to the jet, the Weibel instability is quenched. In the strongperpendicular case, ambient and jet electrons are strongly accelerated becauseof the charge separation between deflected jet electrons and less deflected jetions. Also, the electromagnetic topologies become highly non-linear and complexwith the appearance of anti-parallel field configurations.Comment: 4 pages with five figures. Accepted for publication in ApJ Letter

The Influence of an Ambient Magnetic Field on Relativistic collisionless Plasma Shocks