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Relativistic particle acceleration in collisionless shocks of supernovaremnants is accompanied by magnetic field amplification from cosmic ray (CR)driven plasma instabilities. Bell's fast CR-current instability is predicted toproduce turbulence with a non-zero mean electric field in the shock precursor.We present a Monte Carlo model of Fermi shock acceleration explicitly takinginto account an effective mean upstream electric field. Our model is nonlinearand includes the backreaction effects of efficient Fermi acceleration on theshock structure.

Monte Carlo modelling of particle acceleration in collisionless shocks with an effective mean electric field