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

Relativistic particle acceleration in collisionless shocks of supernova remnants is accompanied with magnetic field amplification by cosmic ray (CR) driven plasma instabilities. Bell’s fast CR-current instability is predicted to produce turbulence with a non-zero mean electric field in the shock precursor. We present a Monte Carlo model of Fermi shock acceleration explicitly taking into account an effective mean upstream electric field. Our model is nonlinear and includes the backreaction effects of efficient Fermi acceleration on the shock structure.