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Magnetic field amplification is needed to accelerate cosmic cays to PeVenergies in supernova remants. Escaping cosmic rays trigger a return current inthe plasma that drives a non-resonant hybrid instability. We run simulations inwhich we represent the escaping cosmic rays with the plasma return current,keeping the maximum cosmic ray energy fixed, and evaluate its effects on theupstream medium. In addition to magnetic field amplification, densityperturbations arise that, when passing through the shock, further increaseamplification levels downstream. As the growth rate of the instability is mostrapid for the smaller scales, the resolution is a limiting factor in theamplification that can be reached with these simulations.

Magnetic field amplification by cosmic rays in supernova remnants