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Magnetic field amplification by cosmic rays in supernova remnants

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