Magnetic field amplification by cosmic-ray-driven turbulence: I. isotropic CR diffusion

We have performed magnetohydrodynamical simulations to study the amplification of magnetic fields in the precursors of shock waves. Strong magnetic fields are required in the precursors of the strong shocks that occur in supernova remnants. Observations also suggest that magnetic field amplification takes place in the weak shocks that occur in galaxy clusters and that produce so-called radio relics. Here, we extend the study of magnetic field amplification by cosmic-ray driven turbulence to weak shocks. The amplification is driven by turbulence that is produced by the cosmic-ray pressure acting on the density inhomogeneities in the upstream fluid. The clumping that has been inferred from X-ray data for the outskirts of galaxy clusters could provide some of the seed inhomogeneities. Magnetic field power spectra and Faraday maps are produced. Furthermore, we investigate how the synchrotron emission in the shock precursor can be used to verify the existence of this instability and constrain essential plasma parameters.