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.
