Magnetic field amplification by relativistic shocks in a turbulent medium

We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneities, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in our two-dimensional simulations. The magnetic energy spectrum is flatter than Kolmogorov and indicates that a so-called small-scale dynamo is operating in the postshock region. We also find that the amount of magnetic-field amplification depends on the direction of the mean preshock magnetic field.