Magnetic field amplification in turbulent astrophysical plasmas
  Magnetic fields play an important role in astrophysical accretion discs, and
in the interstellar and intergalactic medium. They drive jets, suppress
fragmentation in star-forming clouds and can have a significant impact on the
accretion rate of stars. However, the exact amplification mechanisms of cosmic
magnetic fields remain relatively poorly understood. Here I start by reviewing
recent advances in the numerical and theoretical modelling of the 'turbulent
dynamo', which may explain the origin of galactic and inter-galactic magnetic
fields. While dynamo action was previously investigated in great detail for
incompressible plasmas, I here place particular emphasis on highly compressible
astrophysical plasmas, which are characterised by strong density fluctuations
and shocks, such as the interstellar medium. I find that dynamo action works
not only in subsonic plasmas, but also in highly supersonic, compressible
plasmas, as well as for low and high magnetic Prandtl numbers. I further
present new numerical simulations from which I determine the growth of the
turbulent (un-ordered) magnetic field component ($B_\mathrm{turb}$) in the
presence of weak and strong guide fields ($B_0$). I vary $B_0$ over 5 orders of
magnitude and find that the dependence of $B_\mathrm{turb}$ on $B_0$ is
relatively weak, and can be explained with a simple theoretical model in which
the turbulence provides the energy to amplify $B_\mathrm{turb}$. Finally, I
discuss some important implications of magnetic fields for the structure of
accretion discs, the launching of jets, and the star formation rate of
interstellar clouds.
