Saturation of the Turbulent Dynamo
  The origin of strong magnetic fields in the Universe can be explained by
amplifying weak seed fields via turbulent motions on small spatial scales and
subsequently transporting the magnetic energy to larger scales. This process is
known as the turbulent dynamo and depends on the properties of turbulence, i.e.
on the hydrodynamical Reynolds number and the compressibility of the gas, and
on the magnetic diffusivity. While we know the growth rate the magnetic energy
in the linear regime, the saturation level, i.e. the ratio of magnetic energy
to turbulent kinetic energy that can be reached, is not known from analytical
calculations. In this paper we present the first scale-dependent saturation
model based on an effective turbulent resistivity which is determined by the
turnover timescale of turbulent eddies and the magnetic energy density. The
magnetic resistivity increases compared to the Spitzer value and the effective
scale on which the magnetic energy spectrum is at its maximum moves to larger
spatial scales. This process ends when the peak reaches a characteristic
wavenumber k* which is determined by the critical magnetic Reynolds number. The
saturation level of the dynamo also depends on the type of turbulence and
differs for the limits of large and small magnetic Prandtl numbers Pm. With our
model we find saturation levels between 43.8% and 1.3% for Pm>>1 and between
2.43% and 0.135% for Pm<<1, where the higher values refer to incompressible
turbulence and the lower ones to highly compressible turbulence.
