The Nonlinear Turbulent Dynamo

We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers. The field grows exponentially with the Kulsrud-Anderson $k^{3/2}$ spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity. Further growth proceeds more slowly until a saturated state is reached where the magnetic and kinetic energies are equal, and where the magnetic energy exists primarily at the resistive scale. We discuss the structure of this turbulence and the extrapolation of the results to astrophysically-large Prandtl numbers.