  The growth and saturation of magnetic field in conducting turbulent media
with large magnetic Prandtl numbers are investigated. This regime is very
common in low-density hot astrophysical plasmas. During the early (kinematic)
stage, weak magnetic fluctuations grow exponentially and concentrate at the
resistive scale, which lies far below the hydrodynamic viscous scale. The
evolution becomes nonlinear when the magnetic energy is comparable to the
kinetic energy of the viscous-scale eddies. A physical picture of the ensuing
nonlinear evolution of the MHD dynamo is proposed. Phenomenological
considerations are supplemented with a simple Fokker--Planck model of the
nonlinear evolution of the magnetic-energy spectrum. It is found that, while
the shift of the bulk of the magnetic energy from the subviscous scales to the
velocity scales may be possible, it occurs very slowly -- at the resistive,
rather than dynamical, time scale (for galaxies, this means that generation of
large-scale magnetic fields cannot be explained by this mechanism). The role of
Alfvenic motions and the implications for the fully developed isotropic MHD
turbulence are discussed.
