Small-scale turbulent dynamo in astrophysical environments: nonlinear
  dynamo and dynamo in a partially ionized plasma
  Small-scale turbulent dynamo is responsible for the amplification of magnetic
fields on scales smaller than the driving scale of turbulence in diverse
astrophysical media. Most earlier dynamo theories concern the kinematic regime
and small-scale magnetic field amplification. Here we review our recent
progress in developing the theories for the nonlinear dynamo and the dynamo
regime in a partially ionized plasma. The importance of reconnection diffusion
of magnetic fields is identified for both the nonlinear dynamo and magnetic
field amplification during gravitational contraction. For the dynamo in a
partially ionized plasma, the coupling state between neutrals and ions and the
ion-neutral collisional damping can significantly affect the dynamo behavior
and the resulting magnetic field structure. We present both our analytical
predictions and numerical tests with a two-fluid dynamo simulation on the
dynamo features in this regime. In addition, to illustrate the astrophysical
implications, we discuss several examples for the applications of the dynamo
theory to studying magnetic field evolution in both preshock and postshock
regions of supernova remnants, in weakly magnetized molecular clouds, during
the (primordial) star formation, and during the first galaxy formation.
