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Small-scale turbulent dynamo is responsible for the amplification of magneticfields on scales smaller than the driving scale of turbulence in diverseastrophysical media. Most earlier dynamo theories concern the kinematic regimeand small-scale magnetic field amplification. Here we review our recentprogress in developing the theories for the nonlinear dynamo and the dynamoregime in a partially ionized plasma. The importance of reconnection diffusionof magnetic fields is identified for both the nonlinear dynamo and magneticfield amplification during gravitational contraction. For the dynamo in apartially ionized plasma, the coupling state between neutrals and ions and theion-neutral collisional damping can significantly affect the dynamo behaviorand the resulting magnetic field structure. We present both our analyticalpredictions and numerical tests with a two-fluid dynamo simulation on thedynamo features in this regime. In addition, to illustrate the astrophysicalimplications, we discuss several examples for the applications of the dynamotheory to studying magnetic field evolution in both preshock and postshockregions of supernova remnants, in weakly magnetized molecular clouds, duringthe (primordial) star formation, and during the first galaxy formation.

Small-scale turbulent dynamo in astrophysical environments: nonlinear dynamo and dynamo in a partially ionized plasma