  The prevailing theory for the origin of cosmic magnetic fields is that they
have been amplified to their present values by the turbulent dynamo inductive
action in the protogalactic and galactic medium. Up to now, in calculation of
the turbulent dynamo, it has been customary to assume that there is no back
reaction of the magnetic field on the turbulence, as long as the magnetic
energy is less than the turbulent kinetic energy. This assumption leads to the
kinematic dynamo theory. However, the applicability of this theory to
protogalaxies is rather limited. The reason is that in protogalaxies the
temperature is very high, and the viscosity is dominated by magnetized ions. As
the magnetic field strength grows in time, the ion cyclotron time becomes
shorter than the ion collision time, and the plasma becomes strongly
magnetized. As a result, the ion viscosity becomes the Braginskii viscosity.
Thus, in protogalaxies the back reaction sets in much earlier, at field
strengths much lower than those which correspond to field-turbulence energy
equipartition, and the turbulent dynamo becomes what we call the magnetized
turbulent dynamo. In this paper we lay the theoretical groundwork for the
magnetized turbulent dynamo. In particular, we predict that the magnetic energy
growth rate in the magnetized dynamo theory is up to ten time larger than that
in the kinematic dynamo theory. We also briefly discuss how the Braginskii
viscosity can aid the development of the inverse cascade of magnetic energy
after the energy equipartition is reached.
