Magnetic energy spectrum produced by turbulent dynamo: effect of time
  irreversibility
  We consider the kinematic stage of evolution of magnetic field advected by
turbulent hydrodynamic flow. We use a generalization of the Kazantsev-Kraichnan
model to investigate time irreversible flows. In the viscous range of scales,
the infinite-time limit of the spectrum is a power law but its slope is more
flat than that predicted by Kazantsev model. This result agrees with numerical
simulations. The rate of magnetic energy growth is slower than that in the
time-symmetric case. We show that for high magnetic Prandtl turbulent plasma,
the formation of the power-law spectrum shape takes very long time and may
never happen because of the nonlinearity. We propose another ansatz to describe
the spectrum shape at finite time.
