Anomaly-driven inverse cascade and inhomogeneities in a magnetized
  chiral plasma in the early Universe
  By making use of a simple model that captures the key features of the
anomalous Maxwell equations, we study the role of inhomogeneities on the
evolution of magnetic fields in a chiral plasma. We find that inhomogeneities
of the chiral asymmetry by themselves do not prevent the anomaly-driven inverse
cascade and, as in the homogeneous case, the magnetic helicity is transferred
from shorter to longer wavelength helical modes of the magnetic field. However,
we also find that the evolution appears to be sensitive to the effects of
diffusion. In the case when diffusion is negligible, the inverse cascade slows
down considerably compared to the homogeneous scenario. In the case of the
primordial plasma, though, we find that the diffusion is substantial and
efficiently suppresses chiral asymmetry inhomogeneities. As a result, the
inverse cascade proceeds practically in the same way as in the chirally
homogeneous model.
