  We study the dynamical evolution of the so-called chiral magnetic effect in
an electromagnetic conductor. To this end, we consider the coupled set of
corresponding Maxwell and chiral anomaly equations, and we prove that these can
be derived from chiral kinetic theory. After integrating the chiral anomaly
equation over space in a closed volume, it leads to a quantum conservation law
of the total helicity of the system. A change in the magnetic helicity density
comes together with a modification of the chiral fermion density. We study in
Fourier space the coupled set of anomalous equations and we obtain the
dynamical evolution of the magnetic fields, magnetic helicity density, and
chiral fermion imbalance. Depending on the initial conditions we observe how
the helicity might be transferred from the fermions to the magnetic fields, or
vice versa, and find that the rate of this transfer also depends on the scale
of wavelengths of the gauge fields in consideration. We then focus our
attention on the quark-gluon plasma phase, and analyze the dynamical evolution
of the chiral magnetic effect in a very simple toy model. We conclude that an
existing chiral fermion imbalance in peripheral heavy ion collisions would
affect the magnetic field dynamics, and consequently, the charge dependent
correlations measured in these experiments.
