  As a consequence of the chiral anomaly, the hydrodynamics of hot QCD matter
coupled to QED allows for a long-wavelength mode of chiral charge density, the
chiral magnetic wave (CMW), that provides for a mechanism of electric charge
separation along the direction of an external magnetic field. Here, we
investigate the efficiency of this mechanism for values of the time-dependent
magnetic field and of the energy density attained in the hot QCD matter of
ultra-relativistic heavy ion collisions. To this end, we derive the CMW
equations of motion for expanding systems by treating the CMW as a charge
perturbation on top of an expanding Bjorken-type background field in the limit
of small chemical potential. Both, approximate analytical and full numerical
solutions to these equations of motion indicate that for the lifetime and
thermodynamic conditions of ultra-relativistic heavy ion collisions, the
efficiency of CMW-induced electric charge separation decreases with increasing
center of mass energy and that the effect is numerically very small. We note,
however, that if sizable oriented asymmetries in the axial charge distribution
(that are not induced by the CMW) are present in the early fluid dynamic
evolution, then the mechanism of CMW-induced electric charge separation can be
much more efficient.
