  The energy dependence of the local ${\cal P}$ and ${\cal CP}$ violation in
Au+Au and Cu+Cu collisions in a large energy range is estimated within a simple
phenomenological model. It is expected that at LHC the Chiral Magnetic effect
(CME) will be about 20 times weaker than at RHIC. In the lower energy range
this effect should vanish sharply at energy somewhere above the top SPS one. To
elucidate CME background effects a transport model including magnetic field
evolution is put forward.
