Beam-energy and system-size dependence of the CME

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.