Quantum effects in radiation on short bunches

The radiation caused by particles of one bunch in the collective electromagnetic field of the short oncoming bunch is studied. Quantum effects are calculated for the spectrum of radiated photons. Using this spectrum, the dependence of the relative energy loss δ on a quantum parameter κ is dicussed. It is shown that the behaviour of δ changes considerably with the increase of that parameter. In the classical regime ( κ ≪ 1) the energy loss is proportional to the incoming particle energy, while in the extreme quantum regime ( κ ≫ 1) the energy loss becomes a constant. The coherent e + e − pair production for γe colliders as cross-channel to CBS is considered.