Radiation emission by extreme relativistic electrons and pair production by hard photons in a strong plasma wakefield

The radiation spectrum of extreme relativistic electrons and the probability of electron-positron pair production by energetic photons in a strong plasma wakefield are derived in the framework of a semiclassical approach. It is shown that the radiation losses of a relativistic electron in the plasma wakefield scale proportionally to epsilon2/3 in the quantum limit when the energy of the radiated photon becomes close to the electron energy epsilon . The quantum effects will play a key role in future plasma-based accelerators operating at ultrahigh electron energy.