Radiation Emission by Extreme Relativistic Electrons and Pair Production by Hard Photons in a Strong Plasma Wakefield

Radiation spectrum of extreme relativistic electrons and a 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 that the radiation losses of the relativistic electron in the plasma wakefield scale as $ \propto \epsilon ^{2 / 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 energy of the electrons