Radiation by an electron in an electromagnetic plane wave: The quasiclassical formula and other domains of applications

International audienceThe semiclassical Baïer-Katkov (BK) formula is an approximation to the spectrum of the radiation by an ultrarelativistic electron in a nonuniform field, taking into account the recoil and spin effects. The question why it involves only the initial electron trajectory is addressed. When the field is an electromagnetic plane wave, the exact helicity amplitudes in the null-plane frame are derived using Volkov solutions of the Dirac equation and a modified form of the BK formula is obtained. In passing, the application to Compton scattering is outlined and interesting spin properties are noted. For a general field, two conditions of validity of the BK formula are proposed: (1) the field is approximately uniform in the transverse directions, (2) the relative velocity between the field and the electron is close to c. The applications to bremsstrahlung, coherent bremsstrahlung and channeling radiation are discussed