Enhancement of Coherent Emission by Energy-Phase Correlation in a Bunched Electron Beam

A radio-frequency (rf) modulated electron beam passing through a magnetic undulator emits coherent radiation at harmonics of the rf with a phase which depends on the electron drift velocity. Treating the bunches as ensembles of electrons, each with its energy and phase, the radiated field is calculated as a sum over the particle distribution in the phase space. At long wavelengths a proper correlation between the energy and phase distributions of the electrons in the bunch can be exploited to lock the radiated field in phase, resulting in a significant enhancement of the coherent emission.