The free-electron laser harmonic cascade

Free-electron laser (FEL) devices based on a sequence of amplifiers with a harmonic relation between the resonant frequencies of each section have been proposed to extend to shorter wavelengths the FEL operating range. Because of the practical limit on the tunability of undulator magnets, the e-beam energy still represents the main constraint on the shortest reachable wavelength of the cascade. In this paper, we propose a scheme where the undulators of the cascade are tuned at different, not-harmonic, fundamental frequencies having instead one of the higher order harmonics at a common frequency. A short and intense seed pulse in such a system creates a superradiant pulse which harmonically seeds the following undulator at the common multiple frequency. The microbunching at the higher harmonic in the second undulator is enhanced by the modulation of the previous undulator so that lasing at shorter wavelengths may be obtained with a relatively low-energy electron beam.