Analytical Description of Nonlinear Harmonic Generation Close to the Saturation Region in Free Electron Lasers

Abstract

The phenomenological modeling of nonlinear harmonic generation in single-pass free electron laser (FEL) experiments was performed. The gradual saturation of the harmonic power and its evolution around the saturated regime was modeled. The model includes all major losses for each harmonic with account for the fact that the undulator radiation (UR) and the electron-wave interaction at higher harmonic wavelengths are more sensitive to the beam energy spread, divergence, and other factors. The results of the phenomenological modeling are compared with the experimental data of the corresponding FELs and with the numerical simulation. The proposed description of nonlinear harmonic generation appears to be in good agreement with the FEL experiments SALCA, LEUTL, LCLS, and others under various conditions. The results also match their numerical simulations; in contrast to the latter, our phenomenological model allows rapid, still, and accurate modeling of the FEL harmonic power and bunching evolution with a PC or even an engineering calculator. The model permits studying FEL radiation from undulators with arbitrary magnetic field configuration. Using the analytical FEL model, we demonstrate that, in contrast to the helical undulator, in whose spectrum the fundamental and the second harmonics prevail, the FEL radiation from the elliptical undulator with the third field harmonic has a distinct fifth UR harmonic as well as the fundamental one, whereas other harmonics can be ignored even close to the saturation length.