Study of the nonlinear dynamics of the spectrum of a free-electron laser in the Compton regime

In this study, we investigate the spectral dynamics of a free-electron laser (FEL) in the Compton regime for continuous electron beams. In a first part, we develop a formalism including a spectral description of a FEL. Equations of this multifrequency formalism were solved in a numerical multifrequency simulation. In a second part, after validations of this simulation in various well-known regimes, systematic studies of the asymptotic spectral evolution were performed. In the last part a broadening phenomenon with obvious consequences in asymptotic behaviour, was proved in a low noise simulation. The non linear coupling analysis, by means of a perturbative development. allowed to point out the exact mechanism. This mechanism is largely responsible for the spectral broadening of a powerful FEL. (author)