Analytical theory of short-pulse free-electron laser oscillators

A simple model for the nonlinear evolution of a short-pulse free-electron laser oscillator in the small gain regime is derived. An analysis of the linearized system allows the definition and calculation of the eigenmodes characterizing the small signal regime. An arbitrary solution of the nonlinear system can then be expanded in terms of these supermodes. In the single-supermode approximation, the system reduces to a Landau-Ginzburg equation, which allows the efficiency and saturated power to be obtained as functions of cavity detuning and cavity losses. In the limit of small cavity detuning, electrons emit superradiantly, with an efficiency inversely proportional to the number of radiation wavelengths within the optical pulse, and power proportional to the square of the bunch charge. In the multisupermode regime, limit cycles and period doubling behavior are observed and interpreted as a competition between supermodes. Finally, the analytical and numerical results are compared with the experimental observations from the Free-Electron Laser for Infrared eXperiments experiment.