ANALYTICAL THEORY OF SHORT-PULSE FREE-ELECTRON LASER-OSCILLATORS

A simple model for the nonlinear evolution of a short-pulse free-elect ron 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 soluti on of the nonlinear system can then be expanded in terms of these supe rmodes. In the single-supermode approximation, the system reduces to a Landau-Ginzburg equation, which allows the efficiency and saturated p ower 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 s quare of the bunch charge. In the multisupermode regime, limit cycles and period doubling behavior are observed and interpreted as a competi tion between supermodes. Finally, the analytical and numerical results are compared with the experimental observations from the Free-Electro n Laser for Infrared eXperiments experiment.