Abstract
Free Electron Laser(FEL) oscillator is the main working mode to produce infrared and THz wavelength range radiation. At FEL saturation state, the interaction between electron beams and radiation becomes nonlinear. Saturation power can be solved by numerical simulation of macro particle motion in longitudinal phase space or by semi-analytical formulae analogous to conventional laser system from previous study. While in this paper, the motions of macro-particle are depicted with analytical formulae in the assumption that energy transfer is mainly from captured electrons of ponderomotive bucket. Then corresponding electron beam extraction efficiency can be achieved due to initial and final state of electron beams. Therefore laser power is confirmed through equilibrium situation inside resonator cavity. These simple analytical formulae can be used to optimize output laser power and offer a better understanding in FEL oscillator saturation. Taking small signal gain regime as an example, the optimum FEL efficiency is obtained at gain to loss ratio around 4.1. This agrees well with the results of three-dimension simulation.
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