The development of a semi-analytical model, that can describe the saturation dynamics of free electron laser (FEL) oscillator devices is discussed. The model allows a straightforward inclusion of the inhomogeneous broadening effects on the optical-klystron (OK) FEL. It includes the effect of slippage and lethargy and can be exploited for both recirculated devices and single pass. The results show that the gain depends on the cavity length mismatch, slippage and bunch length.
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