Effective narrowing of the spectral distribution at multiple passage of photons through a free electron laser (FEL)

The system of nonlinear equations describing nonlinear phase oscillations in free electron lasers (FEL) is applied to solve two problems. First, the action of an FEL in the linear regime when the incident electron beam is a nonmonoenergetic one is considered. Then, the kinetics of building up a photon bunch during its repeated passages through an optical cavity is treated. It is shown that the spectral density at the center of the radiation line is effectively increased if the gain of an FEL is on the order of unity and when the signal repeatedly passes through an optical cavity because of the nonlinear interaction between harmonics.