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

It is shown that the spectral density at the center of the radiation line is effectively increased if the gain of a FEL is on the order of unity and when the signal repeatedly passes through an optical cavity because of the nonlinear interaction between harmonics. The action of a FEL is studied for the case of a nonmonoenergetic electron beam.