Fel Oscillators with Tapered Undulators: Inclusion of Harmonic Generation and Pulse Propagation

We review the theory of FEL oscillators operating with tapered undulators. We consider the case of a uniform tapering and introduce a parameter which characterizes the effect of the tapering on the gain and on the saturation intensity. We analyze the effect of the tapering on the FEL dynamics by including the pulse propagation effects too. We analyze the importance of tapering as a tool to model the optical pulse shapes and to control the higher harmonic intensities.