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Abstract
We review the theory of free-electron laser (FEL) oscillators operating with tapered undulators. We have considered the case of a uniform tapering and introduced a parameter which characterizes the effect of the tapering on the gain and the saturation intensity. We have analyzed the effect of the tapering on the FEL dynamics by including the pulse propagation effects. We further analyze the importance of tapering as a tool to model the optical pulse shapes and to control the higher harmonic intensities.
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