Area-preserving scheme for efficiency enhancement in single-pass tapered free electron lasers

Efficiency enhancement of a single-pass short-wavelength high-gain tapered free electron laser (FEL) has recently been intensively studied. The goal is to sustain the growth of radiation power in the post-saturation regime. Among the various schemes, the undulator tapering is considered an effective route to achieve higher power extraction efficiency. The tapering strategy can be of constant or varying resonant phase along the undulator axis. In this paper we propose an efficiency-enhancement scheme based on preservation of the longitudinal phase space area which ensures trapping of resonant particles in the ponderomotive bucket as long as possible along the undulator axis before significant particle depletion occurs. In the meanwhile such a scheme takes advantage of the increase of the radiation field amplitude to precipitate the particle deceleration process at the middle stage of undulator tapering. We analyze such an area-preserving scheme of undulator tapering by formulating the post-saturation FEL interaction in a one-dimensional (1-D) model via introduction of the particle trapping fraction. The output performance is evaluated through numerical iteration and confirmed with 1-D particle tracking simulations. The results show that the optimal power extraction efficiency based on the proposed scheme, together with a prebunched beam, can be greatly improved within relatively short taper length compared with other schemes before radiation diffraction effect becomes significant Besides, the undesired sideband effects are found to be effectively suppressed. For the proposed area-preserving taper scheme, we also derive an analytical approximate formula for the resonant phase as a function of undulator axis. We expect that the analysis can shed light on the aim to further enhance the power extraction efficiency in single-pass tapered FELs.11Nscopu