Energy extraction efficiency of a free electron laser (FEL) can be greatly increased using a tapered undulator and self-seeding. However, the extraction rate is limited by various effects that eventually lead to saturation of the peak intensity and power. To better understand these effects, we develop a model extending the Kroll-Morton-Rosenbluth, one-dimensional theory to include the physics of diffraction, optical guiding, and radially resolved particle trapping. The predictions of the model agree well with that of the GENESIS single-frequency numerical simulations. In particular, we discuss the evolution of the electron-radiation interaction along the tapered undulator and show that the decreasing of refractive guiding is the major cause of the efficiency reduction, particle detrapping, and then saturation of the radiation power. With this understanding, we develop a multidimensional optimization scheme based on GENESIS simulations to increase the energy extraction efficiency via an improved taper profile and variation in electron beam radius. We present optimization results for hard x-ray tapered FELs, and the dependence of the maximum extractable radiation power on various parameters of the initial electron beam, radiation field, and the undulator system. We also study the effect of the sideband growth in a tapered FEL. Such growth induces increased particle detrapping and thus decreased refractive guiding that together strongly limit the overall energy extraction efficiency.

Details of the High Energy Photon Source (HEPS), a 6 GeV green-field diffraction-limited storage ring light source to be built in China, are presented.