Studies of self-design taper algorithms for free-electron lasers with planar and helical undulators

The article presents a numerical study of self-design taper algorithms for free-electron lasers (FELs) with planar and helical undulators. Tapering is a technique that changes the undulator parameters in order to increase the efficiency and the radiation power in FELs. Undulator tapering is one of the methods for designing multi-terawatt X-ray FELs (XFELs), which are necessary for research in the field of non-linear optics and 3D bioimaging. In this article, we study methods to optimize the taper profile K(z) that can enhance the efficiency of extracting energy from the electron beam in FELs with planar and helical undulators. Using the numerical code we apply the Kroll-Morton-Rosenbluth (KMR) model and its modification to a case of the FEL at the MAX IV Laboratory, as well as a case of the European XFEL, compare our results with previous ones and discuss the new results. The program was validated on the PAL-XFEL experiment. The application of the modified KMR method for FELs with helical undulators is also studied.