Analysis of the X-ray free-electron laser parameter and determination of the optimal electron energy and undulator

The approximate threshold electron energy, below which the free-electron energy (FEL) design would not be considered optimal in the sense that a slight increase of the beam energy would make the FEL much more efficient, to generate a given wavelength FEL for a given magnet undulator strength is estimated by analyzing the FEL parameter, ρ, with the help of the undulator resonance condition. This threshold energy is converted to the threshold value of the undulator parameter, K.