Design of an online spectrometer for the diagnosis of free-electron lasers

A self-amplified spontaneous emission free-electron laser (FEL) is under construction at the Shanghai Soft X-ray Free-Electron Facility. Therefore, it is necessary to develop a suitable diagnostic tool capable of resolving the natural emission band of each FEL pulse. Thus, an online spectrometer with a plane mirror and plane variable-line-spacing grating at grazing incidence to monitor each single FEL pulse during the propagation of FEL radiation has been designed and is presented in this work. The method of ray tracing is used for monitoring incident radiation in order to understand spectral characteristics, and SHADOW, an X-ray optics simulation tool, and SRW, an X-ray optics wavefront tool, are applied to study the resolving power and focusing properties of the grating. The designed resolving power is ∼3 × 10⁴ at 620 eV. Meanwhile, the effect of the actual slope error of mirrors on the ray-tracing results is also discussed. In order to provide further optimization for the choice of grating, a comparison of resolving powers between 2000 lines mm⁻¹ and 3000 lines mm⁻¹ gratings at different energies is analyzed in detail and radiation damage of mirrors as well as parameters such as the first-order diffraction angle β, the exit-arm length r₂, and the tilt angle θ between the focal plane and the diffraction arm are studied and optimized. This work has provided comprehensive designing methods and detailed data for the design of diagnostic spectrometers in soft X-ray FELs and will be favorable to the design of other similar instruments.