Study of Water Cooling Design for a High Repetition Rate Grating Using FE-Methods

Managing thermal distortion in high heat load optics is crucial for the performance of high-repetition-rate free-electron lasers, including the Shanghai High-repetition-rate XFEL and the Extreme Light facility (SHINE). This paper presents an in-depth investigation of a water-cooling scheme, specifically designed to mitigate thermal deformation in high repetition rate gratings. The study encompasses a comprehensive analysis of the rise of the cooling water temperature, the inner wall temperature of the cooling tube, and the heat transfer coefficient at the fluid-solid interface. By examining the effects of cooling water flow velocity and cooling tube diameter on the grating's temperature and thermal deformation, an enhanced dual-channels cooling design for high-heat load gratings has been developed. The implementation of this optimized design in the FEL-II beamline, operating at a photon energy of 4 keV, has resulted in a significant reduction in maximum thermal deformation by 49.2\%, from 1.93 $\mu$m to 0.98 $\mu$m. The maximum temperature has been substantially lowered by a reduction factor of 31.8\%, from 67.3 $^\circ$C to 45.9 $^\circ$C. These improvements not only demonstrate the efficacy of the enhanced cooling design but also highlight its potential in ensuring the stability and performance of optical components under high-repetition-rate XFEL conditions of the facility SHINE.