Multi-segment cooling design of a reflection mirror based on the finite-element method

High-repetition-rate free-electron lasers impose stringent requirements on thermal deformations of optics in the beamline. The Shanghai HIgh-repetition-rate XFEL aNd Extreme light facility (SHINE) experiences high average thermal power and demands wavefront preservation. To effectively manage thermal deformation in the first reflection mirrors M1, we optimized the cooling length and position of the cooling groove with numerical calculations. For example, the root mean square of the height error of the thermal deformation of the mirror at a photon energy of 900 eV was optimized, resulting in a 12.7× reduction, from 13.76 nm to 1.08 nm. This optimized design also eliminated stray light in the focus spot at the sample and resulted in a 177% increase in the peak intensity of the beam's focus spot at the sample, from 3.08 × 10⁵ to 8.53 × 10⁵. The multi-segment cooling design of the mirror advanced the quality of the beam's focus spot at the sample and ensured the stable operation of SHINE under high repetition rates.