Wavefront-preserved thermal-optical design of a high-heat-load grazing-incidence X-ray mirror

High-repetition-rate X-ray free-electron laser facilities impose stringent requirements on the thermal stability and wavefront preservation of beamline mirrors. In this work, a coupled thermal-optical optimization method is developed for the first reflective mirror of the FEL-III beamline at the SHINE facility under an absorbed heat load of up to 11.12 W at a photon energy of 15 keV and a repetition rate of 200 kHz, with a peak absorbed power density of 0.0718 W/mm². The cooling length and cooling-groove distance from the optical surface are jointly optimized, and their effects on residual height error, slope error, and focal-plane Strehl ratio are evaluated using thermal-structural analysis and X-ray tracing. The results show that the mirror performance is governed by the coupled cooling geometry rather than by either parameter alone. Compared with the initial full-length cooling design, the optimized design reduces the RMS residual height error by 73.7% and the RMS slope error by 68.9%. The system-level Strehl ratio increases from 0.45 to 0.993, exceeding the target value of 0.96, while stray-light features are suppressed and a compact focal intensity distribution is recovered at the sample plane. These results demonstrate that deformation-based thermal optimization, when combined with system-level X-ray tracing, provides an effective thermal-optical design route for preserving wavefront quality in high-heat-load grazing-incidence X-ray optical systems.