Cryocooled Silicon Crystal Optics Performance Study for High-Repetition-Rate X-Ray Free Electron Lasers

The advent of high-repetition-rate X-ray Free Electron Lasers has introduced new challenges for cryogenically cooled silicon crystal optics due to the concurrent high average power and high peak power. This work explores the significant impact of thermal management on the performance of silicon crystals used in X-ray optics. The response of a Si(111) crystal is numerically examined over a parameter space of crystal temperature, pulse energy, repetition rate, and average power. We use the Strehl ratio as a benchmark for optical quality to assess temperature-induced wavefront degradation. The model-based results show that the optimal control temperature remains near the silicon zero-expansion temperature but varies with average power and repetition rate. Most notably, the optimal operational window narrows at lower repetition rates for the same average power. Zernike-mode analysis further shows that removing low-order thermoelastic deformation increases the allowable pulse energy and repetition rate limits. The results provide guidance for Si crystal optics operation conditions at LCLS-II-HE.