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<p>This study systematically quantifies the surface figure error (SFE) of the first reflection mirror (M1) in SHINE’s FEL-I beamline via numerical calculations and experiments, analyzing contributions of thermal SFE (from X-ray heat loads) and non-thermal SFE (mechanical-related: clamping force, mirror self-gravity, In-Ga liquid gravity; manufacturing-induced). Results demonstrate that thermal SFE dominates at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ge \)</EquationSource> </InlineEquation>50 kHz (over 96% of total SFE); at <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\le \)</EquationSource> </InlineEquation>10 kHz, non-thermal SFE accounts for up to 38% (manufacturing-induced SFE leads in effective footprint zone, In-Ga liquid gravity impacts mechanical-related SFE more than other factors). This work clarifies thermal/non-thermal SFE dynamics across repetition rates, providing a basis for M1 optimization and high-repetition-rate XFEL mirror design.</p>

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Numerical and experimental investigation of surface figure error in high-repetition-rate XFEL mirrors

  • 期刊论文

  • 发表日期：

    2025年11月29日

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  • Zhen Wang,
  • Weizhen Lei,
  • Xiaohao Dong,
  • Yajun Tong

摘要

This study systematically quantifies the surface figure error (SFE) of the first reflection mirror (M1) in SHINE’s FEL-I beamline via numerical calculations and experiments, analyzing contributions of thermal SFE (from X-ray heat loads) and non-thermal SFE (mechanical-related: clamping force, mirror self-gravity, In-Ga liquid gravity; manufacturing-induced). Results demonstrate that thermal SFE dominates at \(\ge \) 50 kHz (over 96% of total SFE); at \(\le \) 10 kHz, non-thermal SFE accounts for up to 38% (manufacturing-induced SFE leads in effective footprint zone, In-Ga liquid gravity impacts mechanical-related SFE more than other factors). This work clarifies thermal/non-thermal SFE dynamics across repetition rates, providing a basis for M1 optimization and high-repetition-rate XFEL mirror design.