Enhancing shape control for MHz-repetition-rate XFEL optics using target profile optimization

The ability to mitigate the thermal deformation in X-ray optics under high-repetition-rate free-electron lasers (FEL) is crucial for preserving the ultrahigh brightness and coherence of advanced light sources. However, existing active cooling solutions involve complex systems, time-consuming tests, and high cost, and often tend to be affected by piezoelectric drift or environmental disturbance. In this study, we propose an enhanced shape control method that employs variable cross-section shape correction blocks according to a target thermal profile, enabling sub-nanometer shape control accuracy adaptively even under MHz high-repetition-rate X-ray pulses or significantly varying beam sizes. Furthermore, we present a multi-optic and multi-objective strategy for thermal management in X-ray FEL beamline design, which has been demonstrated to achieve sub-nano accuracy of shape correction over a wide photon energy range, under heat power up to 1000 watts in high-repetition-rate XFELs. This method exhibits potential for generalization to applications beyond the thermal shape compensation, including precisely bent figure generation and gravitational deformation correction.