Mirror Vibration Tolerance Studies in X-ray Free-Electron Laser Oscillator

The X-ray free-electron laser oscillator (XFELO) has received significant attention due to its ability to produce fully coherent, high-brightness, and highly stable X-ray beams. Despite these advantages, the operation of the XFELO can be impeded by the surrounding environment. Specifically, vibrations of the optical components within the cavity can lead to poor alignment, which can diminish the interaction between the light and electrons in the undulator. Consequently, the quality of the output X-rays may be compromised. This study aims to investigate the impact of mirror vibrations on the output laser at various vibration frequencies. Firstly, we develop three single-frequency vibration models at 10 Hz, 0.01 MHz, and 1.1 MHz to investigate the changes in energy, spectral width, beam size, and beam divergence angle of the output laser. Secondly, we build a more complex multi-frequency vibration model based on the single-frequency one to simulate the realistic vibration of the mirror. Finally, we utilize the multi-frequency vibration model to investigate the tolerance limits of the output laser to vibration amplitude at different vibration frequencies of the mirror. The results show that the tolerance of the amplitude near the low and middle frequencies has less effect on the output power, which is approximately 250 nrad or more. However, in certain particular instances, particularly in the vicinity of the resonant frequency, there will be deviations from the tolerance limit. These deviations can result in values that are excessively high or excessively low. The study could prove useful in the future installation of XFELOs.