Nanoradian angular stabilization of x-ray optical components

An x-ray free-electron laser oscillator (XFELO) has been recently proposed [K. Kim et al, Phys. Rev. Lett. 100, 244802 (2008)]. Angular orientation and position in space of Bragg mirrors of the XFELO optical cavity must be continuously adjusted to compensate for the instabilities and maximize the output intensity. An angular stability of about 10 nrad (rms) is required [K. Kim and Y. Shvyd’ko, Phys. Rev. ST Accel. Beams 12, 030703 (2009)]. To approach this goal, a feedback loop based on a null-detection principle was designed and used for stabilization of a high-energy-resolution x-ray monochromator (⁠$ΔE/E≃4×10−8$⁠, $E=23.7keV$⁠) and a high-heat-load monochromator. Angular stability of about 13 nrad (rms) has been demonstrated for x-ray optical elements of the monochromators.