Modelling for metrological analysis of an X-ray diffractometer for bent crystals characterization in crystal-assisted collimation

Higher energy beam demanded by future circular collider and scheduled upgrades for Large Hadron Collider at CERN, set several challenges for the cleaning performances of the actual collimation system. One of the mainly components of the UA9 experiment, since 2009, is framework of crystal- assisted collimation, where bent crystal are used to deflect halo particle away from the beam core, aiming to improve cleaning performances. This thesis concerns the study and design of a double-crystal X-ray diffractometer considering a suitable geometry able to cut the $k_{α2}$ peak present in the X-ray source. Characterization for bent crystal must be performed in terms of bending, miscut and torsion angles with a target uncertainty of few microradians, since deeply understanding of the crystal shape is crucial not only for its positioning through goniometer in LHC accelerator, but also to check his quality to be part of the collimation system and for a better interpretation of the observables. In the first part the anticlastic deformations for anisotropic material and the X-ray diffraction theory are applied to silicon strip crystals for crystallographic planes and the wavelength of interest. Results are used to develop finite element models simulating the curvature imparted to the crystal by its holder and the double-crystal diffractometer. The scan algorithms, on which the measurement procedure is based, is totally reproduced and the resulting rocking curves on the X-ray detector are analyzed to obtain the desired angles, as well as in the experimental procedure. Models are fully scalable and can be adapted to different working conditions or crystal factor form. Afterwards the layout of the diffractometer is presented: requirements for parasitics angles along the travel range are too stringent to rely on the accuracy of mechanical stages and an autocollimator is considered to measure the real crystal orientation for each scanning point. The cornerstone for crystal motion is a high-accuracy hexapod robot: yaw and roll angles are measured by means of an autocollimator during its motion. A complete characterization for backlash and trajectories described are presented, together with the improvements obtained for both aspects. Finally an extended metrological analysis is carried out, highlighting main uncertainty sources arising from unavoidable misalignments and mechanical imperfections, pointing out the aspects to keep under control during measurement.