Application of probabilistic modelling for the uncertainty evaluation of alignment measurements of large accelerator magnets assemblies

Micrometric assembly and alignment requirements for future particle accelerators, and especially large assemblies, create the need for accurate uncertainty budgeting of alignment measurements. Measurements and uncertainties have to be accurately stated and traceable, to international standards, for metre long sized assemblies, in the range of tens of μm. Indeed, these hundreds of assemblies will be produced and measured by several suppliers around the world, and will need to be integrated into a single machine. As part of the PACMAN project at CERN, we proposed and studied a practical application of probabilistic modelling of task-specific alignment uncertainty by applying Simulation By Constraints (SBC) calibration method. Using this method, we calibrated our measurement model using available data from ISO standardised tests (10360 series) for the metrology equipment. We combined this model with reference measurements and analysis of the measured data to quantify the actual specific uncertainty of each alignment measurement procedure. Our methodology was successfully validated against a calibrated and traceable 3D artefact as part of an international inter-laboratory study. The validated models were used to study the expected alignment uncertainty and important sensitivity factors of measuring the shortest and longest of the Compact Linear Collider study assemblies, 0.54 m and 2.1 m respectively. In both cases, the laboratory alignment uncertainty was within the targeted uncertainty budget 12 μm (68% confidence level). It was found that the remaining uncertainty budget for any additional alignment error compensations, such as the thermal drift error caused due to variation in machine operation heat load conditions, need to be within 8.9 $\mu$m and 9.8 $\mu$m (68% confidence level) respectively.