A Linear Framework for Orbit Correction in the High-Luminosity Large Hadron Collider

Abstract: In a circular accelerator the closed orbit can be viewed as the mean position of particles in a beam. The closed orbit is perturbed by machine errors and can be manipulated by dedicated corrector magnets. This thesis introduces a linear algebra framework for closed orbit perturbation and correction, its implementation as a Python package and its use for three studies in HL--LHC: orbit corrector budget, orbit feedback expected performance analysis and specifications for new beam position monitors. The orbit corrector budget is formulated as a convex optimization problem and solved for the current iteration of HL--LHC. Results based on a simplified model for the orbit feedback are presented, showcasing its inefficacy in maintaining collision on its own and the inherent stability in LHC. Necessary short-term beam position monitor stability for adequate position-based correction of beam separation is estimated to be under one micrometer. Finally, optimizing over linear correction strategies is offered as an interesting venue for further research.