Bayesian approach for linear optics correction

• Main Authors: Yongjun Li, Robert Rainer, Weixing Cheng
• Format: Article
• Language: English
• Published: American Physical Society 2019-01-01
• Series: Physical Review Accelerators and Beams
• Online Access: http://doi.org/10.1103/PhysRevAccelBeams.22.012804

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes’ theorem, a complete linear optics model is simplified as “likelihood functions” and “prior probability distributions.” Under some assumptions, the least square algorithm and then the Jacobian matrix approach can be rederived. The coherence of the correction algorithm is ensured through specifying a self-consistent regularization coefficient to prevent overfitting. Optimal weights for different correction objectives are obtained based on their measurement noise level. A new technique has been developed to resolve degenerated quadrupole errors when observed at a few select beam position monitors (BPMs). A necessary condition of being distinguishable is that their optics response vectors seen at these specific BPMs should be near orthogonal.