Li, Y.
Cheng, W.X.
Rainer, R.S.
Bayesian Approach for Linear Optics Correction
JACoW Publishing
Geneva, Switzerland
978-3-95450-208-0
10.18429/JACoW-IPAC2019-MOPGW114
English
390-392
MOPGW114
quadrupole
optics
lattice
GUI
distributed
Contribution to a conference proceedings
2019
2019-06
https://doi.org/10.18429/JACoW-IPAC2019-MOPGW114
http://jacow.org/ipac2019/papers/mopgw114.pdf
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. In modern ring-based accelerators, optics corrections are determined from repetitive measurements which help identify systematic and random quadrupole errors in presence of various measurement noises. This process is a multivariate nonlinear regression problem driven by either a completed lattice model or a Jacobian matrix. Starting from the Bayes’ theorem, ’likelihood functions’ and ’prior probability’ distributions are extracted from a complete linear optics model. Under some assumptions, the least square algorithm and then the Jacobian matrix approach can be re-derived. 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 BPMs. A necessary condition of being distinguishable is that their optics response vectors seen at these specific BPMs should be near-orthogonal.