Bayesian approach for linear optics correction
Abstract
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 selfconsistent 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). As a result, a necessary condition of being distinguishable is that their optics response vectors seen at these specific BPMs should be near orthogonal.
 Authors:

 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1491224
 Alternate Identifier(s):
 OSTI ID: 1491697
 Report Number(s):
 BNL2108892019JAAM
Journal ID: ISSN 24699888; PRABCJ
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Journal Article: Published Article
 Journal Name:
 Physical Review Accelerators and Beams
 Additional Journal Information:
 Journal Volume: 22; Journal Issue: 1; Journal ID: ISSN 24699888
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 43 PARTICLE ACCELERATORS
Citation Formats
Li, Yongjun, Rainer, Robert, and Cheng, Weixing. Bayesian approach for linear optics correction. United States: N. p., 2019.
Web. doi:10.1103/PhysRevAccelBeams.22.012804.
Li, Yongjun, Rainer, Robert, & Cheng, Weixing. Bayesian approach for linear optics correction. United States. doi:10.1103/PhysRevAccelBeams.22.012804.
Li, Yongjun, Rainer, Robert, and Cheng, Weixing. Thu .
"Bayesian approach for linear optics correction". United States. doi:10.1103/PhysRevAccelBeams.22.012804.
@article{osti_1491224,
title = {Bayesian approach for linear optics correction},
author = {Li, Yongjun and Rainer, Robert and Cheng, Weixing},
abstractNote = {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 selfconsistent 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). As a result, a necessary condition of being distinguishable is that their optics response vectors seen at these specific BPMs should be near orthogonal.},
doi = {10.1103/PhysRevAccelBeams.22.012804},
journal = {Physical Review Accelerators and Beams},
issn = {24699888},
number = 1,
volume = 22,
place = {United States},
year = {2019},
month = {1}
}
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