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Title: 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 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). 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:
 [1];  [1];  [1]
  1. 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) (SC-22)
OSTI Identifier:
1491224
Alternate Identifier(s):
OSTI ID: 1491697
Report Number(s):
BNL-210889-2019-JAAM
Journal ID: ISSN 2469-9888; 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 2469-9888
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 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). 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 = {2469-9888},
number = 1,
volume = 22,
place = {United States},
year = {2019},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevAccelBeams.22.012804

Figures / Tables:

FIG. 1 FIG. 1: Statistic illustration of the horizontal β-beat due to the random quadrupole errors. This linear correlation with gradually increasing variance are calculated with the NSLSII ring lattice model in advance. Once an averaged β-beat is measured, its corresponding variance of quadrupole error distribution can be used as the priormore » probability to prevent overfitting« less

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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.