Bayesian approach for linear optics correction

Li, Yongjun; Rainer, Robert; Cheng, Weixing

doi:10.1103/PhysRevAccelBeams.22.012804

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:: Li, Yongjun; Rainer, Robert; Cheng, Weixing

Publication Date:: Thu Jan 17 00:00:00 EST 2019

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1491224

Alternate Identifier(s):: OSTI ID: 1491697

Report Number(s):: BNL-210889-2019-JAAM
Journal ID: ISSN 2469-9888; PRABCJ; 012804

Grant/Contract Number:: SC0012704

Resource Type:: Published Article

Journal Name:: Physical Review Accelerators and Beams

Additional Journal Information:: Journal Name: Physical Review Accelerators and Beams Journal Volume: 22 Journal Issue: 1; Journal ID: ISSN 2469-9888

Publisher:: American Physical Society

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.

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                    Li, Yongjun, Rainer, Robert, & Cheng, Weixing. Bayesian approach for linear optics correction.  United States.  https://doi.org/10.1103/PhysRevAccelBeams.22.012804

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                    Li, Yongjun, Rainer, Robert, and Cheng, Weixing. Thu .  
"Bayesian approach for linear optics correction".  United States.  https://doi.org/10.1103/PhysRevAccelBeams.22.012804.

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@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},

  number       = 1,

  volume       = 22,

  place        = {United States},

  year         = {Thu Jan 17 00:00:00 EST 2019},

  month        = {Thu Jan 17 00:00:00 EST 2019}

}

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Cited by: 6 works

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Figures / Tables:

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 »

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Works referenced in this record:

Model-Independent Beam Dynamics Analysis
journal, February 1999

Irwin, J.; Wang, C. X.; Yan, Y. T.
Physical Review Letters, Vol. 82, Issue 8
DOI: 10.1103/PhysRevLett.82.1684

Application of independent component analysis to Fermilab Booster
journal, June 2005

Huang, Xiaobiao; Lee, S. Y.; Prebys, Eric
Physical Review Special Topics - Accelerators and Beams, Vol. 8, Issue 6
DOI: 10.1103/PhysRevSTAB.8.064001

Theory of the alternating-gradient synchrotron
journal, January 1958

Courant, E. D.; Snyder, H. S.
Annals of Physics, Vol. 3, Issue 1
DOI: 10.1016/0003-4916(58)90012-5

Theory of the Alternating-Gradient Synchrotron
journal, April 2000

Courant, E. D.; Snyder, H. S.
Annals of Physics, Vol. 281, Issue 1-2
DOI: 10.1006/aphy.2000.6012

Experimental determination of storage ring optics using orbit response measurements
journal, March 1997

Safranek, J.
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 388, Issue 1-2
DOI: 10.1016/S0168-9002(97)00309-4

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Effect of undulators on magnet lattice and emittance
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Smaluk, Victor; Li, Yongjun; Hidaka, Yoshiteru
Physical Review Accelerators and Beams, Vol. 22, Issue 12
DOI: 10.1103/physrevaccelbeams.22.124001

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Similar Records

Title: Bayesian approach for linear optics correction

Abstract

Citation Formats

Figures / Tables:

Model-Independent Beam Dynamics Analysis journal, February 1999

Application of independent component analysis to Fermilab Booster journal, June 2005

Theory of the alternating-gradient synchrotron journal, January 1958

Theory of the Alternating-Gradient Synchrotron journal, April 2000

Experimental determination of storage ring optics using orbit response measurements journal, March 1997

Effect of undulators on magnet lattice and emittance journal, December 2019

Model-Independent Beam Dynamics Analysis
journal, February 1999

Application of independent component analysis to Fermilab Booster
journal, June 2005

Theory of the alternating-gradient synchrotron
journal, January 1958

Theory of the Alternating-Gradient Synchrotron
journal, April 2000

Experimental determination of storage ring optics using orbit response measurements
journal, March 1997

Effect of undulators on magnet lattice and emittance
journal, December 2019