# 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:

- 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:
- 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},

number = 1,

volume = 22,

place = {United States},

year = {2019},

month = {1}

}

DOI: 10.1103/PhysRevAccelBeams.22.012804

#### Figures / Tables:

*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 »

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

##
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

##
Theory of the alternating-gradient synchrotron

journal, January 1958

- Courant, E. D.; Snyder, H. S.
- Annals of Physics, Vol. 3, Issue 1

##
Theory of the Alternating-Gradient Synchrotron

journal, April 2000

- Courant, E. D.; Snyder, H. S.
- Annals of Physics, Vol. 281, Issue 1-2

##
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

Figures / Tables found in this record:

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