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  • Letter
  • Open Access

Online optimization of nonlinear lattice using a data-driven chaos indicator

Minghao Song and Yongjun Li*

  • *Contact author: yli@bnl.gov
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Phys. Rev. Accel. Beams 29, L081601 – Published 12 August, 2026

DOI: https://doi.org/10.1103/4ywh-g2cq

Abstract

We report the experimental implementation of a data-driven chaos indicator (DDCI) [Y. Li et al., Data-driven chaos indicator for nonlinear dynamics and applications on storage ring lattice design, Nucl. Instrum. Methods Phys. Res. A 1024, 166060 (2022)] for online optimization of the National Synchrotron Light Source II storage ring. The DDCI quantifies the predictability of electron beam dynamics using turn-by-turn beam position monitor data. A surrogate model of the one-turn map is first trained, and its out-of-sample predictive uncertainty is then employed as a measurable indicator of chaos. By tuning sextupole magnets to mitigate nonlinear effects, a clear enlargement of the dynamic aperture is achieved, accompanied by a corresponding improvement in injection efficiency.

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References (18)

  1. S. Habib and R. D. Ryne, Symplectic calculation of Lyapunov exponents, Phys. Rev. Lett 74, 70 (1995).
  2. F. Schmidt, F. Willeke, and F. Zimmermann, Comparison of methods to determine long-term stability in proton storage rings, Part. Accel. 35, 249 (1991).
  3. W. Fischer, An Experimental Study on the Long-Term Stability of Particle Motion in Hadron Storage Rings, Ph.D. thesis, DESY, 1995.
  4. Y. Li, Y. Hao, K. Hwang, R. Rainer, A. He, and A. Liu, Fast dynamic aperture optimization with forward-reversal integration, Nucl. Instrum. Methods Phys. Res., Sect. A 988, 164936 (2021).
  5. F. Panichi, K. Goździewski, and G. Turchetti, The reversibility error method (REM): A new, dynamical fast indicator for planetary dynamics, Mon. Not. R. Astron. Soc. 468, 469 (2017).
  6. C. Skokos, Alignment indices: A new, simple method for chaos detection, J. Phys. A:Math. Gen. 34, 10029 (2001).
  7. J. Qiang, J. Wan, A. Qiang, and Y. Hao, Fast chaos indicator from auto-differentiation for dynamic aperture optimization, Nucl. Instrum. Methods Phys. Res., Sect. A 1087, 171427 (2026).
  8. Y. Li, J. Wan, A. Liu, Y. Jiao, and R. Rainer, Data-driven chaos indicator for nonlinear dynamics and applications on storage ring lattice design, Nucl. Instrum. Methods Phys. Res., Sect. A 1024, 166060 (2022).
  9. S. Sharma, L. Doom, A. Jain, P. Joshi, F. Lincoln, and V. Ravindranath, Optimization of magnet stability and alignment for NSLS-II, in Proceedings of the 2011 Particle Accelerator Conference (PAC’11) (JACoW Publishing, Geneva, Switzerland, 2011), pp. 2082–2086.
  10. W. X. Cheng, K. Ha, J. Mead, B. Podobedov, O. Singh, Y. Tian, and L. Yu, Characterization of NSLS-II storage ring beam orbit stability, in Proceedings of the 4th International Beam Instrumentation Conference (IBIC2015) (JACoW, Melbourne, Australia, 2015), pp. 625–629.
  11. S. Dierker, NSLS-II Preliminary Design Report (Upton, New York, USA, 2007).
  12. Y. Li, K. Ha, D. Padrazo, B. Kosciuk, B. Bacha, M. Seegitz, R. Rainer, J. Mead, X. Yang, Y. Tian, R. Todd, V. Smaluk, and W. Cheng, Dedicated beam position monitor pair for model-independent lattice characterization at NSLS-II, Nucl. Instrum. Methods Phys. Res., Sect. A 1065, 169557 (2024).
  13. W. Cheng, B. Bacha, and O. Singh, NSLS2 beam position monitor calibration, in Proceedings of the 15-th Beam Instrumentation Workshop (JACoW Publishing, Geneva, Switzerland, 2012).
  14. C. Williams and C. Rasmussen, Gaussian Processes for Machine Learning (MIT Press, Cambridge, MA, 2006), Vol. 2.
  15. R. Roussel et al., Bayesian optimization algorithms for accelerator physics, Phys. Rev. Accel. Beams 27, 084801 (2024).
  16. X. Huang, Beam-Based Correction and Optimization for Accelerators (CRC Press, Boca Raton, Florida, USA, 2019).
  17. Z. Zhang, M. Song, and X. Huang, Online accelerator optimization with a machine learning-based stochastic algorithm, Mach. Learn.: Sci. Technol. 2, 015014 (2020).
  18. Y. Li, K. Anderson, D. Xu, Y. Hao, K. Ha, Y. Hidaka, M. Song, R. Rainer, V. Smaluk, and T. Shaftan, Online regularization of Poincaré map of storage rings with Shannon entropy, Phys. Rev. Accel. Beams 28, 034001 (2025).

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Phys. Rev. Accel. Beams 29, L081601– Published 12 August, 2026
  • Received 26 April 2026
  • Accepted 20 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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