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Orbit correction for a rapid cycling synchrotron using an adjacent-difference-constrained neural network

Hao Zhong1,2, Xiaohan Lu2,3,*, Wei Bao1,2, Yuwen An2,3, Yong Li2,3, Jianliang Chen2,3, Hanyang Liu2,3, Shouyan Xu2,3, Yuliang Zhang2,3 et al.

Mingyang Huang2,3, Yi Jiao2,†, and Sheng Wang2,3,‡

  • *Contact author: luxh@ihep.ac.cn
  • †Contact author: jiaoyi@ihep.ac.cn
  • ‡Contact author: wangs@ihep.ac.cn
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Phys. Rev. Accel. Beams 29, 104001 – Published 13 October, 2026

DOI: https://doi.org/10.1103/dpvk-3vt5

Abstract

In a rapid cycling synchrotron (RCS), closed-orbit correction is an important task for maintaining high beam quality and machine stability. Since the orbits in RCS change during energy ramping, response matrix-based orbit correction is performed in segments, which can result in the corrector current ramp rates exceeding safety limits and accuracy loss in orbits. To address these issues, this paper employs machine learning for orbit correction in RCS. An adjacent-difference-constrained neural network (ADCNN) was built and tested in both simulations and machine experiments at the China Spallation Neutron Source (CSNS). The correction results demonstrate the feasibility of using neural networks for RCS orbit correction. The ADCNN exhibits a correction effect equivalent to that of response matrix-based correction while effectively limiting the current ramp rates of the correctors.

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References (50)

  1. S. Wang, S. X. Fang, S. N. Fu et al., Introduction to the overall physics design of CSNS accelerators, Chin. Phys. C 33, 1 (2009).
  2. M.Y. Huang, S. Xu, Y. An et al., Study on the anti-correlated painting injection scheme for the rapid cycling synchrotron of the China spallation neutron source, Nucl. Instrum. Methods Phys. Res., Sect. A 1007, 165408 (2021).
  3. S. Y. Xu, Y. W. An, J. Chen et al., Achievement of 100-kW beam operation in CSNS/RCS, in Proceedings of the 12th International Particle Accelerator Conference (IPAC’21) (JACoW Publishing, Geneva, Switzerland, 2021), pp. 1869–1871.
  4. S. Xu, K. Zhou, J. Chen, M. Huang, and S. Wang, Commissioning and operation of the transverse collimation system at the RCS of CSNS, J. Instrum. 19, T03004 (2024).
  5. M.-Y. Huang, S. Xu, J. Chen, Y. Li, and S. Wang, Study on the H− stripping injection for the rapid cycling synchrotron of the China spallation neutron source, Radiat. Detect. Technol. Methods 6, 201 (2022).
  6. M.-Y. Huang, Y. Irie, S.-Y. Xu, X. Qi, and S. Wang, Performance of the correlated painting based on the mechanical structure of the anticorrelated painting scheme, Phys. Rev. Accel. Beams 25, 110401 (2022).
  7. W. Jie, F. Shi-Nian, T. Jing-Yu, T. Ju-Zhou, W. Ding-Sheng, W. Fang-Wei, and W. Sheng, China spallation neutron source: An overview of application prospects, Chin. Phys. C 33, 1033 (2009).
  8. S. Xu, H. Liu, J. Peng et al., Beam commissioning and beam loss control for CSNS accelerators, J. Instrum. 15, P07023 (2020).
  9. J. P. Koutchouk, Trajectory and closed orbit correction, in 3rd Joint US-CERN School on Particle Accelerators: Frontiers of Particle Beams, Observation, Diagnosis and Correction (Springer-Verlag, Berlin and Heidelberg, Germany, 1989), pp. 46–64, CERN-LEP-TH/89-2.
  10. Y. W. An and S. Wang, Application of orbit response matrix method at CSNS/RCS, in Proceedings of the 2nd International Particle Accelerator Conference (IPAC’11) (JACoW Publishing, Geneva, Switzerland, 2011), pp. 2505–2507.
  11. T. Schilcher, M. Böge, J. Chrin, P. Pollet, and V. Schlott, Orbit control at the SLS storage ring, Synchrotron Radiat. News 16, 26 (2003).
  12. A. Starritt, A. Pozar, and Y. R. Tan, Orbit feedback and beam stability at the Australian synchrotron, in Proceedings of the 10th International Particle Accelerator Conference (IPAC’19), Melbourne, Australia (JACoW Publishing, Geneva, Switzerland, 2019), pp. 3805–3807.
  13. E. Karantzoulis, Orbit control advances at ELETTRA, in Proceedings of the 7th European Particle Accelerator Conference (EPAC 2000), Vienna, Austria (JACoW Publishing, Geneva, Switzerland, 2000), pp. 1045–1047, Paper TUP1B13.
  14. H. J. Tsai, H. P. Chang, P. J. Chou et al., Closed orbit correction of TPS storage ring, in Proceedings of the 10th European Particle Accelerator Conference (EPAC’06), Edinburgh, Scotland, UK (JACoW Publishing, Geneva, Switzerland, 2006), pp. 2029–2031.
  15. J. Li, G. Liu, W. Li et al., Closed orbit correction of HLS storage ring, in Proceedings of the 2001 Particle Accelerator Conference (IEEE, Piscataway, New Jersey, USA, 2001), Vol. 2, pp. 1255–1257.
  16. S. H. Mirza, R. Singh, P. Forck, and H. Klingbeil, Closed orbit correction at synchrotrons for symmetric and near-symmetric lattices, Phys. Rev. Accel. Beams 22, 072804 (2019).
  17. S. H. Mirza, R. Singh, P. Forck, and B. Lorentz, Performance of the closed orbit feedback systems with spatial model mismatch, Phys. Rev. Accel. Beams 23, 072801 (2020).
  18. Y. An, M. Li, Y. Li et al., Local orbit correction application for CSNS-RCS high intensity commissioning, in Proceedings of the 12th International Particle Accelerator Conference (IPAC’21), Campinas, Brazil (JACoW Publishing, Geneva, Switzerland, 2021).
  19. D. Schirmer, A machine learning approach to electron orbit control at the 1.5 GeV synchrotron light source DELTA, in Proceedings of the 13th International Particle Accelerator Conference (IPAC’22), Bangkok, Thailand (JACoW Publishing, Geneva, Switzerland, 2022), pp. 1137–1140.
  20. X. Chen, Y. Jia, X. Qi, Z. Wang, and Y. He, Orbit correction based on improved reinforcement learning algorithm, Phys. Rev. Accel. Beams 26, 044601 (2023).
  21. E. Meier, Y.-R. E. Tan, and G. S. LeBlanc, Orbit correction studies using neural networks, in Proceedings of the 3rd International Particle Accelerator Conference (IPAC’12), New Orleans, LA, USA (JACoW Publishing, Geneva, Switzerland, 2012), pp. 2837–2839.
  22. A. Scheinker, Adaptive feedback control and machine learning for particle accelerators, in Proceedings of the 11th International Particle Accelerator Conference (IPAC’20), Caen, France (JACoW Publishing, Geneva, Switzerland, 2020), pp. 53–56.
  23. Zeyu Dong, Yuke Tian, and Yu Sun, Adaptive Model-Based Reinforcement Learning for Orbit Feedback Control in NSLS-II Storage Ring (2026), .
  24. P. Forck, P. Kowina, and D. Liakin, Beam position monitors, Beam Diagnostics for Accelerators (CERN, Geneva, Switzerland, 2009), pp. 187–225.
  25. Daheng Ji, Yi Jiao, Qing Qin et al., Optics correction at BEPCII storage ring, in Proceedings of the 1st International Particle Accelerator Conference (IPAC’10), Kyoto, Japan (JACoW Publishing, Geneva, Switzerland, 2010), pp. 1644–1646.
  26. W. Rogers, N. Carmignani, L. Farvacque et al., pyAT: A Python build of accelerator toolbox, in Proceedings of the 8th International Particle Accelerator Conference (IPAC’17), Copenhagen, Denmark (JACoW Publishing, Geneva, Switzerland, 2017), pp. 3855–3857.
  27. H. Hotchi et al., Beam commissioning of the 3-GeV rapid cycling synchrotron of the Japan proton accelerator research complex, Phys. Rev. ST Accel. Beams 12, 040402 (2009).
  28. S. Wang and Q. Qin, The optimization of beam dynamics design for CSNS/RCS, Proceedings of the 1st International Particle Accelerator Conference (IPAC’10), Kyoto, Japan (JACoW Publishing, Geneva, Switzerland, 2010), pp. 630–632.
  29. J. Wei et al., An anti-symmetric lattice for high-intensity rapid-cycling synchrotrons, in Proceedings of the 10th European Particle Accelerator Conference (EPAC’06), Edinburgh, UK (JACoW Publishing, Geneva, Switzerland, 2006), pp. 369–371.
  30. Y. Li, Y. W. An, Z. P. Li, and S. Y. Xu, Study on magnet sorting of the CSNS/RCS dipoles, in Proceedings of the 12th International Particle Accelerator Conference (IPAC’21), Campinas, Brazil (JACoW Publishing, Geneva, Switzerland, 2021), pp. 665–667.
  31. Y. W. An, H. F. Ji, Y. Li, S. Wang, S. Y. Xu, and J. Peng, Study of magnets sorting of the CSNS/RCS dipoles and quadrupoles, in Proceedings of the 57th ICFA Advanced Beam Dynamics Workshop on High-Intensity and High-Brightness Hadron Beams (HB’16), Malmö, Sweden (JACoW Publishing, Geneva, Switzerland, 2016), pp. 247–249.
  32. X. X. Zhu, D. Tuia, L. Mou, G.-S. Xia, L. Zhang, F. Xu, and F. Fraundorfer, Deep learning in remote sensing: A comprehensive review and list of resources, IEEE Geosci. Remote Sens. Mag. 5, 8 (2017).
  33. N. Ahmed, A. K. Saha, M. A. Al Noman, J. R. Jim, M. F. Mridha, and M. M. Kabir, Deep learning-based natural language processing in human–agent interaction: Applications, advancements and challenges, Nat. Lang. Process. J. 9, 100112 (2024).
  34. G. Litjens, T. Kooi, B. E. Bejnordi et al., A survey on deep learning in medical image analysis, Med. Image Anal. 42, 60 (2017).
  35. A. Edelen and X. Huang, Machine learning for design and control of particle accelerators: A look backward and forward, Annu. Rev. Nucl. Part. Sci. 74, 557 (2024).
  36. L. Zdeborová, Machine learning: New tool in the box, Nat. Phys. 13, 420 (2017).
  37. F. Van der Veken et al., Application of machine learning techniques at the CERN Large Hadron Collider, in Proceedings of Science (SISSA Medialab, Trieste, Italy, 2020), p. 006.
  38. Y. Li, W. Cheng, L. H. Yu, and R. Rainer, Genetic algorithm enhanced by machine learning in dynamic aperture optimization, Phys. Rev. Accel. Beams 21, 054601 (2018).
  39. J. Wan, P. Chu, Y. Jiao, and Y. Li, Improvement of machine learning enhanced genetic algorithm for nonlinear beam dynamics optimization, Nucl. Instrum. Methods Phys. Res., Sect. A 946, 162683 (2019).
  40. A. Edelen, N. Neveu, M. Frey, Y. Huber, C. Mayes, and A. Adelmann, Machine learning for orders of magnitude speedup in multiobjective optimization of particle accelerator systems, Phys. Rev. Accel. Beams 23, 044601 (2020).
  41. J. Wan, P. Chu, and Y. Jiao, Neural network-based multiobjective optimization algorithm for nonlinear beam dynamics, Phys. Rev. Accel. Beams 23, 081601 (2020).
  42. L. Tan, S. Xuan, Y. Gong, X. Liu, X. Wu, S. Tian, and W. Zhang, Application of deep learning methods for online beam optics and coupling feedback in synchrotron light sources, Phys. Rev. Accel. Beams 28, 084601 (2025).
  43. J. Schmidhuber, Deep learning in neural networks: An overview, Neural Netw. 61, 85 (2015).
  44. G. Cybenko, Approximation by superpositions of a sigmoidal function, Math. Control Signals Syst. 2, 303 (1989).
  45. N. Kuklev, M. Borland, G. I. Fystro et al., Online accelerator tuning with adaptive Bayesian optimization, in Proceedings of the 5th North American Particle Accelerator Conference (NAPAC’22), Albuquerque, NM, USA (JACoW Publishing, Geneva, Switzerland, 2022), pp. 842–845, Paper THXD4.
  46. J. Fan and J. Wang, Online reinforcement learning control for maintaining an optimum beam collision on an electron-positron collider, Phys. Rev. Accel. Beams 27, 122801 (2024).
  47. A. Scheinker, F. Cropp, S. Paiagua, and D. Filippetto, An adaptive approach to machine learning for compact particle accelerators, Sci. Rep. 11, 19187 (2021).
  48. A. Scheinker, Adaptive machine learning for robust diagnostics and control of time-varying particle accelerator components and beams, Information 12, 161 (2021).
  49. A. Scheinker, S. Gessner, C. Emma, and A. L. Edelen, Adaptive model tuning studies for non-invasive diagnostics and feedback control of plasma wakefield acceleration at FACET-II, Nucl. Instrum. Methods Phys. Res., Sect. A 967, 163902 (2020).
  50. Hao Zhong, Studies in the horizontal orbit correction of CSNS-RCS, GitHub Repository, https://github.com/HaoZhong128/Studies-in-the-horizontal-orbit-correction-of-CSNS-RCS (2026).

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Phys. Rev. Accel. Beams 29, 104001– Published 13 October, 2026
  • Received 8 November 2025
  • Accepted 1 September 2026
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