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Beam-based identification of magnetic field errors in a synchrotron using deep Lie map networks

Conrad Caliari1, Adrian Oeftiger2, and Oliver Boine-Frankenheim1,2

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Phys. Rev. Accel. Beams 28, 024601 – Published 26 February, 2025

DOI: https://doi.org/10.1103/PhysRevAccelBeams.28.024601

Abstract

We report on the recovery of both linear and nonlinear optics in a hadron synchrotron using the novel deep Lie map network (DLMN) approach. The DLMN enables the construction of a detailed accelerator model by integrating charged particle dynamics with machine learning methods within a data-driven framework. The primary observable is the centroid motion over a limited number of turns, captured by beam position monitors. The DLMN generates an updated description of the accelerator in terms of magnetic multipole components, which can be directly utilized in established accelerator physics tools and tracking codes for further analysis. In this study, the DLMN approach is employed to recover a linear optics model, including gradient errors, from a single measured trajectory. Nonlinear optics, including sextupole errors, are recovered using three measured trajectories. We assess the validity of these results by comparison with the linear optics from closed orbits algorithm and through estimates of resonance driving terms. Additionally, we illustrate an application of the deep Lie map network and the predicted synchrotron optics by comparing measured and simulated tune scans.

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References (49)

  1. G. Franchetti, O. Chorniy, I. Hofmann, W. Bayer, F. Becker, P. Forck, T. Giacomini, M. Kirk, T. Mohite, C. Omet, A. Parfenova, and P. Schütt, Experiment on space charge driven nonlinear resonance crossing in an ion synchrotron, Phys. Rev. ST Accel. Beams 13, 114203 (2010).
  2. A. Oeftiger, O. Boine-Frankenheim, V. Chetvertkova, V. Kornilov, D. Rabusov, and S. Sorge, Simulation study of the space charge limit in heavy-ion synchrotrons, Phys. Rev. Accel. Beams 25, 054402 (2022).
  3. H. Bartosik, F. Asvesta, A. Huschauer, Y. Papaphilippou, and F. Schmidt, Space charge induced losses in the CERN injector complex, J. Instrum. 15, P07021 (2020).
  4. A. S. Hernandez, D. Moreno, H. Bartosik, N. Biancacci, S. Hirlander, and A. Huschauer, Space charge studies on LEIR, J. Phys. Conf. Ser. 1067, 062020 (2018).
  5. J. Eldred, V. Lebedev, K. Seiya, and V. Shiltsev, Beam intensity effects in fermilab booster synchrotron, Phys. Rev. Accel. Beams 24, 044001 (2021).
  6. C. Guo, J. Liu, J. Yang, and R. Zhu, Simulation studies on compensation for space-charge-induced half-integer and 3rd-order resonance crossing in HIAF-BRing, arXiv:2408.01954.
  7. P. Spiller, M. Bai, J. Blaurock, O. Boine-Frankenheim, A. Dolinskii, F. Hagenbuck, C. Kleffner, K. Knie, I. Koop, S. Menke et al., Status of the FAIR project, in Proceedings of the 9th International Particle Accelerator Conference (JACoW, Geneva, Switzerland, 2018), pp. 63–68, 10.18429/JACoW-IPAC2018-MOZGBF2.
  8. D. Ondreka, C. Dimopoulou, H. Hüther, H. Liebermann, J. Stadlmann, and R. Steinhagen et al., Recommissioning of SIS18 after FAIR upgrades, in Proceedings of the 10th International Particle Accelerator Conference (IPAC’19), Melbourne, Australia (JACoW, Geneva, Switzerland, 2019), pp. 932–935.
  9. J. Safranek, Experimental determination of storage ring optics using orbit response measurements, Nucl. Instrum. Methods Phys. Res., Sect. A 388, 27 (1997).
  10. R. Dowd, M. Boland, G. LeBlanc, and Y. E. Tan, Achievement of ultralow emittance coupling in the australian synchrotron storage ring, Phys. Rev. ST Accel. Beams 14, 012804 (2011).
  11. L. S. Nadolski, Use of LOCO at synchrotron SOLEIL, Conf. Proc. C 0806233, THPC064 (2008).
  12. R. Tomás, M. Bai, R. Calaga, W. Fischer, A. Franchi, and G. Rumolo, Measurement of global and local resonance terms, Phys. Rev. ST Accel. Beams 8, 024001 (2005).
  13. A. Parfenova and G. Franchetti, Experimental benchmarking of nonlinear tune response matrix with several controlled sextupolar errors, Nucl. Instrum. Methods Phys. Res., Sect. A 646, 7 (2011).
  14. A. Parfenova, G. Franchetti, R. Tomás, and G. Vanbavinckhove, Benchmarking of the NTRM method on octupolar non-linear components at the CERN-SPS synchrotron, CERN, Technical Report No. CERN-ATS-2010-074, 2010.
  15. G. Franchetti, A. Parfenova, and I. Hofmann, Measuring localized nonlinear components in a circular accelerator with a nonlinear tune response matrix, Phys. Rev. ST Accel. Beams 11, 094001 (2008).
  16. A. Ivanov and I. Agapov, Physics-based deep neural networks for beam dynamics in charged particle accelerators, Phys. Rev. Accel. Beams 23, 074601 (2020).
  17. C. Caliari. Identification of field errors with machine learning techniques, Master’s thesis, Technische Universität Darmstadt, 2021.
  18. C. Caliari, A. Oeftiger, and O. Boine-Frankenheim, Identification of magnetic field errors in synchrotrons based on deep Lie map networks, Phys. Rev. Accel. Beams 26, 064601 (2023).
  19. H. Yoshida, Construction of higher order symplectic integrators, Phys. Lett. A 150, 262 (1990).
  20. A. G. Baydin, B. A. Pearlmutter, A. A. Radul, and J. M. Siskind, Automatic differentiation in machine learning: A survey, J. Mach. Learn. Res. 18, 5595 (2018).
  21. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
  22. J. C. Duchi, E. Hazan, and Y. Singer, Adaptive subgradient methods for online learning and stochastic optimization, J. Mach. Learn. Res. 12, 2121 (2011).
  23. M. D. Zeiler, Adadelta: An adaptive learning rate method, arXiv:1212.5701.
  24. A. Graves, Generating sequences with recurrent neural networks, arXiv:1308.0850.
  25. T. Giacomini, P. Forck, D. Liakin, J. Dietrich, and G. v. Villiers, Ionization profile monitors-IPM@ GSI, in Proceedings of the DIPAC2011, Hamburg, Germany (2011), p. 419, https://accelconf.web.cern.ch/DIPAC2011/papers/tupd51.pdf.
  26. D. K. Olsson, Å. Andersson, and M. Sjöström, Nonlinear optics from off-energy closed orbits, Phys. Rev. Accel. Beams 23, 102803 (2020).
  27. J. Laskar, C. Froeschlé, and A. Celletti, The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping, Physica (Amsterdam) 56B, 253 (1992).
  28. R. Bartolini and F. Schmidt, Sussix: A computer code for frequency analysis of non-linear betatron motion, CERN, Geneva, Technical Report No. SL-Note-98-017-AP, 1998.
  29. P. Zisopoulos, Y. Papaphilippou, and J. Laskar, Refined betatron tune measurements by mixing beam position data, Phys. Rev. Accel. Beams 22, 071002 (2019).
  30. N. Biancacci, FFT corrections for tune measurements, in Optics Workshop, OMCM, CERN (2011), pp. 11–19, https://indico.cern.ch/event/132526/contributions/128902/attachments/99707/142376/Meeting1-06-11_FFT_corrections_for_tune_measurements.pdf.
  31. J. S. Bendat, Probability functions for random responses: Prediction of peaks, fatigue damage, and catastrophic failures, NASA, Technical Report No. NASA-CR-33, 1964.
  32. R. Tomás, Normal form of particle motion under the influence of an ac dipole, Phys. Rev. ST Accel. Beams 5, 054001 (2002).
  33. G. Franchetti, B. Franczak, and P. Schütt, A benchmarking experiment in SIS for dynamic aperture induced beam loss, GSI, Text Note No. 05, 2004.
  34. G. Franchetti, P. Schütt, T. Hoffmann, G. Rumolo, and A. Franchi, Mapping of the resonances in SIS18, Gesellschaft für Schwerionenforschung (GSI), Report No. GSI-Acc-Note-2005-02-001, 2005.
  35. C. Caliari and A. Oeftiger, Identification of field errors, Nachlese SIS18 Maschinenexperimente, Gesellschaft für Schwerionenforschung (GSI) (2022).
  36. B. Franczak, K. Blasche, and K. Reich, A variable transition energy lattice for SIS 12/18, Gesellschaft für Schwerionenforschung (GSI), Technical Report No. CERN-PS-BR-83-21, 1983.
  37. J. Berg, R. De Maria, L. Deniau, J. Dilly, J. M. Gray, A. Latina, F. Schmidt, and P. Skowronski, STATUS OF MAD-X V5.09, in Proceedings of the 14th International Particle Accelerator Conference, Venice, Italy (JACoW, Geneva, Switzerland, 2023), 10.18429/JACoW-IPAC2023-WEPL101.
  38. R. Singh, Tune measurement at GSI SIS-18: Methods and applications, Ph.D. thesis, TU Darmstadt, 2014.
  39. O. Chorniy, H. Bräuning, T. Hoffmann, H. Reeg, and A. Reiter, A FESA DAQ for fast current transformer in SIS 18, in Proceedings of the IBIC2013, Oxford (2013), https://accelconf.web.cern.ch/ibic2013/papers/wepf31.pdf.
  40. S.-Y. Lee, Accelerator Physics (World Scientific Publishing Company, Singapore, 2018).
  41. A. Reiter and R. Singh, Comparison of beam position calculation methods for application in digital acquisition systems, Nucl. Instrum. Methods Phys. Res., Sect. A 890, 18 (2018).
  42. S. S. Shapiro and M. B. Wilk, An analysis of variance test for normality (complete samples), Biometrika 52, 591 (1965).
  43. N. M. Razali, Y. B. Wah et al., Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-darling tests, J. Stat. Model. Anal. 2, 21 (2011).
  44. B. W. Yap and C. H. Sim, Comparisons of various types of normality tests, J. Stat. Comput. Simul. 81, 2141 (2011).
  45. Y. El Hayek, Lattice of the SIS18, MAD-X format, Gesellschaft für Schwerionenforschung (GSI) (2024).
  46. S. Appel, O. Boine-Frankenheim, and F. Petrov, Injection optimization in a heavy-ion synchrotron using genetic algorithms, Nucl. Instrum. Methods Phys. Res., Sect. A 852, 73 (2017).
  47. V. Isensee, Measurement of the orbit response matrix for the SIS18 doublet optics, Gesellschaft für Schwerionenforschung (GSI), Technical Report No. GSI-2024-00625, 2024.
  48. R. Bartolini and F. Schmidt, Normal form via tracking or beam data, Part. Accel. 59, 93 (1997).
  49. G. Iadarola, R. De Maria, S. Lopaciuk, A. Abramov, X. Buffat, D. Demetriadou, L. Deniau, P. Hermes, P. Kicsiny, P. Kruyt et al., xsuite: An integrated beam physics simulation framework, arXiv:2310.00317.

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Phys. Rev. Accel. Beams 28, 024601– Published 26 February, 2025
  • Received 26 August 2024
  • Accepted 14 January 2025
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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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