- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Accelerators and Beams

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Toward high-performance tracking simulation of long-range resistive-wall driven transverse coupled-bunch instabilities

Xin Huang, Tianlong He*, Hongliang Xu†, Weiwei Li, Zhenghe Bai, and Guangyao Feng

  • *Contact author: htlong@ustc.edu.cn
  • †Contact author: hlxu@ustc.edu.cn
PDF

Phys. Rev. Accel. Beams 29, 114901 – Published 5 November, 2026

DOI: https://doi.org/10.1103/hfw9-6759

Abstract

The long-range transverse resistive-wall (RW) wakefield is a key driver of transverse coupled-bunch instabilities in high-current storage rings. Simulating these instabilities accurately is typically time-consuming, because conventional time-domain tracking codes such as Pelegant store the turn-by-turn bunch-centroid history and perform discrete convolutions with the wakefield, which poses a bottleneck for long-term tracking. To overcome this limitation, this work reformulates the long-range RW wakefield calculation, converting the explicit history-dependent convolution into a recursive update by representing the wakefield as a sum-of-exponential functions. This approach avoids storing the bunch-centroid history and is well suited to parallel graphics-processing-unit architectures; it has been implemented in the tracking code STABLE. Benchmark tests, using parameters of the Hefei Advanced Light Facility (HALF), show that STABLE with the proposed method maintains high accuracy in the growth rate while achieving a speedup of at least 2 orders of magnitude over Pelegant. Leveraging this computational efficiency, we conduct a systematic study of RW instabilities for HALF, with particular focus on the interplay among filling pattern, chromaticity, and harmonic-cavity bunch lengthening.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (57)

  1. W. Li, T. He, and Z. Bai, Terahertz scale microbunching instability driven by high resistivity nonevaporable getter coating resistive-wall impedance, Phys. Rev. Accel. Beams 27, 034401 (2024).
  2. L. R. Carver, T. Brochard, E. Buratin, N. Carmignani, F. Ewald, L. Hoummi, S. M. Liuzzo, T. Perron, B. Roche, and S. White, Beam based characterization of the European synchrotron radiation facility extremely brilliant source short range wakefield model, Phys. Rev. Accel. Beams 26, 044402 (2023).
  3. V. Gubaidulin, A. Gamelin, A. Loulergue, R. Nagaoka, and P. Schreiber, Transverse instabilities in SOLEIL II storage ring in the presence of a harmonic cavity, in Proc. IPAC’24, Nashville, TN, USA (JACoW Publishing, Geneva, Switzerland, 2024), pp. 821–824, MOPS45.
  4. F. J. Cullinan, R. Nagaoka, G. Skripka, and P. F. Tavares, Transverse coupled-bunch instability thresholds in the presence of a harmonic-cavity-flattened rf potential, Phys. Rev. Accel. Beams 19, 124401 (2016).
  5. S. Dastan, E. Karantzoulis, K. Manukyan, S. Krecic, and R. Nagaoka, Study on transverse multi-bunch instability in Elettra 2.0, in Proc. IPAC’23, Venice, Italy (JACoW Publishing, Geneva, Switzerland, 2023), pp. 1106–1109, MOPM050.
  6. N. Wang, J. T. Li, S. K. Tian, S. Yue, and X. Y. Liu, Narrowband impedance studies in the HEPS storage ring, in Proc. IPAC’24, Nashville, TN, USA (JACoW Publishing, Geneva, Switzerland, 2024), pp. 3144–3147, THPC58.
  7. S. W. Wang, H. C. Chao, R. T. Fielder, I. P. S. Martin, and T. Olsson, Studies of transverse coupled-bunch instabilities from resistive-wall and cavity higher order modes for Diamond-II, in Proc. IPAC’22, Bangkok, Thailand (JACoW Publishing, Geneva, Switzerland, 2022), pp. 2253–2256, WEPOMS010.
  8. X. Ai et al., Conceptual design report of the Super Tau-Charm Facility: The accelerator, Nucl. Sci. Tech. 36, 242 (2025).
  9. E. Belli, M. Migliorati, G. Castorina, B. Spataro, M. Zobov, A. Novokhatski, and S. Persichelli, Coupling impedances and collective effects for FCC-ee, in Proc. IPAC’17, Copenhagen, Denmark (JACoW Publishing, Geneva, Switzerland, 2017), pp. 3734–3737, THPAB020.
  10. N. Wang, C. T. Lin, Y. D. Liu, S. K. Tian, H. S. Xu, and Y. Zhang, Collective effects studies for CEPC, in Proc. eeFACT’22, Frascati, Italy (JACoW Publishing, Geneva, Switzerland, 2022), pp. 141–145, WEYAT0101.
  11. D. Zhou, M. Tobiyama, G. Mitsuka, T. Ishibashi, and M. Migliorati, Transverse coupled-bunch instability driven by the resistive wall impedance at SuperKEKB, in Proc. IPAC’23, Venice, Italy (JACoW Publishing, Geneva, Switzerland, 2023), pp. 3562–3565, WEPL187.
  12. N. Mounet, The LHC Transverse Coupled-Bunch Instability, Ph.D. thesis, EPFL, Lausanne, 2012.
  13. S. Persichelli, M. Migliorati, N. Biancacci, S. Gilardoni, E. Metral, and B. Salvant, Transverse beam coupling impedance of the CERN proton synchrotron, Phys. Rev. Accel. Beams 19, 041001 (2016).
  14. A. W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (Wiley, New York, 1993), https://books.google.com.hk/books?id=MjRoQgAACAAJ.
  15. F. J. Sacherer, Transverse bunched beam instabilities: Theory, in Proc. HEACC’74, Stanford, CA, USA (A.E.C., Washington, DC, 1975), pp. 347–351, https://cds.cern.ch/record/322645.
  16. J. L. Laclare, Bunched beam coherent instabilities, in CAS–CERN Accelerator School: Accelerator Physics, Oxford, UK, 16-25 September 1985, edited by S. Turner (CERN, Geneva, Switzerland, 1987), pp. 264–326.
  17. G. Bassi, A. Blednykh, and V. Smaluk, Coupled-bunch instability for arbitrary multibunch configurations, Phys. Rev. Accel. Beams 25, 014402 (2022).
  18. R. R. Lindberg, Stabilizing effects of chromaticity and synchrotron emission on coupled-bunch transverse dynamics in storage rings, Phys. Rev. Accel. Beams 24, 024402 (2021).
  19. F. J. Cullinan, Å. Andersson, and P. F. Tavares, Harmonic-cavity stabilization of longitudinal coupled-bunch instabilities with a nonuniform fill, Phys. Rev. Accel. Beams 23, 074402 (2020).
  20. M. Borland, ELEGANT: A flexible SDDS-compliant code for accelerator simulation, Tech. Rep., Argonne National Lab., IL, USA, 2000.
  21. Y. Wang and M. Borland, Pelegant: A parallel accelerator simulation code for electron generation and tracking, in AIP Conference Proceedings (AIP, Melville, NY, 2006), pp. 241–247.
  22. A. Gamelin, W. Foosang, and R. Nagaoka, mbtrack2, a collective effect library in Python, in Proc. IPAC’21, Campinas, SP, Brazil (JACoW Publishing, Geneva, Switzerland, 2021), pp. 282–285, MOPAB070.
  23. A. Gamelin, W. Foosang, N. Yamamoto, V. Gubaidulin, and R. Nagaoka, mbtrack2 (Version 0.10.0), Zenodo, 10.5281/zenodo.20607804 (2026).
  24. G. Iadarola et al., Xsuite: An integrated beam physics simulation framework, in Proc. IPAC’24, Nashville, TN, USA (JACoW Publishing, Geneva, Switzerland, 2024), pp. 2623–2626, WEPR56.
  25. Xsuite Collaboration, xsuite/xtrack:Xtrack version 0.111.5, Zenodo, 10.5281/zenodo.22040751 (2026).
  26. C. Li and Y.-C. Chae, CETASim: A numerical tool for beam collective effect study in storage rings, Nucl. Instrum. Methods Phys. Res., Sect. A 1070, 170031 (2025).
  27. M. Migliorati and L. Palumbo, Multibunch and multiparticle simulation code with an alternative approach to wakefield effects, Phys. Rev. ST Accel. Beams 18, 031001 (2015).
  28. T. He and Z. Bai, Graphics-processing-unit-accelerated simulation for longitudinal beam dynamics of arbitrary bunch trains in electron storage rings, Phys. Rev. Accel. Beams 24, 104401 (2021).
  29. W. W. Li, Y. Sun, X. Y. Liu, T. L. He, and Z. H. Bai, Study on transverse coupled-bunch instabilities driven by high order modes in the HALF storage ring, Nucl. Instrum. Methods Phys. Res., Sect. A 1083, 171104 (2026).
  30. Z. Bai et al., Progress on the storage ring physics design of Hefei Advanced Light Facility (HALF), in Proc. IPAC’23, Venice, Italy (JACoW Publishing, Geneva, Switzerland, 2023), pp. 1075–1078, MOPM038.
  31. Y. Shobuda and Y. H. Chin, Resistive-wall impedances of a thin non-evaporable getter coating on a conductive chamber, Prog. Theor. Exp. Phys. 2017, 123G01 (2017).
  32. A. Blednykh, G. Bassi, V. Smaluk, and R. Lindberg, Impedance modeling and its application to the analysis of the collective effects, Phys. Rev. Accel. Beams 24, 104801 (2021).
  33. J. Kennedy and R. Eberhart, Particle swarm optimization, in Proc. ICNN’95–International Conference on Neural Networks (IEEE, New York, 1995), Vol. 4, pp. 1942–1948.
  34. S. Katoch, S. S. Chauhan, and V. Kumar, A review on genetic algorithm: Past, present, and future, Multimedia Tools Appl. 80, 8091 (2021).
  35. P. I. Frazier, Bayesian optimization, in Recent Advances in Optimization and Modeling of Contemporary Problems (INFORMS, Catonsville, MD, 2018), pp. 255–278.
  36. J. Blank and K. Deb, Pymoo: Multi-objective optimization in Python, IEEE Access 8, 89497 (2020).
  37. W. McLean, Exponential sum approximations for t−β, in Contemporary Computational Mathematics–A Celebration of the 80th Birthday of Ian Sloan, edited by J. Dick, F. Y. Kuo, and H. Woźniakowski (Springer International Publishing, Cham, 2018), pp. 911–930.
  38. X. Huang, H. Yao, T. He, W. Li, X. Liu, Z. Bai, and H. Xu, Exponential sum fitting of the long-range transverse resistive-wall wakefield, in Proc. SAP’25, Urumqi, China (JACoW Publishing, Geneva, Switzerland, 2025), pp. 61–64, THP22.
  39. T. He, W. Li, Z. Bai, and L. Wang, Periodic transient beam loading effect with passive harmonic cavities in electron storage rings, Phys. Rev. Accel. Beams 25, 024401 (2022).
  40. T. He, W. Li, Z. Bai, and W. Li, Analytic formulas for the D-mode Robinson instability, Phys. Rev. Accel. Beams 27, 064402 (2024).
  41. R. Nagaoka and K. L. F. Bane, Collective effects in a diffraction-limited storage ring, J. Synchrotron Radiat. 21, 937 (2014).
  42. T. He, W. Li, Z. Bai, and L. Wang, Longitudinal equilibrium density distribution of arbitrary filled bunches in presence of a passive harmonic cavity and the short range wakefield, Phys. Rev. Accel. Beams 24, 044401 (2021).
  43. A. Poncet, Ion trapping and clearing, in Frontiers of Particle Beams: Factories with e+e- Rings (Springer, Berlin, Heidelberg, 1994), pp. 202–221.
  44. K. Holldack, R. Ovsyannikov, P. Kuske, R. Müller, A. Schälicke, M. Scheer, M. Gorgoi, D. Kühn, T. Leitner, S. Svensson, N. Mårtensson, and A. Föhlisch, Single bunch X-ray pulses on demand from a multi-bunch synchrotron radiation source, Nat. Commun. 5, 4010 (2014).
  45. Z. T. Zhao, Y. N. Liang, and B. C. Jiang, Filling patterns in the SSRF storage ring, Nucl. Sci. Tech. 21, 129 (2010).
  46. R. Warnock and M. Venturini, Equilibrium of an arbitrary bunch train in presence of a passive harmonic cavity: Solution through coupled Haïssinski equations, Phys. Rev. Accel. Beams 23, 064403 (2020).
  47. T. Olsson, F. J. Cullinan, and Å. Andersson, Self-consistent calculation of transient beam loading in electron storage rings with passive harmonic cavities, Phys. Rev. Accel. Beams 21, 120701 (2018).
  48. L. Wang, Y. Cai, T. O. Raubenheimer, and H. Fukuma, Suppression of beam-ion instability in electron rings with multibunch train beam fillings, Phys. Rev. ST Accel. Beams 14, 084401 (2011).
  49. V. Gubaidulin, A. Gamelin, and R. Nagaoka, Beam-ion instabilities and their mitigation for SOLEIL II, in Proc. IPAC’23, Venice, Italy (JACoW Publishing, Geneva, Switzerland, 2023), pp. 2650–2653, WEPA004.
  50. M. Dehler, Ion trapping and instabilities in SLS 2.0, in Proc. IPAC’23, Venice, Italy (JACoW Publishing, Geneva, Switzerland, 2023), pp. 3578–3581, WEPL192.
  51. S. Prabhakar, J. D. Fox, and D. Teytelman, Curing coupled-bunch instabilities with uneven fills, Phys. Rev. Lett. 86, 2022 (2001).
  52. R. Roussel et al., Bayesian optimization algorithms for accelerator physics, Phys. Rev. Accel. Beams 27, 084801 (2024).
  53. T. Hellert, D. Bertwistle, S. C. Leemann, A. Sulc, and M. Venturini, Agentic artificial intelligence for multistage physics experiments at a large-scale user facility particle accelerator, Phys. Rev. Res. 8, L012017 (2026).
  54. N. Mounet, N. Biancacci, D. Amorim, and E. Vik, ImpedanceWake2D, CERN GitLab repository, https://gitlab.cern.ch/IRIS/IW2D.
  55. K. Yokoya, Resistive wall impedance of beam pipes of general cross-section, Part. Accel. 41, 221 (1993). https://api.semanticscholar.org/CorpusID:34843045
  56. G. Bassi, A. Blednykh, W. Cheng, F. Gao, J. Rose, and D. Teytelman, Analysis of coupled-bunch instabilities for the NSLS-II storage ring with a 500 MHz 7-cell PETRA-III cavity, Nucl. Instrum. Methods Phys. Res., Sect. A 810, 151 (2016).
  57. T. L. He, J. C. Xiao, W. W. Li, Z. H. Bai, and W. M. Li, Impact of short-range wakefields from radio-frequency cavity resonant modes on bunch lengthening, Nucl. Instrum. Methods Phys. Res. Sect. A 1080, 170672 (2025).

Outline

Information

Phys. Rev. Accel. Beams 29, 114901– Published 5 November, 2026
  • Received 7 July 2026
  • Accepted 16 September 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation