- 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
  • Editors' Suggestion
  • Open Access

Measurement, modeling, and correction of decapolar Hamiltonian terms in the LHC

Maël Le Garrec*

Ewen Hamish Maclean, Félix Simon Carlier, and Rogelio Tomás

  • CERN, Geneva, Switzerland

  • *Contact author: mael.le.garrec@cern.ch
PDF

Phys. Rev. Accel. Beams 29, 113501 – Published 5 November, 2026

DOI: https://doi.org/10.1103/v1pv-svvx

Abstract

Understanding and mitigating high-order nonlinearities is essential for ensuring long-term beam storage in high-energy colliders. The stability of particles at the Large Hadron Collider (LHC) is indeed strongly influenced by nonlinear effects, particularly at injection energy where the beam occupies a large fraction of the vacuum chamber. Among these effects, third-order chromaticity, primarily driven by decapolar fields, limits dynamic aperture and beam lifetime. Despite corrections based on magnetic measurements and model predictions, a discrepancy remains between the measured and expected third-order chromaticity, indicating the presence of residual decapolar components. In this study, the decapolar fields in the LHC at injection energy are investigated and their impact on beam dynamics assessed. Chromatic amplitude detuning and decapolar resonance driving terms are directly measured for the first time, using forced oscillations driven by an ac dipole. These measurements provide new insights into the source and impact of decapolar fields in the LHC and indicate that refined correction strategies could enhance beam lifetime, particularly for high-brightness operation in future runs.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. O. S. Brüning, J. Poole, P. Collier, P. Lebrun, R. Ostojic, S. Myers, and P. Proudlock, LHC design report, 2004.
  2. E. H. Maclean, F. Schmidt, R. Tomás, R. Bartolini, E. Todesco, R. Steinhagen, G. Vanbavinckhove, and M. Giovannozzi, Non-linear chromaticity studies of the LHC at injection, in IPAC’11 (JACoW Publishing, San Sebastián, Spain, 2011), pp. 2199–2201.
  3. E. H. Maclean, F. Carlier, J. M. Coello de Portugal, A. Garcia-Tabares, A. S. Langner, L. Malina, T. Persson, P. K. Skowronski, and R. Tomás, Commissioning of non-linear optics in the LHC at injection energy, in IPAC’16 (JACoW Publishing, Busan, Korea, 2016), pp. 3476–3479.
  4. E. H. Maclean, R. Tomás, F. Schmidt, and T. H. B. Persson, Measurement of nonlinear observables in the large hadron collider using kicked beams, Phys. Rev. ST Accel. Beams 17, 081002 (2014).
  5. CERN, FiDeL - the magnetic model of the LHC, https://web.archive.org/web/20220121041323/https://lhc-div-mms.web.cern.ch/tests/MAG/Fidel/, original page (https://lhc-div-mms.web.cern.ch/tests/MAG/Fidel/) no longer resolves; Wayback Machine snapshot cited (2021).
  6. F. S. Carlier, M. Giovannozzi, E. H. Maclean, T. Persson, and R. Tomás, Probing the forced dynamic aperture in the LHC at top energy using AC dipoles, in Proceedings of IPAC’18, Vancouver, BC, Canada (JACoW Publishing, Geneva, Switzerland, 2018), pp. 165–168, 10.18429/JACoW-IPAC2018-MOPMF033.
  7. W. Fischer, J. Beebe-Wang, Y. Luo, S. Nemesure, and L. Rajulapati, RHIC proton beam lifetime increase with 10- and 12-pole correctors, in Proceedings of the First International Particle Accelerator Conference (IPAC’10), Kyoto, Japan (2010), pp. 4752–4754.
  8. F. Pilat, Y. Luo, N. Malitsky, and V. Ptitsyn, Beam-based Non-linear optics corrections in colliders, in Proceedings of the 2005 Particle Accelerator Conference (IEEE, Knoxville, TN, USA, 2005), pp. 601–605.
  9. L. C. Teng, Error analysis for the low beta quadrupoles of the Tevatron collider/location and strengths of correction dipoles in the low beta insertion, Fermilab, Tech. Rep. FERMILAB-TM-1097, 1982.
  10. J. Dilly, V. Ferrentino, M. Le Garrec, E. H. Maclean, L. Malina, T. Persson, T. Pugnat, L. van Riesen-Haupt, F. Soubelet, and R. Tomás, First operational dodecapole correction in the LHC, Phys. Rev. Accel. Beams 26, 121001 (2023).
  11. E. H. Maclean, F. S. Carlier, J. Dilly, M. Le Garrec, M. Giovannozzi, and R. Tomás, Prospects for beam-based study of dodecapole nonlinearities in the CERN high-luminosity large hadron collider, Eur. Phys. J. Plus 137, 1249 (2022).
  12. M. Le Garrec, V. Ferrentino, J. Dilly, R. Tomás, K. Paraschou, E. Maclean, and F. Carlier, Measurement and modelling of decapole errors in the LHC from beam-based studies, in IPAC’23 (JACoW Publishing, Venice, Italy, 2023), pp. 567–570.
  13. M. Le Garrec, LHC effective model for optics corrections : Measurements and corrections of high-order non-linear optics, Ph.D. thesis, Goethe-Universität, 2025.
  14. S. Liuzzo and A. Franchi, Implementation of fully analytic orbit response analysis in python, in Low Emittance Rings Workshop 2024 (CERN, Geneva, 2024), https://indico.cern.ch/event/1326603/contributions/5773961/.
  15. P. Raimondi, FCC lattice evolution, in Optics Tuning and Corrections for Future Colliders Workshop (CERN, Geneva, 2023), https://indico.cern.ch/event/1242395/contributions/5417974/.
  16. Optics tuning and corrections for future colliders workshop, https://indico.cern.ch/event/1242395/timetable/#20230626 (2023).
  17. R. Tomás et al., Towards a high luminosity LHC with even higher performance, in IPAC’25 (JACoW Publishing, Taipei, Taiwan, 2025), pp. 278–281.
  18. L. Deniau, H. Grote, G. Roy, and F. Schmidt, MAD-X user guide, https://madx.web.cern.ch/releases/last-rel/madxuguide.pdf (2021).
  19. J. Keintzel, L. Malina, and R. Tomás García, Momentum compaction factor measurements in the large hadron collider, in IPAC’21 (JACoW Publishing, Campinas, SP, Brazil, 2021), pp. 1360–1363.
  20. J. Bengtsson and J. Irwin, Analytical calculations of smear and tune shift, Superconducting Super Collider Laboratory, Dallas, TX, Tech. Rep. SSC-232, 1990.
  21. A. Franchi, Studies and measurements of linear coupling and nonlinearities in hadron circular accelerators Doctoral Thesis, Johann Wolfgang Goethe-Universität, 2006.
  22. E. Forest, Beam Dynamics: A New Attitude and Framework, The Physics and Technology of Particle and Photon Beams, Vol. 8 (Harwood Academic, Amsterdam, 1998).
  23. F. Casas and A. Murua, An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications, J. Math. Phys. 50, 033513 (2009).
  24. F. S. Carlier, A nonlinear future: Measurements and corrections of nonlinear beam dynamics using forced transverse oscillations, Ph.D. thesis, Universiteit van Amsterdam, 2020.
  25. R. Bartolini and F. Schmidt, Normal form via tracking or beam data, Part. Accel. 59, 93 (1998); also CERN LHC Project Report 132, 1997.
  26. R. Tomás, Normal form of particle motion under the influence of an ac dipole, Phys. Rev. ST Accel. Beams 5, 054001 (2002).
  27. R. Bartolini, Resonance driving term experiments: An overview, in Proceedings of ICAP’06, Chamonix, France (JACoW, Geneva, Switzerland, 2006), pp. 22–27.
  28. R. Miyamoto, R. Calaga, M. Aiba, R. Tomás, and G. Vanbavinckhove, Measurement of coupling resonance driving terms in the LHC with AC dipoles, in IPAC’11 (JACoW Publishing, San Sebastián, Spain, 2011), pp. 2067–2069.
  29. S. J. Horney, E. Maclean, P. Burrows, F. Carlier, J. Dilly, L. Deniau, V. Ferrentino, E. Fol, M. Hofer, J. Keintzel, M. Le Garrec, T. Persson, L. van Riesen-Haupt, F. Soubelet, R. Tomás, and A. Wegscheider, Sextupole RDTs in the LHC at injection and in the ramp, in IPAC’24 (JACoW Publishing, Nashville, Tennessee, USA, 2024), pp. 71–74.
  30. A. Wegscheider and R. Tomás García, Forced coupling resonance driving terms, in IPAC’21 (JACoW Publishing, Campinas, SP, Brazil, 2021), pp. 3646–3649.
  31. W. Venturini Delsolaro and R. Wolf, Magnetic behavior of LHC superconducting correctors: Issues for machine operation, in LHC Project Workshop Chamonix XIV (CERN, Geneva, 2005).
  32. CERN, Ten Out of Ten for LHC Decapole Magnets, CERN, CERN Bulletin BUL-NA-2001-041, 2001.
  33. E. Forest, F. Schmidt, and E. McIntosh, Introduction to the polymorphic tracking code, CERN, SPS and LHC Division Note CERN-SL-2002-044 (AP), 2002.
  34. J. Keintzel, M. Le Garrec, E. Todesco, J. Wenninger, S. Fartoukh, R. Tomás, T. Persson, and M. Solfaroli, 60° phase advance optics measurements in the large hadron collider at CERN, in IPAC’23 (JACoW Publishing, Venice, Italy, 2023), pp. 571–574.
  35. R. Tomás, S. Fartoukh, and J. Serrano, Reliable operation of the AC dipole in the LHC, CERN, LHC Project Report 1095, 2008.
  36. S. White, E. H. Maclean, and R. Tomás, Direct amplitude detuning measurement with ac dipole, Phys. Rev. ST Accel. Beams 16, 071002 (2013).
  37. R. Tomás, X. Buffat, S. White, J. Barranco, P. Gonçalves Jorge, and T. Pieloni, Beam-beam amplitude detuning with forced oscillations, Phys. Rev. Accel. Beams 20, 101002 (2017).
  38. N. Sammut, L. Bottura, and J. Micallef, Mathematical formulation to predict the harmonics of the superconducting large hadron collider magnets, Phys. Rev. ST Accel. Beams 9, 012402 (2006).
  39. M. Haverkamp, L. Bottura, and M. Schneider, Studies of decay and snapback effects on LHC dipole magnets, in Proceedings of EUCAS’99, Sitges, Spain, Inst. Phys. Conf. Ser. 167 (IOP Publishing, Bristol, 1999), pp. 1183–1186; also CERN LHC Project Report 336.
  40. L. Deniau, Magnetic model of main dipoles, CERN, Technology Department EDMS 2458910, 2009.
  41. W. Fischer, A. Jain, and S. Tepikian, Beam-based measurements of persistent current decay in the relativistic heavy ion collider, Phys. Rev. ST Accel. Beams 4, 041002 (2001).
  42. Y. Papaphilippou, Detecting chaos in particle accelerators through the frequency map analysis method, Chaos 24, 024412 (2014).
  43. M. Lamont and O. Johnson, LHC beam and luminosity lifetimes revisited, https://cds.cern.ch/record/1967453 (2014).
  44. F. S. Carlier, R. Tomás, E. H. Maclean, and T. H. B. Persson, First experimental demonstration of forced dynamic aperture measurements with LHC ac dipoles, Phys. Rev. Accel. Beams 22, 031002 (2019).
  45. N. Merminga and K. Ng, Two-fifth resonance islands generated by sextupoles, Fermi National Accelerator Laboratory, Tech. Rep. FERMILAB-FN-0506, 1992.
  46. J. Gareyte, J. P. Koutchouk, and F. Ruggiero, Landau damping, dynamic aperture and octupoles in LHC, CERN, LHC Project Report 91, 1997.
  47. R. Tomás, Adiabaticity of the ramping process of an ac dipole, Phys. Rev. ST Accel. Beams 8, 024401 (2005).
  48. R. Tomás, F. Carlier, F. Chudoba, L. Deniau, J. Dilly, V. Ferrentino, S. Horney, M. Hostettler, J. Keintzel, S. Kostoglou, M. Le Garrec, E. H. Maclean, T. Nissinen, K. Paraschou, T. Persson, M. Solfaroli, F. Soubelet, A. Wegscheider, and J. Wenninger, Optics for Landau damping with minimized octupolar resonances in the LHC, J. Instrum. 19, T05010 (2024).

Outline

Information

Phys. Rev. Accel. Beams 29, 113501– Published 5 November, 2026
  • Received 4 December 2025
  • Accepted 29 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