- 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

Coupling local and global rf feedback loops for macroparticle tracking simulations

B. E. Karlsen-Baeck1,2,*, T. Argyropoulos2, J. Flowerdew2, L. Intelisano2, I. Karpov2, A. Lasheen2, and H. Timko2

  • *Contact author: birk.beck@cern.ch
PDF

Phys. Rev. Accel. Beams 29, 032802 – Published 10 March, 2026

DOI: https://doi.org/10.1103/bxs4-f9nl

Abstract

Radio frequency (rf) control loops are vital components for the optimal operation of rf systems in synchrotron particle accelerators. Modeling these systems in macroparticle tracking simulations provides improved understanding of the complex interaction between the control loops, the beam-induced voltages in the rf cavities, and the circulating beam. This paper details an implementation of local and global rf control loops in the beam longitudinal dynamics (blond) simulation suite, which allow for the coupling of the two systems in a macroparticle tracking code for the first time. First, benchmarks of the local control loops in the CERN Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC) are given. The implementation coupling the local and global loops is then tested in the SPS with momentum shifts at constant magnetic field and through the damping of phase offsets at injection into the LHC. Both test cases show the expected behavior and validate the model in blond. Finally, the SPS simulation model, which now is able to combine beam-induced voltages, global control loops and local ones, is benchmarked against measurements at the bunch-to-bucket transfer into the real accelerator. The simulations, using the coupled implementation of the loops, are able to reproduce bunch-by-bunch beam parameters at flat bottom as well as uncaptured beam generated at injection.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. D. Boussard, Design of a ring rf system, Technical Report No. CERN-SL-91-02-RFS, CERN, 1991.
  2. U. Bigliani, The beam control system for the CERN PS booster, IEEE Trans. Nucl. Sci. 18, 352 (1971).
  3. J. M. Brennan, RF beam control for the AGS booster, Technical Reports No. BNL-52438, AGS/AD-94-6, Brookhaven National Laboratory, 1994.
  4. P. Baudrenghien, G. Hagmann, J. C. Molendijk, R. Olsen, A. Rohlev, V. Rossi, D. Stellfeld, D. Valuch, and U. Wehrle, The LHC low level rf, in Proceedings of the 10th European Particle Accelerator Conference, Edinburgh, United Kingdom (JACoW, Geneva, Switzerland, 2006).
  5. J. Grieser, J. Adamy, T. Ferrand, K. Gross, U. Hartel, H. Klingbeil, U. Laier, D. Lens, K.-P. Ningel, S. Schäfer, and B. Zipfel, A digital beam-phase control system for a heavy-ion synchrotron with a dual-harmonic cavity system, IEEE Trans. Nucl. Sci. 61, 3584 (2014).
  6. E. Cullerton, B. Schupbach, B. Pellico, B. Chase, P. Varghese, and D. Klepec, Fermilab PIP-II booster LLRF upgrade, Technical Report No. FERMILAB-CONF-19-530-AD-PIP2, Fermi National Accelerator Laboratory (FNAL), Batavia, IL, 2018.
  7. A. Spierer, P. Baudrenghien, J. Egli, G. Hagmann, P. Kuzmanović, I. Stachon, M. Sumiński, and T. Włostowski, The CERN SPS low level rf: The beam-control, in Proceedings of the 13th International Particle Accelerator Conference, Bangkok, Thailand (JACoW, Geneva, Switzerland, 2022), 10.18429/JACoW-IPAC2022-TUPOST021.
  8. O. Naumenko and A. Lasheen, Modelling of the PS beam phase and radial feedback loops, Technical Report No. CERN-ACC-NOTE-2024-0011, CERN, 2024.
  9. A. Gamp, J. Kibinski, A. Millhouse, M. Schweiger, and H. J. Stuckenberg, Damping of coherent synchrotron oscillations occuring at injection of 7.5 GeV protons into PETRA II, in Proceedings of the 2nd European Particle Accelerator Conference, Nice, France (Ed. Frontieres, Gif-sur-Yvette, France, 1990).
  10. T. Mastoridis, P. Baudrenghien, A. Butterworth, J. Molendijk, C. Rivetta, and J. D. Fox, Radio frequency noise effects on the CERN Large Hadron Collider beam diffusion, Phys. Rev. ST Accel. Beams 14, 092802 (2011).
  11. P. Baudrenghien, A. Butterworth, M. Jaussi, T. Mastoridis, G. Papotti, and E. Shaposhnikova, Longitudinal emittance blow-up in the LHC, in Proceedings of the 2nd International Particle Accelerator Conference, San Sebastián, Spain (JACoW, Geneva, Switzerland, 2011).
  12. K. Meisner, RF synchronous transfer into specific buckets between Fermilab main ring and Tevatron accelerators, in Proceedings of the 15th IEEE Particle Accelerator Conference, Washington, DC, USA (IEEE, Piscataway, NJ, 1993).
  13. P. L. Corredoura, L. Sapozhnikov, and R. Tighe, RF feedback development for the PEP-II B factory, in Proceedings of the 4th European Particle Accelerator Conference, London, United Kingdom (World Scientific, Singapore, 1994).
  14. K. Akai, E. Ezura, and S. Yashimoto, Experiment of rf feedback using an improved parallel comb-filter, in Proceedings of the 5th European Particle Accelerator Conference, Sitges, Spain (IOP, Bristol, 1996).
  15. P. Baudrenghien and T. Mastoridis, Fundamental cavity impedance and longitudinal coupled-bunch instabilities at the High Luminosity Large Hadron Collider, Phys. Rev. Accel. Beams 20, 011004 (2017).
  16. T. Mastoridis and P. Baudrenghien, CERN’s super proton synchrotron 200 MHz cavity regulation upgrade: Modeling, design optimization, and performance estimation, Phys. Rev. Accel. Beams 25, 021002 (2022).
  17. G. Iadarola et al., xsuite: An integrated beam physics simulation framework, in Proceedings of the 68th Advanced Beam Dynamics Workshop High-Intensity High-Brightness Hadron Beams, Geneva, Switzerland (JACoW, Geneva, Switzerland, 2024).
  18. R. De Maria et al., SixTrack version 5: Status and new developments, in Proceedings of the 10th International Particle Accelerator Conference, Melbourne, Australia (2019).
  19. A. Gamelin, W. Foosang, and R. Nagaoka, mbtrack2, a collective effect library in python, in Proceedings of the 12th International Particle Accelerator Conference, Campinas, SP, Brazil (JACoW, Geneva, Switzerland, 2021).
  20. M. Borland, elegant: A flexible SDDS-compliant code for accelerator simulation, in Proceedings of the 6th International Computational Accelerator Physics Conference, Darmstadt, Germany (GSI, Darmstadt, 2000).
  21. M. Zampetakis, T. Argyropoulos, Y. Brischetto, R. Calaga, L. Giacomel, B. E. Karlsen-Baeck, I. Karpov, N. Mounet, B. Salvant, and H. Timko, Refining the LHC longitudinal impedance model, in Proceedings of the 68th Advanced Beam Dynamics Workshop High-intensity High-brightness Hadron Beams, Geneva, Switzerland (JACoW, Geneva, Switzerland, 2023).
  22. D. Quartullo, L. Intelisano, I. Karpov, and G. Papotti, Simulation studies of longitudinal stability for high-intensity LHC-type beams in the CERN SPS, in Proceedings of the 13th International Particle Accelerator Conference, Bangkok, Thailand (JACoW, Geneva, Switzerland, 2022).
  23. O. S. Brüning, P. Collier, P. Lebrun, S. Myers, R. Ostojic, J. Poole, and P. Proudlock, LHC Design Report, CERN Yellow Reports: Monographs (CERN, Geneva, 2004).
  24. O. Aberle et al., High-Luminosity Large Hadron Collider (HL-LHC): Technical Design Report, CERN Yellow Reports: Monographs (CERN, Geneva, 2020).
  25. H. Timko, T. Argyropoulos, R. Calaga, N. Catalan Lasheras, K. Iliakis, B. E. Karlsen-Baeck, I. Karpov, and M. Zampetakis, Advances on LHC rf power limitation studies at injection, in Proceedings of the 68th Advanced Beam Dynamics Workshop High-intensity High-brightness Hadron Beams, Geneva, Switzerland (JACoW, Geneva, Switzerland, 2023).
  26. B. E. Karlsen-Bæck, B. Salvachua, H. Timko, M. Zampetakis, and S. Morales Vigo, Correlating start-of-ramp losses with beam observables at flat-bottom in the LHC, in Proceedings of the 15th International Particle Accelerator Conference, Nashville, TN, USA (JACoW, Geneva, Switzerland, 2024).
  27. M. Schwarz, H. Bartosik, A. Lasheen, J. Repond, E. Shaposhnikova, and H. Timko, Studies of capture and flat-bottom losses in the SPS, in Proceedings of the 61st ICFA ABDW on High-intensity and High-brightness Hadron Beams, Daejeon, Korea (JACoW, Geneva, Switzerland, 2018).
  28. H. Timko, S. Albright, T. Argyropoulos, H. Damerau, K. Iliakis, L. Intelisano, B. E. Karlsen-Baeck, I. Karpov, A. Lasheen, L. Medina, D. Quartullo, J. Repond, A. L. Vanel, J. E. Müller, M. Schwarz, P. Tsapatsaris, and G. Typaldos, Beam longitudinal dynamics simulation studies, Phys. Rev. Accel. Beams 26, 114602 (2023).
  29. H. Timko, J. Esteban Müller, A. Lasheen, and D. Quartullo, Benchmarking the beam longitudinal dynamics code blond, in Proceedings of the 7th International Particle Accelerator Conference, Busan, Korea (JACoW, Geneva, Switzerland, 2016).
  30. B. E. Karlsen-Baeck. Modelling control loops for SPS-LHC beam transfer studies, Master’s thesis, Norwegian University of Science and Technology, 2022.
  31. B. E. Karlsen-Bæck, T. Argyropoulos, R. Calaga, I. Karpov, and H. Timko, Validation of control loop modeling for power limitation studies with beams for HL-LHC, in Proceedings of the 14th International Particle Accelerator Conference, Venice, Italy (JACoW, Geneva, Switzerland, 2023).
  32. P. Corredoura, Architecture and performance of the PEP-II low-level rf system, in Proceedings of the 18th IEEE Particle Accelerator Conference, New York, NY, USA (IEEE Computer Society Press, Piscataway, NJ, 1999).
  33. G. Hagmann, P. Baudrenghien, J. Egli, A. Spierer, M. Suminski, and T. Wlostowski, The CERN SPS low level rf: The cavity-controller, in Proceedings of the 13th International Particle Accelerator Conference, Bangkok, Thailand (JACoW, Geneva, Switzerland, 2022).
  34. J. Tückmantel, Cavity-beam-transmitter interaction formula collection with derivation, Technical Report No. CERN-ATS-Note-2011-002 TECH, CERN, 2010.
  35. G. Dôme, The SPS acceleration system travelling wave drift-tube structure for the CERN SPS, in Proceedings of the 9th Linear Accelerator Conference, Chalk River, Canada (A.E.C.L., Chalk River, 1976).
  36. J. Holma, The model and simulations of the LHC 400 MHz cavity controller, Technical Report No. CERN-AB-Note-2007-012, CERN, 2007.
  37. P. Baudrenghien and T. Mastoridis, I/Q model of the SPS 200 MHz travelling wave cavity and feedforward design, Technical Report No. CERN-ACC-NOTE-2020-0032, CERN, 2020.
  38. J. Coupard et al., LHC injectors upgrade, technical design report—volume 1: Protons, Technical Report No. CERN-ACC-2014-0337, CERN, 2014.
  39. R. Garoby, A non-adiabatic procedure in the PS to supply the nominal proton bunches for LHC into 200 MHz RF buckets in SPS, Technical Report No. CERN-PS-RF-Note-93-17, CERN, 1993.
  40. H. Timko, T. Argyropoulos, T. Bohl, H. Damerau, J. F. Esteban Müller, S. Hancock, and E. Shaposhnikova, Longitudinal transfer of rotated bunches in the CERN injectors, Phys. Rev. ST Accel. Beams 16, 051004 (2013).
  41. J. L. Laclare, Bunched beam coherent instabilities, in Proceedings of the CAS 1985, Oxford, United Kingdom (CERN, Geneva, Switzerland, 1987).
  42. A. Lasheen, T. Argyropoulos, T. Bohl, J. F. Esteban Müller, H. Timko, and E. Shaposhnikova, Beam measurement of the high frequency impedance sources with long bunches in the CERN Super Proton Synchrotron, Phys. Rev. Accel. Beams 21, 034401 (2018).
  43. L. Intelisano, H. Damerau, and I. Karpov, Threshold for loss of Landau damping in double-harmonic rf systems, Phys. Rev. Accel. Beams 28, 104402 (2025).
  44. D. Quartullo, S. Albright, H. Damerau, A. Lasheen, G. Papotti, and C. Zisou, RF voltage calibration using phase space tomography in the CERN SPS, in Proceedings of the 13th International Particle Accelerator Conference, Bangkok, Thailand (JACoW, Geneva, Switzerland, 2022).
  45. A. Lasheen, H. Damerau, I. Karpov, G. Papotti, and E. Vinten, Longitudinal collective effects at beam transfer from PS to SPS at CERN, in Proceedings of the 68th Advanced Beam Dynamics Workshop High-Intensity High-Brightness Hadron Beams (JACoW, Geneva, Switzerland, 2023).
  46. F. Antoniou, H. Bartosik, A. Huschauer, and A. Saa Hernandez, Transverse studies with ions at SPS flat bottom. in Proceedings of the Injector MD Days (CERN, Geneva, Switzerland, 2017).
  47. A. Saa Hernandez, F. Antoniuo, H. Bartosik, and A. Huschauer, Characterization of losses and emittance growth for ion beams on the SPS injection plateau, in Proceedings of the 9th International Particle Accelerator Conference, Vancouver, BC, Canada (JACoW, Geneva, Switzerland, 2018).
  48. G. Hagmann, P. Baudrenghien, J. D. Betz, J. Egli, G. Kotzian, M. Rizzi, L. Schmid, A. Spierer, T. Wlostowski, and F. J. Galindo Guarch, The CERN SPS low level rf upgrade project, in Proceedings of the 10th International Particle Accelerator Conference, Melbourne, Australia (JACoW, Geneva, Switzerland, 2019).
  49. K. Iliakis, H. Timko, S. Xydis, and D. Soudris, blond++: Performance analysis and optimizations for enabling complex, accurate and fast beam dynamics studies, in Proceedings of the 18th International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulations, Pythagorion, Greece (ACM, New York, NY, 2018).

Outline

Information

Phys. Rev. Accel. Beams 29, 032802– Published 10 March, 2026
  • Received 24 September 2025
  • Accepted 12 December 2025
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