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Transverse beam instabilities in low-emittance booster synchrotrons

W. Foosang, A. Gamelin*, V. Gubaidulin, and R. Nagaoka

  • *Contact author: alexis.gamelin@synchrotron-soleil.fr
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Phys. Rev. Accel. Beams 28, 094402 – Published 16 September, 2025

DOI: https://doi.org/10.1103/w638-psr8

Abstract

As the ring-based light source community is moving toward fourth-generation light sources, many facilities plan to upgrade their boosters in parallel to meet the more demanding beam properties for the storage ring, especially in terms of a much lower emittance. Concerns over collective effects have, therefore, risen, particularly in the transverse planes, since the vacuum chamber dimensions tend to be reduced as a way to achieve a stronger focusing force on the beam. In this article, we present numerical studies on transverse beam instabilities, both in the single- and multibunch regimes, in the SOLEIL II booster as an example of a low-emittance booster. We show that Landau damping is an efficient mechanism for suppressing both transverse single-bunch and coupled-bunch instabilities. We also prove that the damping in the longitudinal plane can diffuse to the transverse plane and limit the transverse emittance growth. Moreover, we have discovered that the beam can exhibit sawtooth instability at high energy and that broadband impedance is one of the key factors in suppressing transverse coupled-bunch instability.

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References (40)

  1. Synchrotron SOLEIL, Conceptual design report for the SOLEIL upgrade, https://www.synchrotron-soleil.fr/en/news/conceptual-design-report-soleil-upgrade (2021).
  2. A. Nadji and L. S. Nadolski, Upgrade project of the SOLEIL accelerator complex, Synchrotron Radiat. News 36, 1 (2023).
  3. J. Susini, J.-M. Cassagne, B. Gagey, A. Nadji, A. Taleb, A. Thompson, and J. Daillant, A brief introduction to the synchrotron SOLEIL and its upgrade programme, Eur. Phys. J. Plus 139, 80 (2024).
  4. H. Xu, Y. Peng, and N. Wang, Studies of transverse single-bunch instabilities in booster synchrotrons, Nucl. Instrum. Methods Phys. Res., Sect. A 940, 313 (2019).
  5. R. Husain, P. Burrows, R. T. Fielder, and I. P. S. Martin, Evolution of equilibrium parameters ramp including collective effects in the Diamond-II booster, in Proceedings of the FLS’23 (JACoW, Geneva, Switzerland, 2024), Vol. 67, pp. 120–123, 10.18429/JACoW-FLS2023-TU4P19.
  6. R. Husain, R. Fielder, I. Martin, and S. Wang, Studies for single bunch and multi-bunch beam instabilities in the Diamond-II booster, in Proceedings of the IPAC-2024 (JACoW, Geneva, Switzerland, 2024), Vol. 15, pp. 1243–1246, 10.18429/JACoW-IPAC2024-TUPG18.
  7. M.-A. Tordeux, P. Alexandre, R. Ben El Fekih, P. Brunelle, L. Hoummi, A. Loulergue, L. Nadolski, and R. Nagaoka, Injection schemes for the SOLEIL upgrade, in Proceedings of the IPAC-2021 (JACoW, Geneva, Switzerland, 2021), pp. 796–798, 10.18429/JACoW-IPAC2021-MOPAB248.
  8. M.-A. Tordeux, Z. Bai, G. Liu, A. Loulergue, R. Nagaoka, and T. Zhang, A low-emittance booster lattice design for the SOLEIL upgrade, in Proceedings of the IPAC-2021, International Particle Accelerator Conference No. 12 (JACoW, Geneva, Switzerland, 2021), Vol. 12, pp. 410–413, 10.18429/JACoW-IPAC2021-MOPAB113.
  9. M.-A. Tordeux, P. Alexandre, F. Marteau, C. Kitegi, T. Souské, V. Leroux, N. Bechu, F. Bouvet, E. Dupuy, N. Hubert, M. Labat, A. Moutardier, A. Lejollec, S. Thoreau, M. Diop et al., Progress on the new booster for SOLEIL II, in Proceedings of the IPAC-2023 (JACoW, Geneva, Switzerland, 2023), pp. 2025–2030, https://accelconf.web.cern.ch/ipac2023/pdf/WEPL072.pdf.
  10. W. Foosang, Study of transverse beam instabilities in the SOLEIL II synchrotron booster, Ph.D. thesis, Université Paris-Saclay, 2023, https://theses.hal.science/tel-04496043.
  11. A. Gamelin, W. Foosang, and R. Nagaoka, mbtrack2, a collective effect library in python, in Proceedings of the IPAC-2021 (JACoW, Geneva, Switzerland, 2021), pp. 282–285, 10.18429/JACoW-IPAC2021-MOPAB070.
  12. A. Gamelin, W. Foosang, N. Yamamoto, V. Gubaidulin, and R. Nagaoka, mbtrack2 (0.7.0), 10.5281/zenodo.12749990 (2024).
  13. L. Tosi, V. Smaluk, and E. Karantzoulis, Landau damping via the harmonic sextupole, Phys. Rev. ST Accel. Beams 6, 054401 (2003).
  14. L. D. Landau, On the vibrations of the electronic plasma, in Collected Papers of L.D. Landau, edited by D. Ter Haar (Pergamon, New York, 1965), p. 460, 10.1016/B978-0-08-010586-4.50066-3.
  15. H. G. Hereward, Landau damping, in CERN Accelerator School: Accelerator Physics, Oxford, UK, 1985 (CERN, 1987), https://cds.cern.ch/record/1542436.
  16. W. Herr, Introduction to Landau damping, in CERN Accelerator School: Advanced Accelerator Physics Course, Trondheim, Norway, 2013 (CERN, 2014), 10.5170/CERN-2014-009.377.
  17. E. Métral et al., Beam instabilities in hadron synchrotrons, IEEE Trans. Nucl. Sci. 63, 1001 (2016).
  18. E. Métral, General mitigation techniques for coherent beam instabilities in particle accelerators, Eur. Phys. J. Plus 137, 47 (2022).
  19. X. Buffat, W. Herr, N. Mounet, T. Pieloni, and S. White, Stability diagrams of colliding beams in the Large Hadron Collider, Phys. Rev. ST Accel. Beams 17, 111002 (2014).
  20. J. S. Berg and F. Ruggiero, Landau damping with two-dimensional betatron tune spread, Technical Report No. CERN-SL-AP-96-071-AP, CERN, 1996, https://inspirehep.net/literature/428328.
  21. A. Burov, Nested head-tail Vlasov solver, Phys. Rev. ST Accel. Beams 17, 021007 (2014).
  22. V. Gubaidulin, V. Kornilov, O. Boine-Frankenheim, and E. Métral, Landau damping of transverse head-tail instabilities with a pulsed electron lens in hadron synchrotrons, Phys. Rev. Accel. Beams, 25, 084401 (2022).
  23. W. Foosang, A. Gamelin, M.-A. Tordeux, and P. Alexandre, Resistive-wall instability evaluation along the ramp in the SOLEIL II booster, J. Phys. Conf. Ser. 2687, 062017 (2024).
  24. R. D. Kohaupt, Single beam instabilities in petra, IEEE Trans. Nucl. Sci. 26, 3480 (1979).
  25. R. Ruth, CERN report LEP-TH/83-22, in Proceedings of IEEE Particle Accelerator Conference (IEEE, New York, 1983), p. 503.
  26. A. W. Chao, Physics of Collective Beam Instabilities in High-Energy Accelerators, 1st ed. (Wiley-VCH, New York, 1993), pp. 178–191.
  27. M. Schenk, X. Buffat, K. Li, and A. Maillard, Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities, Phys. Rev. Accel. Beams 21, 084402 (2018).
  28. K. C. Harkay, M. Borland, Y. Chae, L. Emery, Z. Huang, E. S. Lessner, A. H. Lumpkin, S. Milton, N. S. Sereno, and B. X. Yang, Impedance and the single bunch limit in the APS storage ring, in Proceedings of the 18th Biennial Particle Accelerator Conference (IEEE Computer Society Press, Piscataway, NJ, 1999), pp. 1644–1646, https://cds.cern.ch/record/553749.
  29. K. C. Harkay, Z. Huang, E. Lessner, and B. X. Yang, Transverse Sawtooth instability at the advanced photon source, in Proceedings of the 19th IEEE Particle Accelerator Conference (IEEE, New York, 2001), pp. 1915–1917, https://cds.cern.ch/record/556224.
  30. M. Brosi, F. Cullinan, A. Andersson, J. Breunlin, and P. F. Tavares, Asymmetric influence of the amplitude-dependent tune shift on the transverse mode-coupling instability, Phys. Rev. Accel. Beams 27, 104402 (2024).
  31. T. Suzuki, Fokker-Planck theory of transverse mode coupling instability, Part. Accel. 20, 79 (1986), https://inspirehep.net/literature/228210.
  32. 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).
  33. N. Mounet, Vlasov solvers and macroparticle simulations, in Proceedings of ICFA Mini-Workshop on Impedances and Beam Instabilities in Particle Accelerators (CERN, Geneva, 2018), Vol. 1, 10.23732/CYRCP-2018-001.77.
  34. R. Nagaoka and K. L. F. Bane, Collective effects in a diffraction-limited storage ring, J. Synchrotron Radiat. 21, 937 (2014).
  35. A. Wolski, Low-emittance storage rings, presented at the CERN Accelerator School (2014), arXiv:1507.02213.
  36. G. Skripka, R. Nagaoka, M. Klein, F. Cullinan, and P. F. Tavares, Simultaneous computation of intrabunch and interbunch collective beam motions in storage rings, Nucl. Instrum. Methods Phys. Res., Sect. A 806, 221 (2016).
  37. F. Pedersen, Multibunch instabilities, Technical Report No. CERN-PS-93-36-RF, CERN, 1994, http://cds.cern.ch/record/254071.
  38. S. White, L. Carver, L. Farvacque, and S. Liuzzo, Status and recent developments of python accelerator toolbox, in Proceedings of the IPAC-2023 (JACoW, Geneva, Switzerland, 2023), pp. 3185–3188, 10.18429/JACOW-IPAC2023-WEPL031.
  39. F. J. Sacherer, Transverse bunched beam instabilities-theory, in Proceedings of the HEACC’74 (US Atomic Energy Commission, Washington, DC, 1974), pp. 347–351, https://cds.cern.ch/record/322645/files/HEACC74_368-372.pdf.
  40. A. W. Chao and M. Tigner, Effective impedance, in Handbook of Accelerator Physics and Engineering, 3rd ed. (World Scientific, Singapore, 2006), p. 238.

Outline

Information

Phys. Rev. Accel. Beams 28, 094402– Published 16 September, 2025
  • Received 10 October 2024
  • Revised 14 June 2025
  • Accepted 27 August 2025
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