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  • Open Access

Vlasov solver for transverse mode coupling instability of double-rf system under arbitrary settings

Jingye Xu, Liyan Qin, and Haisheng Xu*

  • *Contact author: xuhs@ihep.ac.cn
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Phys. Rev. Accel. Beams 28, 114401 – Published 24 November, 2025

DOI: https://doi.org/10.1103/x4gh-6c78

Abstract

The Vlasov solver provides an efficient method to analyze transverse mode coupling instability (TMCI). However, many traditional Vlasov solvers are based on the small amplitude approximation, and are applicable only to single rf (radio frequency) systems, whereas harmonic cavities are widely utilized in colliders and synchrotron light sources to improve beam stability. In this paper, we have developed a new Vlasov solver suitable for any double rf system to study TMCI. The results of the Vlasov solver are in good agreement with the simulation results obtained using elegant.

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References (33)

  1. P. F. Tavares, S. C. Leemann, M. Sjöström, and Å. Andersson, The MAXIV storage ring project, J. Synchrotron Radiat. 21, 862 (2014).
  2. L. Liu, N. Milas, A. H. C. Mukai, X. R. Resende, and F. H. de Sá, The Sirius project, J. Synchrotron Radiat. 21, 904 (2014).
  3. A. Streun, T. Garvey, L. Rivkin, V. Schlott, T. Schmidt, P. Willmott, and A. Wrulich, SLS-2–The upgrade of the Swiss Light Source, J. Synchrotron Radiat. 25, 631 (2018).
  4. Y. Jiao, G. Xu, X.-H. Cui, Z. Duan, Y.-Y. Guo, P. He, D.-H. Ji, J.-Y. Li, X.-Y. Li, C. Meng, Y.-M. Peng, S.-K. Tian, J.-Q. Wang, N. Wang, Y.-Y. Wei, H.-S. Xu, F. Yan, C.-H. Yu, Y.-L. Zhao, and Q. Qin, The HEPS project, J. Synchrotron Radiat. 25, 1611 (2018).
  5. H. Xu et al., Equilibrium electron beam parameters of the high energy photon source, Radiat. Detect. Technol. Methods 7, 279 (2023).
  6. R. Hettel, Status of the APS-U project, in Proceedings of the 12th International Particle Accelerator Conference, IPAC-2021, Campinas, SP, Brazil (JACoW, Geneva, Switzerland, 2021), pp. 7–12.
  7. A. Hofmann and S. Myers, Beam dynamics in a double rf system, in 11th International Conference on High-Energy Accelerators: Geneva, Switzerland (Birkhäuser, Basel, 1980), pp. 610–614.
  8. R. Biscardi, S. Kramer, and G. Ramirez, Bunch length control in the NSLS VUV ring, Nucl. Instrum. Methods Phys. Res., Sect. A 366, 26 (1995).
  9. Joseph M. Kats. Bucket parameters and bunching factor for double rf system, Technical Note AGS/AD/Technical Note No. 378, Accelerator Division, Brookhaven National Laboratory, Upton, NY, 1993.
  10. Y.-C. Chae and J. Keil, Control of collective effects by active harmonic cavity in an MBA-based light source with application to the PETRA upgrade, in Proceedings of the 9th International Particle Accelerator Conference IPAC’-2018, Vancouver, BC, Canada (JACoW, Geneva, Switzerland, 2018), pp. 1433–1435, 10.18429/JACoW-IPAC2018-TUPMF074.
  11. J. Byrd, S. Santis, M. Georgsson, G. Stover, J. Fox, and D. Teytelman, Commissioning of a higher harmonic rf system for the advanced light source, Nucl. Instrum. Methods Phys. Res., Sect. A 455, 271 (2000).
  12. J. M. Byrd and M. Georgsson, Lifetime increase using passive harmonic cavities in synchrotron light sources, Phys. Rev. ST Accel. Beams 4, 030701 (2001).
  13. 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).
  14. T. Phimsen, B.-C. Jiang, H.-T. Hou, S.-Q. Tian, M.-Z. Zhang, Q.-L. Zhang, and Z.-T. Zhao, Improving Touschek lifetime and synchrotron frequency spread by passive harmonic cavity in the storage ring of SSRF, Nucl. Sci. Tech. 282017).
  15. H.-S. Xu, J.-Y. Xu, and N. Wang, Influences of harmonic cavities on single-bunch instabilities in electron storage rings, Nucl. Sci. Tech. 322021).
  16. R. Nagaoka and K. L. F. Bane, Collective effects in a diffraction-limited storage ring, J. Synchrotron Radiat. 21, 937 (2014).
  17. F. Sacherer, Methods for computing bunched-beam instabilities, Reports No. CERN-SI-BR-72-5, No. CERN-SI-Int-BR-72-5, CERN, Geneva, 1972.
  18. N. Mounet, Delphi: An analytic Vlasov solver for impedance-driven modes, Report No. CERN-ACC-SLIDES-2014-0066, CERN, Geneva, 2014.
  19. A. Burov, Nested head-tail Vlasov solver, Phys. Rev. ST Accel. Beams 17, 021007 (2014).
  20. M. Venturini, Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall, Phys. Rev. Accel. Beams 21, 024402 (2018).
  21. A. W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (John Wiley & Sons, Inc., New York, 1993).
  22. J. Haïssinski, Exact longitudinal equilibrium distribution of stored electrons in the presence of self-fields, Nuovo Cimento Soc. Ital. Fis. 18B, 72 (1973).
  23. A. Mosnier, Microwave instability in electron storage rings, Nucl. Instrum. Methods Phys. Res., Sect. A 438, 225 (1999).
  24. Y. Cai, Linear theory of microwave instability in electron storage rings, Phys. Rev. ST Accel. Beams 14, 061002 (2011).
  25. K. Oide, A mechanism of longitudinal single bunch instability in storage rings, Part. Accel. 51, 43 (1995), https://inspirehep.net/literature/379763.
  26. J. W. Connor, R. J. Hastie, and J. B. Taylor, Shear, periodicity, and plasma ballooning modes, Phys. Rev. Lett. 40, 396 (1978).
  27. J. W. Connor, R. J. Hastie, and J. B. Taylor, High mode number stability of an axisymmetric toroidal plasma, Proc. R. Soc. A 365, 1 (1979).
  28. C. Lin, K. Ohmi, and Y. Zhang, Coupling effects of beam-beam interaction and longitudinal impedance, Phys. Rev. Accel. Beams 25, 011001 (2022).
  29. H.-S. Xu, C.-T. Lin, N. Wang, J.-Y. Xu, and Y. Zhang, Transverse mode-coupling instability with longitudinal impedance, Nucl. Sci. Tech. 352024).
  30. N. Kuroo, K. Ohmi, K. Oide, D. Zhou, and F. Zimmermann, Cross-wake force and correlated head-tail instability in beam-beam collisions with a large crossing angle, Phys. Rev. Accel. Beams 21, 031002 (2018).
  31. https://github.com/LiyanQ1n/TMCI_Vlasov_Solver_Arbitary_double_RF_Settings.git.
  32. S. Y. Lee, Accelerator Physics, 4th ed. (World Scientific, Singapore, 2019).
  33. A. W. Chao, Coherent instabilities of a relativistic bunched beam, AIP Conf. Proc. 105, 353 (1983).

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Phys. Rev. Accel. Beams 28, 114401– Published 24 November, 2025
  • Received 17 March 2025
  • Accepted 10 October 2025
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