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Analytical modeling and experimental verification of oscillatory ponderomotive instabilities in closed-loop superconducting rf cavities

Feng Qiu1,2,*, Jiayi Peng1,2, Shihui Wei1, Yilin Miao1,2, Zongheng Xue1, Rihua Zeng3, Zhenglong Zhu1, Tiancai Jiang1,2, Guirong Huang1,2 et al.

Zheng Gao1,2, Jinying Ma1,2, Chengye Xu1, Lijuan Yang1, Zhaojie Chen1,2, Qizheng Hou1,2, Ziqin Yang1,2, Liepeng Sun1,2, Zhijun Wang1,2, and Yuan He1,2,†

  • *Contact author: qiufeng@impcas.ac.cn
  • †Contact author: hey@impcas.ac.cn
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Phys. Rev. Accel. Beams 28, 112001 – Published 13 November, 2025

DOI: https://doi.org/10.1103/hs5q-q5xc

Abstract

Superconducting radio-frequency (SRF) cavities with high-loaded-Q are susceptible to ponderomotive instabilities arising from nonlinear electromechanical coupling. Under low-level rf feedback control, stability analysis is challenging and has, until now, lacked comprehensive experimental verification. In this work, we linearize the coupled cavity electromagnetic and mechanical equations about the operating point, deriving explicit small-signal stability criteria for both open- and closed-loop operation. A characteristic equation approach is used to map the oscillatory instability threshold in the detuning–gradient plane. Time-domain simulations confirm the predicted onset of self-excited oscillations at these thresholds. Furthermore, experiments on a 162.5 MHz SRF linac (CAFE2) show that the observed oscillation onset agrees with our analytical predictions within a small margin. By combining analytical modeling, numerical simulation, and direct experimentation, this study providescomprehensive validation of oscillatory ponderomotive instability theory under feedback control, offering practical guidance for the stable operation of high-gradient SRF accelerators.

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References (38)

  1. D. Gonnella, S. Aderhold, A. Burrill et al., Industrialization of the nitrogen-doping preparation for SRF cavities for LCLS-II, Nucl. Instrum. Methods Phys. Res., Sect. A 883, 143 (2018).
  2. E. R. Harms et al., LCSL-II cryomodule testing at Fermilab, in Proceedings of the 20th International Conference on RF Superconductivity, SRF’21, East Lansing, MI (JACoW, Geneva, Switzerland, 2021), THPFAV005, 10.18429/JACoW-SRF2021-THPFAV005.
  3. J. Branlard et al., Four years of successful operation of the European XFEL, in Proceedings of the 20th International Conference on RF Superconductivity, SRF’21, East Lansing, MI (JACoW, Geneva, Switzerland, 2021), MOOFAV06, 10.18429/JACoW-SRF2021-MOOFAV06.
  4. M. Martinello, D. J. Bice, C. Boffo et al., Q-factor optimization for high-beta 650 MHz cavities for PIP-II, J. Appl. Phys. 130, 174501 (2021).
  5. P. Sha, W. M. Pan, S. Jin et al., Ultrahigh accelerating gradient and quality factor of CEPC 650 MHz superconducting radio-frequency cavity, Nucl. Sci. Tech. 33, 125 (2022).
  6. M. X. Xu, Y. He, S. X. Zhang et al., Low beta superconducting cavity system design for HIAF iLinac, Nucl. Eng. Technol. 55, 2466 (2023).
  7. M. M. Yu, S. C. Huang, Y. Zhao et al., Study on the interstitial oxygen diffusion to understand the reduction of cryogenic rf loss for the superconducting radio-frequency niobium cavities, Supercond. Sci. Technol. 37, 105014 (2024).
  8. J. F. Chang, Y. Zong, X. Y. Pu et al., Ultra-high quality factor and ultra-high accelerating gradient achievements in a 1.3 GHz continuous wave cryomodule, Nucl. Sci. Tech. 36, 25 (2025).
  9. A. Neumann, W. Anders, O. Kugeler et al., Analysis and active compensation of microphonics in continuous-wave narrow-bandwidth superconducting cavities, Phys. Rev. ST Accel. Beams 13, 082001 (2010).
  10. A. Neumann, Ph.D. thesis, Humboldt-Universität zu Berlin, 2008, 10.18452/15848.
  11. Ziqin Yang, Yuan He, Zhijun Wang et al., Stable acceleration of a LHe-Free Nb3Sn demo SRF e-linac based on conduction cooling, in Proceedings of the TESLA Technology Collaboration Meeting, Lund, Sweden (2024), arXiv:2404.09187.
  12. F. Qiu, Z. L. Zhu, J. Y. Ma et al., An approach to characterize Lorentz-force transfer function for superconducting cavities, Nucl. Instrum. Methods Phys. Res., Sect. A 1012, 165633 (2021).
  13. D. Schulze, Ph.D. thesis, Argonne National Laboratory, 1971, https://inis.iaea.org/collection/NCLCollectionStore/_Public/05/094/5094490.pdf.
  14. J. R. Delayen, Ph.D. thesis, California Institute of Technology, 1978, https://www.researchgate.net/publication/236469097_Phase_and_amplitude_stabilization_of_beam-loaded_superconducting_resonators.
  15. S. R. Koscielniak, Ponderomotive instability of rf cavities with vector-sum control, and cure by difference control, in Proceedings of the LLRF Workshop 2019, Chicago, IL (2019), arXiv:1910.07106.
  16. S. R. Koscielniak, Ponderomotive instability of generator-driven cavity, in Proceedings of the 10th International Particle Accelerator Conference, IPAC-2019, Melbourne, Australia (JACoW, Geneva, Switzerland, 2019), THPRB010, 10.18429/JACoW-IPAC2019-THPRB010.
  17. S. R. Koscielniak, Ponderomotive instability of self-excited cavity, in Proceedings of the 10th International Particle Accelerator Conference, IPAC-2019, Melbourne, Australia (JACoW, Geneva, Switzerland, 2019), THPRB007, 10.18429/JACoW-IPAC2019-THPRB007.
  18. R. Leewe and K. Fong, Simulation analysis of Lorentz force induced oscillations in rf cavities in vector sum and cw operation, in Proceedings of the 10th International Particle Accelerator Conference, IPAC-2019, Melbourne, Australia (JACoW, Geneva, Switzerland, 2019), THPRB010, 10.18429/JACoW-SRF2019-THP076.
  19. A. Bellandi, Ph.D. thesis, Universität Hamburg, 2021, https://ediss.sub.uni-hamburg.de/bitstream/ediss/9139/1/LLRF_Control_Techniques_for_the_European_XFEL_Continuous_Wave_Upgrade__Copy_%285%29.pdf.
  20. A. Bellandi, J. Branlard, A. Eichler et al., Integral resonance control in continuous-wave superconducting particle accelerators, IFAC-Pap. Online 53, 361 (2020).
  21. L. Y. Gong, Z. J. Wang, W. P. Dou et al., Development of the heavy-ion RFQ for CAFE2, Nucl. Instrum. Methods Phys. Res., Sect. A 1058, 168819 (2024)..
  22. M. M. Zhang, J. G. Wang, L. Ma et al., Discovery of the α-emitting isotope Pa210, Nat. Commun. 16, 5003 (2025).
  23. X. Chen, Z. Wang, Y. He et al., Machine learning for online control of particle accelerators, Chin. Phys. B 68, 220511 (2025).
  24. L.-J. Yang, J.-Y. Peng, F. Qiu et al., Classification of superconducting radio-frequency cavity faults of CAFE2 using machine learning, Nucl. Sci. Tech. 36, 104 (2025).
  25. W. L. Zhan, Accelerator-driven sustainable fission energy, in Proceedings of the 7th International Particle Accelerator Conference, IPAC-2016, Busan, Korea (JACoW, Geneva, Switzerland, 2016), MOOFAV03.
  26. Z. J. Wang, S. H. Liu, W. L. Chen et al., Beam physics design of a superconducting linac, Phys. Rev. Accel. Beams 27, 010101 (2024).
  27. Z. J. Wang, Y. He, H. Jia et al., Beam commissioning for a superconducting proton linac, Phys. Rev. Accel. Beams 19, 120101 (2016).
  28. Y. He, Operation experience at CAFe, in Proceedings of the SRF-2021, Virtual Conference (2021), https://proceedings.jacow.org/srf2021/talks/moofav03_talk.pdf.
  29. F. Qiu, Y. He, A. D. Wu et al., In situ mitigation strategies for field emission-induced cavity faults using low-level radiofrequency system, Nucl. Sci. Tech. 33, 140 (2022).
  30. C. Xu, Z. Zhu, F. Qiu et al., Application of a modified iterative learning control algorithm for superconducting radio-frequency cavities, Nucl. Instrum. Methods Phys. Res., Sect. A 1026, 166237 (2022).
  31. Y. He, L. Shi, K. Jin et al., Development of solid-state amplifier for accelerator project based on the concept of standardization, Phys. Rev. Accel. Beams 26, 112002 (2023).
  32. T. Schilcher, Ph.D. thesis, Universität Hamburg, 1998, https://bib-pubdb1.desy.de/record/291638/files/schilcher.pdf.
  33. F. Qiu, S. Michizono, T. Miura et al., Real-time cavity simulator-based low-level radio-frequency test bench and applications for accelerators, Phys. Rev. Accel. Beams 21, 032003 (2018).
  34. F. Qiu, S. Michizono, T. Miura et al., Application of disturbance observer-based control in low-level radio-frequency system in a compact energy recovery linac at KEK, Phys. Rev. ST Accel. Beams 18, 092801 (2015).
  35. G. D. Jiang, C. Y. Xu, F. Qiu et al., Feedforward control strategies for rapid phase adjustment of superconducting cavities, IEEE Trans. Nucl. Sci. 70, 93 (2023).
  36. J. Y. Ma, F. Qiu, L. B. Shi et al., Precise calibration of cavity forward and reflected signals using a low-level radio-frequency system, Nucl. Sci. Tech. 33, 4 (2022).
  37. J. Y. Ma, C. Y. Xu, A. D. Wu et al., Measurement of the cavity-loaded quality factor in superconducting radio-frequency systems with mismatched source impedance, Nucl. Sci. Tech. 34, 123 (2023).
  38. J. Ma, L. Yang, F. Qiu et al., Application of a new cavity-loaded factor calibration algorithm on the test stand 2 facility at the European Spallation Source, Radiat. Detect. Technol. Methods 8, 1520 (2024).

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Phys. Rev. Accel. Beams 28, 112001– Published 13 November, 2025
  • Received 19 July 2025
  • Accepted 28 October 2025
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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.

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