- 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

Method for calculating the longitudinal space-charge tune shift suitable for arbitrary bunch lengths

Zihang Zhao*, Haisheng Xu†, and Na Wang‡

Zhilong Pan§

  • *Contact author: zhaozihang@ihep.ac.cn
  • †Contact author: xuhs@ihep.ac.cn
  • ‡Contact author: wangn@ihep.ac.cn
  • §Contact author: panzl@mail.tsinghua.edu.cn
PDF

Phys. Rev. Accel. Beams 28, 104201 – Published 15 October, 2025

DOI: https://doi.org/10.1103/kxbb-n27x

Abstract

The space-charge tune shift is a critical issue in circular proton, heavy-ion, and also low energy electron storage accelerators. Recently, some special electron rings with energies of several hundred MeV, nanometer-scale bunch lengths, and micrometer-scale bunch spacings have been proposed. In these novel rings, a significant longitudinal space-charge tune shift could be predicted by conventional methods. However, these methods may not be suitable when the bunches are extremely short. To address this issue, we derive a new set of formulas to calculate the longitudinal space-charge tune shift, which is applicable to arbitrary bunch lengths. These formulas incorporate the multibunch effects on the longitudinal space-charge tune shift, which have not been included in previous analyses of longitudinal space-charge tune shift calculations. The calculation results indicate that the tune shift predicted by our formulas is noticeably smaller than that obtained using the classical method. Moreover, our analysis demonstrates that the multibunch effect is not dominant in the longitudinal direction, even when the bunch spacing is extremely small.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (17)

  1. S. Machida, Space-charge-induced resonances in a synchrotron, Nucl. Instrum. Methods Phys. Res., Sect. A 384, 316 (1997).
  2. I. Hofmann, Typology of space charge resonances, in Proceedings of the ICFA Advanced Beam Dynamics Workshop on High-Intensity and High-Brightness Hadron Beams (HB’16), Malmö, Sweden (JACoW, Geneva, Switzerland, 2016), pp. 486–490, http://jacow.org/hb2016/papers/thpm1x01.pdf.
  3. F. Asvesta, H. Bartosik, A. Huschauer, and Y. Papaphilippou, Space charge driven resonances in the CERN PS, in Proceedings of the International Particle Accelerator Conference (IPAC’19), Melbourne, Australia (JACoW, Geneva, Switzerland, 2019), pp. 3216–3219, 10.18429/JACoW-IPAC2019-WEPTS047.
  4. D. F. Ratner and A. W. Chao, Steady-state microbunching in a storage ring for generating coherent radiation, Phys. Rev. Lett. 105, 154801 (2010).
  5. A. Chao, E. Granados, X. Huang, H. Luo, and D. Ratner, High power radiation sources using the steady-state microbunching mechanism, in Proceedings of the International Particle Accelerator Conference (IPAC’16), Busan, Korea (JACoW, Geneva, Switzerland, 2016), pp. 1048–1053, 10.18429/JACoW-IPAC2016-TUXB01.
  6. X. Deng. Theoretical and experimental studies on steady-state microbunching, Ph.D. thesis, Tsinghua University, 2021.
  7. X. Deng, A. W. Chao, J. Feikes, A. Hoehl, W. Huang, R. M. Klein, A. Kruschinski, J. Li, A. Matveenko, Y. Petenev, M. Ries, C. Tang, and L. Yan, Experimental demonstration of the mechanism of steady-state microbunching, Nature (London) 590, 576 (2021).
  8. C. Li, B. Jiang, C. Feng, D. Huang, Q. Zhang, and K. Wang, Lattice design for angular dispersion enhanced microbunching in storage rings lattice design for angular dispersion enhanced microbunching in storage rings, J. Instrum. 16, P03004 (2021).
  9. C. Steier et al., Design progress of ALS-U, the soft x-ray diffraction limited upgrade of the advanced light source, in Proceedings of the 10th International Particle Accelerator Conference (IPAC’19), Melbourne, Australia (JACoW, Geneva, Switzerland, 2019), pp. 1639–1642, 10.18429/JACoW-IPAC2019-TUPGW097.
  10. R. Hettel, Status of the APS-U project, in Proceedings of the 12th International Particle Accelerator Conference (IPAC’21), Campinas, SP, Brazil (JACoW, Geneva, Switzerland, 2021), pp. 7–12, 10.18429/JACoW-IPAC2021-MOXA02.
  11. H. Xu, C. Meng, Y. Peng, T. Saike, N. Wang, X. Cui, C. Du, Z. Duan, Y. Guo, P. He, X. Huang, D. Ji, H. Ji, Y. Jiao, J. Li, N. Li, X. Li, X. Lu, P. Liang, and Y. Zhao, Equilibrium electron beam parameters of the high energy photon source, Radiat. Detect. Technol. Methods 7, 279 (2023).
  12. Z. Zhao, N. Wang, H. Xu, and Z. Pan, Calculations of space-charge tune shifts in storage rings with extremely short bunches and small bunch spacing, Phys. Rev. Accel. Beams 27, 094201 (2024).
  13. V. N. Litvinenko and G. Wang, Compensating tune spread induced by space charge in bunched beams, Phys. Rev. ST Accel. Beams 17, 114401 (2014).
  14. https://github.com/zhaozihang229-spec/PRAB25.git.
  15. A. W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (Wiley-Interscience Publication, New York, 1993), Chap. 1, pp. 13–20.
  16. H. Wiedemann, Particle Accelerator Physics (Springer, California, 2015), Chaps. 2.1, 2.6, pp. 725–726.
  17. M. Ferrario, M. Migliorati, and L. Palumbo, Space charge effects, arXiv:1601.05214.

Outline

Information

Phys. Rev. Accel. Beams 28, 104201– Published 15 October, 2025
  • Received 20 December 2024
  • Accepted 19 September 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