- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Determination of few femtosecond to attosecond electron bunch durations using a passive plasma lens

Andreas Seidel1,2,3,*, Carola Zepter1,2, Alexander Sävert1,2,3, Stephan Kuschel4,†, and Matt Zepf1,2,3

  • *Contact author: seidel.andreas@uni-jena.de
  • †Contact author: stephan.kuschel@tu-darmstadt.de
PDF

Phys. Rev. Research 8, 023131 – Published 7 May, 2026

DOI: https://doi.org/10.1103/zj11-6zxc

Abstract

Determining the pulse duration of femtosecond electron bunches is challenging and often experimentally invasive. An effective method for measuring the duration based on the time-dependent variations in electron beam divergence induced by a passive plasma lens is described. Reconstruction of the temporal shape of the electron bunch down to c×dt=10nm (∼30as) without external RF cavities or multioctave spanning spectrometer is shown numerically. Experimental data from an ∼3 fs electron bunch demonstrates practical applicability of this method. While this approach can be used with any high-current electron beam, it is particularly well suited to laser-driven and particle-driven wakefield accelerators, which accommodate electron beams with a time-dependent beam energy (e.g., “chirp”).

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (36)

  1. T. Tajima and J. M. Dawson, Laser electron accelerator, Phys. Rev. Lett. 43, 267 (1979).
  2. A. J. Gonsalves, K. Nakamura, J. Daniels, C. Benedetti, C. Pieronek, T. C. H. de Raadt, S. Steinke, J. H. Bin, S. S. Bulanov, J. van Tilborg, et al., Petawatt laser guiding and electron beam acceleration to 8 GeV in a laser-heated capillary discharge waveguide, Phys. Rev. Lett. 122, 084801 (2019).
  3. O. Zarini, J. C. Cabadağ, Y.-Y. Chang, A. Köhler, T. Kurz, S. Schöbel, W. Seidel, M. Bussmann, U. Schramm, A. Irman, and A. Debus, Multioctave high-dynamic range optical spectrometer for single-pulse, longitudinal characterization of ultrashort electron bunches, Phys. Rev. Accel. Beams 25, 012801 (2022).
  4. K. Huang, Z. Jin, N. Nakanii, T. Hosokai, and M. Kando, Electro-optic 3D snapshot of a laser wakefield accelerated kilo-ampere electron bunch, Light: Sci. Appl. 13, 84 (2024).
  5. M. Galletti, R. Assmann, M. E. Couprie, M. Ferrario, L. Giannessi, A. Irman, R. Pompili, and W. Wang, Prospects for free-electron lasers powered by plasma-wakefield-accelerated beams, Nat. Photonics 18, 780 (2024).
  6. B. Hidding, R. Assmann, M. Bussmann, D. Campbell, Y.-Y. Chang, S. Corde, J. C. Cabadağ, A. Debus, A. Döpp, M. Gilljohann, et al., Progress in hybrid plasma wakefield acceleration, Photonics 10, 99 (2023).
  7. B. Foster, R. D’Arcy, and C. A. Lindstrøm, A hybrid, asymmetric, linear Higgs factory based on plasma-wakefield and radio-frequency acceleration, New J. Phys. 25, 093037 (2023).
  8. S. A. Antipov, A. F. Pousa, I. Agapov, R. Brinkmann, A. R. Maier, S. Jalas, L. Jeppe, M. Kirchen, W. P. Leemans, A. M. de la Ossa, J. Osterhoff, M. Thévenet, and P. Winkler, Design of a prototype laser-plasma injector for an electron synchrotron, Phys. Rev. Accel. Beams 24, 111301 (2021).
  9. C. Behrens, F.-J. Decker, Y. Ding, V. A. Dolgashev, J. Frisch, Z. Huang, P. Krejcik, H. Loos, A. Lutman, T. J. Maxwell, J. Turner, J. Wang, M.-H. Wang, J. Welch, and J. Wu, Few-femtosecond time-resolved measurements of X-ray free-electron lasers, Nat. Commun. 5, 3762 (2014).
  10. V. A. Dolgashev, G. Bowden, Y. Ding, P. Emma, P. Krejcik, J. Lewandowski, C. Limborg, M. Litos, J. Wang, and D. Xiang, Design and application of multimegawatt x-band deflectors for femtosecond electron beam diagnostics, Phys. Rev. Spec. Top. Accel. Beams 17, 102801 (2014).
  11. L. Zhao, Z. Wang, C. Lu, R. Wang, C. Hu, P. Wang, J. Qi, T. Jiang, S. Liu, Z. Ma, et al., Terahertz streaking of few-femtosecond relativistic electron beams, Phys. Rev. X 8, 021061 (2018).
  12. M. Kozák, J. McNeur, K. J. Leedle, H. Deng, N. Schönenberger, A. Ruehl, I. Hartl, J. S. Harris, R. L. Byer, and P. Hommelhoff, Optical gating and streaking of free electrons with sub-optical cycle precision, Nat. Commun. 8, 14342 (2017).
  13. 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).
  14. A. Buck, M. Nicolai, K. Schmid, C. M. S. Sears, A. Sävert, J. M. Mikhailova, F. Krausz, M. C. Kaluza, and L. Veisz, Real-time observation of laser-driven electron acceleration, Nat. Phys. 7, 543 (2011).
  15. S. K. Barber, J. H. Bin, A. J. Gonsalves, F. Isono, J. van Tilborg, S. Steinke, K. Nakamura, A. Zingale, N. A. Czapla, D. Schumacher, C. B. Schroeder, C. G. R. Geddes, W. P. Leemans, and E. Esarey, A compact, high resolution energy, and emittance diagnostic for electron beams using active plasma lenses, Appl. Phys. Lett. 116, 234108 (2020).
  16. S. K. Barber, J. V. Tilborg, C. B. Schroeder, R. Lehe, H. E. Tsai, K. K. Swanson, S. Steinke, K. Nakamura, C. G. R. Geddes, C. Benedetti, E. Esarey, and W. P. Leemans, Measured emittance dependence on the injection method in laser plasma accelerators, Phys. Rev. Lett. 119, 104801 (2017).
  17. C. A. Lindstrøm, E. Adli, G. Boyle, R. Corsini, A. E. Dyson, W. Farabolini, S. M. Hooker, M. Meisel, J. Osterhoff, J.-H. Röckemann, L. Schaper, and K. N. Sjobak, Emittance preservation in an aberration-free active plasma lens, Phys. Rev. Lett. 121, 194801 (2018).
  18. S. Kuschel, D. Hollatz, T. Heinemann, O. Karger, M. B. Schwab, D. Ullmann, A. Knetsch, A. Seidel, C. Rödel, M. Yeung, M. Leier, A. Blinne, H. Ding, T. Kurz, D. J. Corvan, A. Sävert, S. Karsch, M. C. Kaluza, B. Hidding, and M. Zepf, Demonstration of passive plasma lensing of a laser wakefield accelerated electron bunch, Phys. Rev. Accel. Beams 19, 071301 (2016).
  19. C. Thaury, E. Guillaume, A. Döpp, R. Lehe, A. Lifschitz, K. Ta Phuoc, J. Gautier, J.-P. Goddet, A. Tafzi, A. Flacco, F. Tissandier, S. Sebban, A. Rousse, and V. Malka, Demonstration of relativistic electron beam focusing by a laser-plasma lens, Nat. Commun. 6, 6860 (2015).
  20. C. E. Doss, E. Adli, R. Ariniello, J. Cary, S. Corde, B. Hidding, M. J. Hogan, K. Hunt-Stone, C. Joshi, K. A. Marsh, J. B. Rosenzweig, N. Vafaei-Najafabadi, V. Yakimenko, and M. Litos, Laser-ionized, beam-driven, underdense, passive thin plasma lens, Phys. Rev. Accel. Beams 22, 111001 (2019).
  21. C. E. Doss, R. Ariniello, J. R. Cary, S. Corde, H. Ekerfelt, E. Gerstmayr, S. J. Gessner, M. Gilljohann, C. Hansel, B. Hidding, M. J. Hogan, A. Knetsch, V. Lee, K. Marsh, B. O’Shea, P. San Miguel Claveria, D. Storey, A. Sutherland, C. Zhang, and M. D. Litos, Underdense plasma lens with a transverse density gradient, Phys. Rev. Accel. Beams 26, 031302 (2023).
  22. R. Keinigs and M. E. Jones, Two-dimensional dynamics of the plasma wakefield accelerator, Phys. Fluids 30, 252 (1987).
  23. L. Verra, Electron bunch seeding of the self-modulation instability in plasma, Ph.D. thesis, Technische Universität München, 2022.
  24. B. Allen, V. Yakimenko, M. Babzien, M. Fedurin, K. Kusche, and P. Muggli, Experimental study of current filamentation instability, Phys. Rev. Lett. 109, 185007 (2012).
  25. E. Esarey and M. Pilloff, Trapping and acceleration in nonlinear plasma waves, Phys. Plasmas 2, 1432 (1995).
  26. M. Reiser, Theory and Design of Charged Particle Beams (WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2008).
  27. E. D. Courant and H. S. Snyder, Theory of the alternating-gradient synchrotron, Ann. Phys. 3, 1 (1958).
  28. ANSYS, Inc., ANSYS Fluent User’s Guide, version 2019R1, 2019.
  29. M. J. Hüther, Design and characterisation of supersonic nozzles for shock front electron injection in laser wakefield acceleration, Master’s thesis, Ludwig-Maximilians-Universität München, 2015.
  30. T. Kurz, J. P. Couperus, J. M. Krämer, H. Ding, S. Kuschel, A. Köhler, O. Zarini, D. Hollatz, D. Schinkel, R. D’Arcy, J.-P. Schwinkendorf, J. Osterhoff, A. Irman, U. Schramm, and S. Karsch, Calibration and cross-laboratory implementation of scintillating screens for electron bunch charge determination, Rev. Sci. Instrum. 89, 093303 (2018).
  31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zj11-6zxc for a description of the focusing with constant magnetic field gradient down to an electron energy of 1 MeV.
  32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zj11-6zxc for a detailed description of the analytic reconstruction of the longitudinal bunch profile.
  33. R. Lehe, M. Kirchen, I. A. Andriyash, B. B. Godfrey, and J.-L. Vay, A spectral, quasi-cylindrical and dispersion-free particle-in-cell algorithm, Comput. Phys. Commun. 203, 66 (2016).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zj11-6zxc for guidelines about the correct parameters for the plasma lens with respect to the electron bunch.
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zj11-6zxc for insights on the impact of a short initial bandwidth of 20 MeV of the electron bunch on the bunch-plasma lens interaction.
  36. A. Seidel, C. Zepter, A. Sävert, S. Kuschel, and M. Zepf, Determination of few femtosecond to attosecond electron bunch durations using a passive plasma lens, Zenodo (2025), http://doi.org/10.5281/zenodo.15784529.

Outline

Information

Phys. Rev. Research 8, 023131– Published 7 May, 2026
  • Received 1 July 2025
  • Accepted 23 February 2026
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