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

Noninterferometric method for transverse electron beam size diagnostic with synchrotron radiation at a free-electron laser

Andrei Trebushinin*,†

Svitozar Serkez†

Wolfgang Freund, Giovanni Perosa, Andreas Koch, Jan Grünert, and Gianluca Geloni

Weilun Qin‡ and Sergey Tomin2

  • *Contact author: andrei.trebushinin@xfel.eu.
  • †These authors contributed equally to this work.
  • ‡Present address: Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China and Spallation Neutron Source Science Center, Dongguan 523803, China.

Phys. Rev. Accel. Beams 28, 112801 – Published 20 November, 2025

DOI: https://doi.org/10.1103/31gl-qyk7

Abstract

We present a noninterferometric method for measuring the transverse electron beam size at the European XFEL based on synchrotron radiation intensity autocorrelation. The technique enables cell-by-cell diagnostics along the SASE1 undulator using existing hardware: a commissioning monochromator and a spatial x-ray detector. We extend the results of [A. Trebushinin et al., companion paper, First observation of synchrotron radiation spikes for transverse electron beam size measurements at a free-electron laser, Phys. Rev. Lett. 135, 215001 (2025).] focusing on data analysis procedures and technical implementation. Our method allows for extraction of the beam size from noisy measured intensity distributions with a signal-to-noise ratio as low as 0.9 and is capable of distinguishing between the projected and slice sizes. To validate our approach, we introduced a mismatch in the magnetic lattice, inducing a controlled sinusoidal variation in the beam size along the undulator. The corresponding modulation was clearly reproduced in the electron beam size values extracted from the autocorrelation measurements. This method offers a practical solution for transverse electron beam size diagnostics in high-energy linacs, with direct application to the operation and tuning of free-electron laser facilities.

View figure in article

Physics Subject Headings (PhySH)

See Also

Observation of Synchrotron Radiation Spikes for Transverse Electron Beam Size Measurements at a Free-Electron Laser

Andrei Trebushinin, Svitozar Serkez, Wolfgang Freund, Andreas Koch, Jan Grünert, Gianluca Geloni, Weilun Qin, and Sergey Tomin
Phys. Rev. Lett. 135, 215001 (2025)

Article Text

Supplemental Material

References (61)

  1. P. Emma, J. Frisch, and P. Krejcik, A transverse RF deflecting structure for bunch length and phase space diagnostics, SLAC National Accelerator Laboratory Technical Report No. LCLS-TN-00-12, https://www-ssrl.slac.stanford.edu/lcls/technotes/lcls-tn-00-12.pdf.
  2. R. Akre, L. Bentson, P. Emma, and P. Krejcik, A transverse rf deflecting structure for bunch length and phase space diagnostics, in PACS2001, in Proceedings of the 19th Particle Accelerator Conference, Chicago, IL, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 3, pp. 2353–2355, 10.1109/PAC.2001.987379.
  3. Y. Ding, C. Behrens, P. Emma, J. Frisch, Z. Huang, H. Loos, P. Krejcik, and M.-H. Wang, Femtosecond x-ray pulse temporal characterization in free-electron lasers using a transverse deflector, Phys. Rev. ST Accel. Beams 14, 120701 (2011).
  4. 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).
  5. A. A. Lutman, Y. Ding, Y. Feng, Z. Huang, M. Messerschmidt, J. Wu, and J. Krzywinski, Femtosecond x-ray free electron laser pulse duration measurement from spectral correlation function, Phys. Rev. ST Accel. Beams 15, 030705 (2012).
  6. S. Serkez, O. Gorobtsov, D. E. Rivas, M. Meyer, B. Sobko, N. Gerasimova, N. Kujala, and G. Geloni, Wigner distribution of self-amplified spontaneous emission free-electron laser pulses and extracting its autocorrelation, J. Synchrotron Radiat. 28, 3 (2021).
  7. G. Geloni, K. Vitali, and E. Saldin, A novel self-seeding scheme for hard X-ray FELs, J. Mod. Opt. 58, 1391 (2011).
  8. J. Amann et al., Demonstration of self-seeding in a hard-x-ray free-electron laser, Nat. Photonics 6, 693 (2012).
  9. E. Allaria et al., The FERMI free-electron lasers, J. Synchrotron Radiat. 22, 485 (2015).
  10. S. Serkez, Self-seeding XFELs: Operation principle and challenges, Synchrotron Radiat. News 29, 10 (2016).
  11. C.-K. Min et al., Hard X-ray self-seeding commissioning at PAL-XFEL, J. Synchrotron Radiat. 26, 1101 (2019).
  12. S. Liu et al., Cascaded hard X-ray self-seeded free-electron laser at megahertz repetition rate, Nat. Photonics 17, 984 (2023).
  13. J. Wu et al., Hard X-ray self-seeding at LCLS and LCLS-II, Synchrotron Radiat. News 38, 23 (2025).
  14. S. Liu, G. Geloni, T. Long, W. Qin, V. Kocharyan, J. Yan, L. Cao, N. Kujala, M. Guetg, M. Scholz, and W. Decking, Updates on the hard X-ray self-seeding at the European XFEL, Synchrotron Radiat. News 38, 11 (2025).
  15. W. Liu, Y. Liu, K. Zhang, T. Liu, and H. Deng, Progress of the hard X-ray self-seeding system at the SHINE, Synchrotron Radiat. News 38, 30 (2025).
  16. I. Inoue, T. Osaka, T. Hara, H. Tanaka, and M. Yabashi, Reflection self-seeding at SACLA, Synchrotron Radiat News 38, 17 (2025).
  17. W. Liu, Y. Liu, K. Zhang, T. Liu, and H. Deng, Progress of the hard X-ray self-seeding system at the SHINE, Synchrotron Radiat. News 38, 30 (2025).
  18. T. Long, Y. Chen, W. Decking, G. Geloni, M. Guetg, S. Huang, V. Kocharyan, S. Liu, W. Qin, S. Serkez, and J. YanControl of bandwidth and signal-to-noise ratio for hard-x-ray self-seeded free-electron lasers, Phys. Rev. Appl. 23, 044038 (2025).
  19. A. Lutman, F.-J. Decker, J. Arthur, M. Chollet, Y. Feng, J. Hastings, Z. Huang, H. Lemke, H.-D. Nuhn, A. Marinelli, J. Turner, S. Wakatsuki, J. Welch, and D. Zhu, Demonstration of single-crystal self-seeded two-color X-ray free-electron lasers, Phys. Rev. Lett. 113, 254801 (2014).
  20. A. A. Lutman, T. J. Maxwell, J. P. MacArthur, M. W. Guetg, N. Berrah, R. N. Coffee, Y. Ding, Z. Huang, A. Marinelli, S. Moeller, and J. C. U. Zemella, Fresh-slice multicolour X-ray free-electron lasers, Nat. Photonics 10, 745 (2016).
  21. G. Geloni, V. Kocharyan, T. Mazza, M. Meyer, E. Saldin, and S. Serkez, Opportunities for two-color experiments at the SASE3 undulator line of the European XFEL, arXiv:1706.00423.
  22. S. Serkez et al., Opportunities for two-color experiments in the soft X-ray regime at the European XFEL, Appl. Sci. 10, 2728 (2020).
  23. S. Serkez, Short pulses and 2-color capabilities at the SASE3 FEL line of the European XFEL (2022), https://accelconf.web.cern.ch/fel2022/pdf/TUAI2_slides.pdf.
  24. R. R. Robles, K. A. Larsen, D. Cesar, T. Driver, J. Duris, P. Franz, D. Garratt, V. Guo, G. Just, R. Lemons, M.-F. Lin, R. Obaid, N. Sudar, J. Wang, Z. Zhang, J. Cryan, and A. Marinelli, Spectrotemporal shaping of attosecond x-ray pulses with a fresh-slice free-electron laser, Phys. Rev. Lett. 134, 115001 (2025).
  25. J. Duris et al., Tunable isolated attosecond X-ray pulses with gigawatt peak power from a free-electron laser, Nat. Photonics 14, 30 (2020).
  26. A. Malyzhenkov, Y. P. Arbelo, P. Craievich, P. Dijkstal, E. Ferrari, S. Reiche, T. Schietinger, P. Juranić, and E. Prat, Single- and two-color attosecond hard x-ray free-electron laser pulses with nonlinear compression, Phys. Rev. Res. 2, 042018 (2020).
  27. S. Huang, Y. Ding, Z. Huang, and G. Marcus, Generation of subterawatt-attosecond pulses in a soft x-ray free-electron laser, Phys. Rev. Accel. Beams 19, 080702 (2016).
  28. E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, Self-amplified spontaneous emission FEL with energy-chirped electron beam and its application for generation of attosecond x-ray pulses, Phys. Rev. ST Accel. Beams 9, 050702 (2006).
  29. Z. Guo et al., Experimental demonstration of attosecond pump-probe spectroscopy with an X-ray free-electron laser, Nat. Photonics 18, 691 (2024).
  30. P. Franz et al., Terawatt-scale attosecond X-ray pulses from a cascaded superradiant free-electron laser, Nat. Photonics 18, 698 (2024).
  31. S. Usenko, A. Przystawik, M. A. Jakob, L. L. Lazzarino, G. Brenner, S. Toleikis, C. Haunhorst, D. Kip, and T. Laarmann, Attosecond interferometry with self-amplified spontaneous emission of a free-electron laser, Nat. Commun. 8, 15626 (2017).
  32. G. Orlandi, P. Heimgartner, R. Ischebeck, C. O. Loch, S. Trovati, P. Valitutti, V. Schlott, M. Ferianis, and G. Penco, Design and experimental tests of free electron laser wire scanners, Phys. Rev. Accel. Beams 19, 092802 (2016).
  33. T. Lensch, S. Liu, and M. Scholz, The European XFEL wire scanner system, in Proceedings of the 7th International Beam Instrumentation Conference, IBIC-2018, Shanghai, China (JACoW, Geneva, Switzerland, 2019), 10.18429/JACOW-IBIC2018-WEPC05.
  34. W. Decking et al., A MHz-repetition-rate hard X-ray free-electron laser driven by a superconducting linear accelerator, Nat. Photonics 14, 391 (2020).
  35. P. H. van Cittert, Die Wahrscheinliche Schwingungsverteilung in Einer von Einer Lichtquelle Direkt Oder Mittels Einer Linse Beleuchteten Ebene, Physica (Utrecht) 1, 201 (1934).
  36. F. Zernike, The concept of degree of coherence and its application to optical problems, Physica (Utrecht) 5, 785 (1938).
  37. R. H. Brown and R. Q. Twiss, Correlation between photons in two coherent beams of light, Nature (London) 177, 27 (1956).
  38. R. Hanbury Brown and R. Q. Twiss, A test of a new type of stellar interferometer on Sirius, Nature (London) 178, 1046 (1956).
  39. G. Baym, The physics of Hanbury Brown–Twiss intensity interferometry: From stars to nuclear collisions, arXiv:nucl-th/9804026.
  40. P. Michler, A. Imamoğlu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, Quantum correlation among photons from a single quantum dot at room temperature, Nature (London) 406, 968 (2000).
  41. D. Dravins, Intensity interferometry: Optical imaging with kilometer baselines, arXiv:1607.03490.
  42. F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, Optical two-way time and frequency transfer over free space, Nat. Photonics 7, 434 (2013).
  43. M. Yabashi, K. Tamasaku, and T. Ishikawa, Characterization of the transverse coherence of hard synchrotron radiation by intensity interferometry, Phys. Rev. Lett. 87, 140801 (2001).
  44. M. Yabashi, K. Tamasaku, and T. Ishikawa, Measurement of x-ray pulse widths by intensity interferometry, Phys. Rev. Lett. 88, 244801 (2002).
  45. E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, Statistical properties of radiation from VUV and X-ray free electron laser, Opt. Commun. 148, 383 (1998).
  46. G. Geloni, E. Saldin, E. Schneidmiller, and M. Yurkov, Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources, Nucl. Instrum. Methods Phys. Res., Sect. A 588, 463 (2008).
  47. E. Saldin, E. V. Schneidmiller, and M. V. Yurkov, The Physics of Free Electron Lasers (Springer Science & Business Media, Berlin, Heidelberg, 1999).
  48. W. Freund, L. Fröhlich, S. Karabekyan, A. Koch, J. Liu, D. Nölle, J. Wilgen, and J. Grünert, First measurements with the K-monochromator at the European XFEL, J. Synchrotron Radiat. 26, 1037 (2019).
  49. A. Koch, W. Freund, J. Grünert, M. Planas, T. Roth, L. Samoylova, and V. Lyamayev, Design and initial characterisation of X-ray beam diagnostic imagers for the European XFEL, in Advances in X-ray Free-Electron Lasers Instrumentation III, SPIE Proceedings Vol. 9512 (SPIE-International Society for Optical Engineering, Bellingham, WA, 2015), pp. 291–302, 10.1117/12.2182463.
  50. N. Wiener, Generalized harmonic analysis, Acta Math. 55, 117 (1930).
  51. A. Khintchine, Korrelationstheorie der stationären stochastischen prozesse, Math. Ann. 109, 604 (1934).
  52. J. W. Goodman, Statistical Optics (Wiley, New York, 2000), https://www.wiley.com/en-sg/Statistical+Optics%2C+2nd+Edition-p-9781119009450.
  53. J. Goodman, Some effects of target-induced scintillation on optical radar performance, Proc. IEEE 53, 1688 (1965).
  54. S. Bochner, Monotone funktionen, stieltjessche integrale und harmonische analyse, Math. Ann. 108, 378 (1933).
  55. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995), 10.1017/CBO9781139644105.
  56. N. M. Lockmann, C. Gerth, B. Schmidt, and S. Wesch, Noninvasive THz spectroscopy for bunch current profile reconstructions at MHz repetition rates, Phys Rev Accel Beams 23, 112801 (2020).
  57. A. Trebushinin, G. Geloni, Y. Rakshun, and S. Serkez, Gaussian random field generator for simulating partially coherent undulator radiation, Optica 9, 842 (2022).
  58. See Supplemental Material at http://link.aps.org/supplemental/10.1103/31gl-qyk7 for an animated version of Fig. 9, showing the recorded events.
  59. A. Trebushinin et al., companion paper, First observation of synchrotron radiation spikes for transverse electron beam size measurements at a free-electron laser, Phys. Rev. Lett. 135, 215001 (2025).
  60. Ocelot simulation toolkit, https://github.com/ocelot-collab/ocelot.
  61. G. Geloni, E. Saldin, E. Schneidmiller, and M. Yurkov, Paraxial Green’s functions in synchrotron radiation theory, arXiv:physics/0502120.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation