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

Collective and surface charge effects in high-brightness ultrafast electron sources

Anahita Omoumi1,*, Miguel M. Calderon1, Lee Jones2, Andrea Latina1, and Eduardo Granados1,†

  • *Contact author: anahita.omoumi@cern.ch
  • †Contact author: eduardo.granados@cern.ch

Phys. Rev. Accel. Beams 29, 063401 – Published 29 June, 2026

DOI: https://doi.org/10.1103/c5zh-6xsv

Abstract

We present a photoemission model based on the Fowler-DuBridge equation that accounts for the dynamic modulation of the Schottky barrier during the emission of high-charge-density electron bunches. By incorporating the time-dependent effective electric field normal to the photocathode surface (including real-time emission-induced electric fields), our model captures the ultrafast transient modulation of the electron emission potential barrier that governs the instantaneous current density. This approach links single-electron photoemission effects with macroscopic collective charge effects, enabling accurate predictions of the time-dependent charge production for high-brightness photoinjectors. Furthermore, we validate the model by comparing it with the experimental results obtained with a high-gradient photoinjector equipped with ultraviolet pulse shaping capabilities. Our model highlights the importance of dynamic surface effects in shaping the initial phase space of electron bunches. The effects are particularly relevant for future lepton colliders where producing on-demand bunch charge with a tailored phase space is required, including the top-up injection scheme for CERN’s Future Circular Collider (FCC).

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. M. Aiba, B. Goddard, K. Oide, Y. Papaphilippou, Á. Saá Hernández, D. Shwartz, S. White, and F. Zimmermann, Top-up injection schemes for future circular lepton collider, Nucl. Instrum. Methods Phys. Res., Sect. A 880, 98 (2018).
  2. K. L. Jensen, A thermal-field-photoemission model and its application, in Modern Developments in Vacuum Electron Sources (Springer International Publishing, Cham, 2020), pp. 345–385.
  3. M. Martinez-Calderon, E. Chevallay, R. E. Rossel, L. B. Jones, G. Zevi Della Porta, B. Marsh, and E. Granados, Fabrication and rejuvenation of high quantum efficiency caesium telluride photocathodes for high brightness and high average current photoinjectors, Phys. Rev. Accel. Beams 27, 023401 (2024).
  4. J. B. Rosenzweig, A. Cahill, V. Dolgashev, C. Emma, A. Fukasawa, R. Li, C. Limborg, J. Maxson, P. Musumeci, A. Nause, R. Pakter, R. Pompili, R. Roussel, B. Spataro, and S. Tantawi, Next generation high brightness electron beams from ultrahigh field cryogenic rf photocathode sources, Phys. Rev. Accel. Beams 22, 023403 (2019).
  5. K. L. Jensen, J. J. Petillo, D. N. Panagos, S. Ovtchinnikov, and N. A. Moody, Delayed photo-emission model for beam optics codes, J. Vacuum Sci. Technol. B 35, 02C102 (2016).
  6. K. Floettmann, Rf-induced beam dynamics in rf guns and accelerating cavities, Phys. Rev. ST Accel. Beams 18, 064801 (2015).
  7. K. L. Jensen, A. R. Shabaev, and M. Osofsky, Theory and modeling of ultrafast electron emission from nanostructures, Defense Technical Information Center, Report No. AD1149647, 2021.
  8. K. L. Jensen, J. J. Petillo, S. Ovtchinnikov, D. N. Panagos, N. A. Moody, and S. G. Lambrakos, Modeling emission lag after photoexcitation, J. Appl. Phys. 122, 164501 (2017).
  9. Y. Zhou and P. Zhang, A quantum model for photoemission from metal surfaces and its comparison with the three-step model and Fowler–DuBridge model, J. Appl. Phys. 127, 164903 (2020).
  10. K. L. Jensen, A. Shabaev, S. G. Lambrakos, D. Finkenstadt, N. A. Moody, A. J. Neukirch, S. Tretiak, D. A. Shiffler, and J. J. Petillo, Analytic model of electron transport through and over non-linear barriers, J. Appl. Phys. 127, 235301 (2020).
  11. Y. Chen, M. Krasilnikov, F. Stephan, E. Gjonaj, T. Weiland, and M. Dohlus, Modeling and simulation of rf photoinjectors for coherent light sources, Nucl. Instrum. Methods Phys. Res., Sect. A 889, 129 (2018).
  12. M. Krasilnikov, An improved model for photoemission of space charge dominated picosecond electron bunches: Theory and experiment, in Proceedings of the 12th International Particle Accelerator Conference (IPAC2021) (JACoW, 2021), pp. 2830–2833, 10.18429/JACoW-IPAC2021-WEPAB101.
  13. Y. Liu and L. K. Ang, Transition from ultrafast laser photo-electron emission to space-charge-limited current in a 1D gap, J. Phys. D 47, 125502 (2014).
  14. M. Gordon, S B. van der Geer, J. Maxson, and Y.-K. Kim, Point-to-point Coulomb effects in high brightness photoelectron beam lines for ultrafast electron diffraction, Phys. Rev. Accel. Beams 24, 084202 (2021).
  15. J. Portman, H. Zhang, K. Makino, C. Y. Ruan, M. Berz, and P. M. Duxbury, Untangling the contributions of image charge and laser profile for optimal photoemission of high-brightness electron beams, J. Appl. Phys. 116, 174302 (2014).
  16. P. Musumeci, J. T. Moody, R. J. England, J. B. Rosenzweig, and T. Tran, Experimental generation and characterization of uniformly filled ellipsoidal electron-beam distributions, Phys. Rev. Lett. 100, 244801 (2008).
  17. P. Musumeci, R. K. Li, and A. Marinelli, Nonlinear longitudinal space charge oscillations in relativistic electron beams, Phys. Rev. Lett. 106, 184801 (2011).
  18. P. Denham, D. Garcia, A. Kulkarni, B. Schaap, Z. Liu, P. Musumeci, and D. Filippetto, Experimental verification of space-charge saturation scaling laws in high-gradient photocathode rf guns, arXiv:2511.02035.
  19. K. Jensen, Electron emission models for simulation, in Presented at Photocathode Physics for Photoinjectors Workshop (2021), pp. 10–12, https://indico.fnal.gov/event/49191/.
  20. K. L. Jensen, D. W. Feldman, M. Virgo, and P. G. O’Shea, Measurement and analysis of thermal photoemission from a dispenser cathode, Phys. Rev. ST Accel. Beams 6, 083501 (2003).
  21. R. G. Forbes, The Murphy–Good plot: A better method of analysing field emission data, R. Soc. Open Sci. 6, 190912 (2019).
  22. Y. Zhou and P. Zhang, A quantum model for photoemission from metal surfaces and its comparison with the three-step model and Fowler–DuBridge model, J. Appl. Phys. 127, 164903 (2020).
  23. K. L. Jensen, Introduction to the Physics of Electron Emission (John Wiley & Sons, Hoboken, New Jersey, 2017).
  24. I. Langmuir, The effect of space charge and residual gases on thermionic currents in high vacuum, Phys. Rev. 2, 450 (1913).
  25. P. Denham, D. Garcia, A. Kulkarni, B. Schaap, Z. Liu, P. Musumeci, and D. Filippetto, Experimental verification of space-charge saturation scaling laws in high-gradient photocathode rf guns, arXiv:2511.02035.
  26. S. Van der Geer, M. De Loos, and O. Luiten, Pancakes versus beer-cans in terms of 6D phase-space density, in Proceedings of the European Particle Accelerator Conference (EPAC) (2008), Vol. 8, p. 151, https://accelconf.web.cern.ch/e08/papers/mopc036.pdf.
  27. Z. Tao, H. Zhang, P. M. Duxbury, M. Berz, and C.-Y. Ruan, Space charge effects in ultrafast electron diffraction and imaging, J. Appl. Phys. 111, 044316 (2012).
  28. D. H. Dowell, Topological cathodes: Controlling the space charge limit of electron emission using metamaterials, Phys. Rev. Accel. Beams 22, 084201 (2019).
  29. L. Serafini and J. B. Rosenzweig, Envelope analysis of intense relativistic quasilaminar beams in rf photoinjectors: mA theory of emittance compensation, Phys. Rev. E 55, 7565 (1997).
  30. D. H. Dowell and J. F. Schmerge, Quantum efficiency and thermal emittance of metal photocathodes, Phys. Rev. ST Accel. Beams 12, 074201 (2009).
  31. L. Jones, D. Juarez-Lopez, B. Militsyn, C. Welsch, and T. Noakes, Transverse energy distribution measurements for polycrystalline and (100) copper photocathodes with known levels of surface roughness, in Proceedings of the 9th International Particle Accelerator Conference (IPAC2018), Canada (JACoW Publishing, Geneva, 2018), pp. 3855–3858, 10.18429/JACoW-IPAC2018-THPMK059.
  32. J. Maxson, P. Musumeci, L. Cultrera, S. Karkare, and H. Padmore, Ultrafast laser pulse heating of metallic photocathodes and its contribution to intrinsic emittance, Nucl. Instrum. Methods Phys. Res., Sect. A 865, 99 (2017).
  33. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).
  34. E. Gschwendtner, K. Lotov, P. Muggli, M. Wing, R. Agnello, C. C. Ahdida, M. C. Amoedo Goncalves, Y. Andrebe, O. Apsimon, R. Apsimon et al., The awake run 2 programme and beyond, Symmetry 14, 1680 (2022).
  35. APE GmbH, Pulsecheck autocorrelator for pulse width measurements, https://www.ape-berlin.de/en/autocorrelator/pulsecheck/ [Accessed 6 April, 2026].
  36. D. Palmer, X. Wang, R. Miller, M. Babzien, I. Ben-Zvi, C. Pellegrini, J. Sheehan, J. Skaritka, H. Winick, M. Woodle, and V. Yakimenko, Emittance studies of the BNL/SLAC/UCLA 1.6 cell photocathode rf gun, in Proceedings of the 1997 Particle Accelerator Conference (IEEE, Piscataway, NJ, 1997), Vol. 3, pp. 2687–2689, 10.1109/PAC.1997.752723.
  37. J. Rosenzweig, N. Barov, S. Hartman, M. Hogan, S. Park, C. Pellegrini, G. Travish, R. Zhang, P. Davis, G. Hairapetian, and C. Joshi, Initial measurements of the UCLA rf photoinjector, Nucl. Instrum. Methods Phys. Res., Sect. A 341, 379 (1994).
  38. A. Valfells, D. Feldman, M. Virgo, P. O’shea, and Y. Lau, Effects of pulse-length and emitter area on virtual cathode formation in electron guns, Phys. Plasmas 9, 2377 (2002).
  39. Z. Vostrel and S. Doebert, Design of an electron source for the FCC-ee with top-up injection capability, Nucl. Instrum. Methods Phys. Res., Sect. A 1063, 169261 (2024).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation