- 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

Multiphysics analysis of cryogenically cooled photocathode in a continuous wave SRF injector cavity

Dmitry Bazyl*, Klaus Floettmann, Elmar Vogel, and Igor Zagorodnov

  • *Contact author: dmitry.bazyl@desy.de
PDF

Phys. Rev. Accel. Beams 29, 013402 – Published 20 January, 2026

DOI: https://doi.org/10.1103/9jyv-hfxy

Abstract

The paper evaluates the thermal regime of a cryogenically cooled copper photocathode integrated into a continuous-wave superconducting radio-frequency injector cavity with direct thermal contact. Such a photoinjector layout is being developed at DESY and has recently demonstrated a record-high 50  MV/m axial electric field in radio-frequency tests, marking an important milestone. To address the thermal effect of the picosecond excitation laser, we first develop a two-temperature model to describe the temperature of the emitting surface at cryogenic temperatures and solve it numerically. Subsequently, we present a one-temperature model of the bulk photocathode coupled with an electromagnetic model of the injector cavity. For the current injector design, we predict a negligible impact of the laser on the intrinsic quality factor of the cavity, identifying instead the cryogenic stability of the copper cathode as the primary operational limit. To overcome cooling challenges, we propose an improved configuration of the cathode plug. For the proposed geometry, the multiphysics analysis confirms stable performance at a nominal 2 W laser power, sufficient for 100 pC beams at 1 MHz under optimistic quantum efficiency assumptions. Operation at higher laser loads will benefit from further dedicated cryogenic analysis.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (54)

  1. 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).
  2. R. Brinkmann, E. Schneidmiller, J. Sekutowicz, and M. Yurkov, Prospects for CW and LP operation of the European XFEL in hard x-ray regime, Nucl. Instrum. Methods Phys. Res., Sect. A 768, 20 (2014).
  3. E. Vogel et al., SRF gun development at DESY, in Proceedings of the 29th International Linear Accelerator Conference, Beijing, China (JACoW, Geneva, Switzerland, 2018), MOPO037, 10.18429/JACoW-LINAC2018-MOPO037.
  4. E. Vogel, J. Sekutowicz, D. Bazyl, T. Büttner, B. van der Horst, J. Iversen, D. Klinke, A. Muhs, D. Reschke, S. Sägebarth, P. Schilling, M. Schmökel, L. Steder, J. H. Thie, H. Weise, and M. Wiencek, High gradients at SRF photoinjector cavities with low RRR copper cathode plug screwed to the cavity back wall, arXiv:2310.02974.
  5. D. Bazyl et al., CW operation of the European XFEL: SC-gun injector optimization, S2E calculations and SASE performance, arXiv:2111.01756.
  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. M. Tonouchi, Cutting-edge terahertz technology, Nat. Photonics 1, 97 (2007).
  8. J. R. Harris et al., Temperature dependence of photoemission from copper and niobium, in Proceedings of the PAC2013, Pasadena, CA USA (JACoW, Geneva, Switzerland, 2013), pp. 1184–1186, https://proceedings.jacow.org/PAC2013/papers/thpac19.pdf?n=PAC2013/papers/THPAC19.pdf.
  9. J. Kühn et al., A Cu photocathode for the superconducting RF photoinjector of BERLinPro, in Proceedings of the 9th International Particle Accelerator Conference (IPAC’18), Vancouver, BC, Canada (JACoW, Geneva, Switzerland, 2018), pp. 1247–1250, 10.18429/JACoW-IPAC2018-TUPMF002.
  10. S. Karkare, G. Adhikari, W. A. Schroeder, J. K. Nangoi, T. A. Arias, J. Maxson, and H. Padmore, Ultracold electrons via near-threshold photoemission from single-crystal Cu(100), Phys. Rev. Lett. 125, 054801 (2020).
  11. J. Kühn, N. Al–Saokal, M. Bürger, M. Dirsat, A. Frahm, A. Jankowiak, T. Kamps, G. Klemz, S. Mistry, A. Neumann, and H. Plötz, Thermal load studies on the photocathode insert with exchangeable plug for the BERLinPro SRF–photoinjector, in Proceedings of the International Conference on RF Superconductivity, SRF2019, Dresden, Germany (JACoW, Geneva, Switzerland, 2019), p. 705, 10.18429/JACoW-SRF2019-TUP100.
  12. R. A. Kostin, A. Kanareykin, I. V. Gonin, and E. N. Zaplatin, SRF cavity breakdown calculation procedure using fea-software, in Proceedings of the International Conference on RF Superconductivity, SRF2015 (JACoW, Whistler, BC, 2015), p. 140.
  13. T. J. Schultheiss, M. Cole, and J. Rathke, Thermal/structural analysis of a SCRF photocathode electron gun cavity, in Proceedings of the XX International Linac Conference International Linear Accelerator Conference, Monterey, CA, USA (JACoW, Geneva, Switzerland, 2000).
  14. S. Barbanotti, P. Pierini, K. Jensch, R. Lange, and W. Maschmann, Thermal and structural modeling of the TTF cryomodule cooldown and comparison with experimental data, in Proceedings of the European Particle Accelerator Conference, EPAC08, Genoa, Italy (JACoW, Geneva, Switzerland, 2008), WEPD038.
  15. M. H. Awida, I. Gonin, T. Khabiboulline, and V. P. Yakovlev, Modeling of thermal quench in superconducting RF cavities, IEEE Trans. Appl. Supercond. 30, 1 (2020).
  16. H. Padamsee, J. Knobloch, and T. Hays, RF Superconductivity for Accelerators, 2nd ed. (Wiley-VCH, Berlin, Germany, 2008).
  17. T. P. Wangler, RF Linear Accelerators, 2nd ed. (Wiley-VCH, Berlin, Germany, 2008).
  18. Light conversion, PHAROS femtosecond lasers (2025), https://lightcon.com/products/pharos-femtosecond-lasers/.
  19. H. J. Qian, C. Li, Y. C. Du, L. X. Yan, J. F. Hua, W. H. Huang, and C. X. Tang, Experimental investigation of thermal emittance components of copper photocathode, Phys. Rev. ST Accel. Beams 15, 040102 (2012).
  20. T. Noakes et al., Copper photocathodes for the modified 10 Hz gun on the CLARA accelerator, in Proceedings of the 14th International Particle Accelerator Conference, IPAC2023, Venice, Italy (JACoW, Geneva, Switzerland, 2023), TUPA032, 10.18429/JACoW-IPAC2023-TUPA032.
  21. COMSOL AB, comsol multiphysics® simulation software (2025), https://www.comsol.com/ [accessed: 2025-08-01].
  22. J. Sekutowicz et al., Cathodes and shape modification of cavity for DESY superconducting photoinjector, arXiv:2507.01658.
  23. S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, Electron emission from metal surfaces exposed to ultrashort laser pulses, J. Exp. Theor. Phys. 39, 375 (1974), https://ui.adsabs.harvard.edu/abs/1974JETP...39..375A/abstract.
  24. 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).
  25. Z. Tong, S. Li, X. Ruan, and H. Bao, Comprehensive first-principles analysis of phonon thermal conductivity and electron-phonon coupling in different metals, Phys. Rev. B 100, 144306 (2019).
  26. M. I. Kaganov, I. M. Lifshitz, and L. V. Tanatarov, Relaxation between electrons and the crystalline lattice, Zh. Eksp. Teor. Fiz. 31, 232 (1956) [Sov. Phys. JETP 4, 173 (1957)].
  27. P. B. Allen, Theory of thermal relaxation of electrons in metals, Phys. Rev. Lett. 59, 1460 (1987).
  28. F. C. Wellstood, C. Urbina, and J. Clarke, Hot-electron effects in metals, Phys. Rev. B 49, 5942 (1994).
  29. F. Giazotto, T. T. Heikkilä, A. Luukanen, A. M. Savin, and J. P. Pekola, Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications, Rev. Mod. Phys. 78, 217 (2006).
  30. L. B. Wang, O.-P. Saira, D. S. Golubev, and J. P. Pekola, Crossover between electron-phonon and boundary-resistance limits to thermal relaxation in copper films, Phys. Rev. Appl. 12, 024051 (2019).
  31. M. Z. Mo, V. Becker, B. K. Ofori-Okai, X. Shen, Z. Chen, B. Witte, R. Redmer, R. K. Li, M. Dunning, S. P. Weathersby, X. J. Wang, and S. H. Glenzer, Determination of the electron-lattice coupling strength of copper with ultrafast MeV electron diffraction, Rev. Sci. Instrum. 89, 10C108 (2018).
  32. J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, Electron and lattice dynamics following optical excitation of metals, Chem. Phys. 251, 237 (2000).
  33. Z. Lin, L. V. Zhigilei, and V. Celli, Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium, Phys. Rev. B 77, 075133 (2008).
  34. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
  35. C. Kittel, Introduction to Solid State Physics, 8th ed. (John Wiley & Sons, Hoboken, NJ, 2005).
  36. J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford University Press, Oxford, 1960).
  37. P. B. Johnson and R. W. Christy, Optical constants of the noble metals, Phys. Rev. B 6, 4370 (1972).
  38. B. Rethfeld, A. Kaiser, M. Vicanek, and G. Simon, Ultrafast dynamics of nonequilibrium electrons in metals under femtosecond laser irradiation, Phys. Rev. B 65, 214303 (2002).
  39. R. H. M. Groeneveld, R. Sprik, and A. Lagendijk, Femtosecond spectroscopy of electron-electron and electron-phonon energy relaxation in Ag and Au, Phys. Rev. B 51, 11433 (1995).
  40. E. Carpene, Ultrafast laser irradiation of metals: Beyond the two-temperature model, Phys. Rev. B 74, 024301 (2006).
  41. G. D. Tsibidis, Ultrafast dynamics of non-equilibrium electrons and strain generation under femtosecond laser irradiation of nickel, Appl. Phys. A 124, 311 (2018).
  42. M. Uehlein, S. T. Weber, and B. Rethfeld, Influence of electronic non-equilibrium on energy distribution and dissipation in aluminum studied with an extended two-temperature model, Nanomater. Nanotechnol. 12, 1655 (2022).
  43. N. J. Simon, E. S. Drexler, and R. P. Reed, Properties of Copper and Copper Alloys at Cryogenic Temperatures, NIST Monograph Vol. 177 (National Institute of Standards and Technology, Gaithersburg, MD, 1992).
  44. E. T. Swartz and R. O. Pohl, Thermal boundary resistance, Rev. Mod. Phys. 61, 605 (1989).
  45. R. C. Dhuley, M. I. Geelhoed, and J. C. T. Thangaraj, Thermal resistance of pressed contacts of aluminum and niobium at liquid helium temperatures, Cryogenics 93, 86 (2018).
  46. T. Schilcher, Wärmeleitvermögen von Niob bei kryogenischen Temperaturen, Diplomarbeit, Universität Regensburg/DESY, 1995; TESLA Report No. 1995-12, in German.
  47. P. Lebrun and L. Tavian, Cooling with superfluid helium, arXiv:1501.07156.
  48. J. Amrit and M. X. François, Heat flow at the niobium-superfluid helium interface: Kapitza resistance and superconducting cavities, J. Low Temp. Phys. 119, 27 (2000).
  49. A. Aizaz, T. L. Grimm, and N. T. Wright, Thermal design studies in superconducting rf cavities: Phonon peak and Kapitza conductance, Phys. Rev. ST Accel. Beams 13, 093503 (2010).
  50. P. Dhakal, G. Ciovati, and G. R. Myneni, Role of thermal resistance on the performance of superconducting radio frequency cavities, Phys. Rev. Accel. Beams 20, 032003 (2017).
  51. S. W. V. Sciver, Helium Cryogenics, International Cryogenics Monograph Series 2nd ed. (Springer, Boston, MA, 2012).
  52. S. Inui, M. Hulse, T. Kanai, and W. Guo, Boiling peak heat flux for steady inhomogeneous heat transfer in superfluid He4, Phys. Rev. B 108, 174509 (2023).
  53. M. W. McGee, E. R. Harms, A. L. Klebaner, J. R. Leibfritz, A. Martinez, Y. M. Pischalnikov, and W. Schappert, Investigation of thermal acoustic effects on SRF cavities within CM1 at Fermilab, in Proceedings of International Particle Accelerator Conference, IPAC 2016 (JACoW, Geneva, Switzerland, 2016), WEPMR005.
  54. S. Barbanotti (private communication).

Outline

Information

Phys. Rev. Accel. Beams 29, 013402– Published 20 January, 2026
  • Received 15 August 2025
  • Accepted 12 December 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