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Geometric scaling of laser-driven proton focusing from hemispherical foils

J. Griff-McMahon1,2,*, X. Vaisseau3, W. Fox1,2,4, K. Lezhnin2, K. Bhutwala2, R. Nedbailo5, V. Ospina-Bohórquez3, T. Karpowski6, P. K. Patel3 et al.

S. Malko2

  • *Contact author: jgriffmc@pppl.gov
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Phys. Rev. Research 8, 013182 – Published 19 February, 2026

DOI: https://doi.org/10.1103/3cs1-8r6s

Abstract

We systematically characterize the focusing behavior of laser-driven proton beams from hemispherical targets of various diameters using mesh radiography. The proton focal location is inferred to be near the geometrical center for the smallest tested hemisphere (Ψ=Dhemi/DLaser=6.1). However, larger hemispheres (Ψ=14.6) degrade the focusing behavior and behave more like flat foils with focal location significantly inside the hemisphere. We also infer a tight virtual focus of 9±3μm through a mesh transition analysis.

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References (26)

  1. P. K. Patel, A. J. Mackinnon, M. H. Key, T. E. Cowan, M. E. Foord, M. Allen, D. F. Price, H. Ruhl, P. T. Springer, and R. Stephens, Isochoric heating of solid-density matter with an ultrafast proton beam, Phys. Rev. Lett. 91, 125004 (2003).
  2. M. Bailly-Grandvaux, S. Bolaños, J. Kim, J. Saret, C. McGuffey, K. Bhutwala, P. M. Nilson, T. Filkins, W. Theobald, A. Haid, S. Ivancic, and F. N. Beg, Creation and characterization of warm dense matter isochorically heated by an intense laser-driven proton beam to temperatures exceeding 100 eV, Commun. Phys. 8, 285 (2025).
  3. M. Roth, T. E. Cowan, M. H. Key, S. P. Hatchett, C. Brown, W. Fountain, J. Johnson, D. M. Pennington, R. A. Snavely, S. C. Wilks, K. Yasuike, H. Ruhl, F. Pegoraro, S. V. Bulanov, E. M. Campbell, M. D. Perry, and H. Powell, Fast ignition by intense laser-accelerated proton beams, Phys. Rev. Lett. 86, 436 (2001).
  4. S. Atzeni, M. Temporal, and J. J. Honrubia, A first analysis of fast ignition of precompressed ICF fuel by laser-accelerated protons, Nucl. Fusion 42, L1 (2002).
  5. M. Tabak, D. Hinkel, S. Atzeni, M. Campbell, and K. A. Tanaka, Fast ignition: Overview and background, Fusion Sci. Technol. 49, 254 (2006).
  6. J. J. Honrubia and M. Murakami, Ion beam requirements for fast ignition of inertial fusion targets, Phys. Plasmas 22, 012703 (2015).
  7. S. C. Wilks, A. B. Langdon, T. E. Cowan, M. Roth, M. Singh, S. Hatchett, M. H. Key, D. Pennington, A. MacKinnon, and R. A. Snavely, Energetic proton generation in ultra-intense laser–solid interactions, Phys. Plasmas 8, 542 (2001).
  8. T. Bartal, M. E. Foord, C. Bellei, M. H. Key, K. A. Flippo, S. A. Gaillard, D. T. Offermann, P. K. Patel, L. C. Jarrott, D. P. Higginson, M. Roth, A. Otten, D. Kraus, R. B. Stephens, H. S. McLean, E. M. Giraldez, M. S. Wei, D. C. Gautier, and F. N. Beg, Focusing of short-pulse high-intensity laser-accelerated proton beams, Nat. Phys. 8, 139 (2012).
  9. B. Qiao, M. E. Foord, M. S. Wei, R. B. Stephens, M. H. Key, H. McLean, P. K. Patel, and F. N. Beg, Dynamics of high-energy proton beam acceleration and focusing from hemisphere-cone targets by high-intensity lasers, Phys. Rev. E 87, 013108 (2013).
  10. C. McGuffey, J. Kim, M. S. Wei, P. M. Nilson, S. N. Chen, J. Fuchs, P. Fitzsimmons, M. E. Foord, D. Mariscal, H. S. McLean, P. K. Patel, R. B. Stephens, and F. N. Beg, Focussing protons from a kilojoule laser for intense beam heating using proximal target structures, Sci. Rep. 10, 9415 (2020).
  11. P. K. Patel, M. H. Key, A. J. Mackinnon, R. Berry, M. Borghesi, D. M. Chambers, H. Chen, R. Clarke, C. Damian, R. Eagleton, R. Freeman, S. Glenzer, G. Gregori, R. Heathcote, D. Hey, N. Izumi, S. Kar, J. King, A. Nikroo, A. Niles, et al., Integrated laser–target interaction experiments on the RAL petawatt laser, Plasma Phys. Controlled Fusion 47, B833 (2005).
  12. R. A. Snavely, B. Zhang, K. Akli, Z. Chen, R. R. Freeman, P. Gu, S. P. Hatchett, D. Hey, J. Hill, M. H. Key, et al., Laser generated proton beam focusing and high temperature isochoric heating of solid matter, Phys. Plasmas 14, 092703 (2007).
  13. D. T. Offermann, K. A. Flippo, J. Cobble, M. J. Schmitt, S. A. Gaillard, T. Bartal, D. V. Rose, D. R. Welch, M. Geissel, and M. Schollmeier, Characterization and focusing of light ion beams generated by ultra-intensely irradiated thin foils at the kilojoule scale, Phys. Plasmas 18, 056713 (2011).
  14. S. Kar, K. Markey, M. Borghesi, D. C. Carroll, P. McKenna, D. Neely, M. N. Quinn, and M. Zepf, Ballistic focusing of polyenergetic protons driven by petawatt laser pulses, Phys. Rev. Lett. 106, 225003 (2011).
  15. S. N. Chen, E. d’Humières, E. Lefebvre, L. Romagnani, T. Toncian, P. Antici, P. Audebert, E. Brambrink, C. A. Cecchetti, T. Kudyakov, A. Pipahl, Y. Sentoku, M. Borghesi, O. Willi, and J. Fuchs, Focusing dynamics of high-energy density, laser-driven ion beams, Phys. Rev. Lett. 108, 055001 (2012).
  16. V. Ospina-Bohórquez and X. Vaisseau, Scaling and performance analysis of Smilei in hemispherical foil target simulations for inertial fusion energy, Proc. Comput. Sci. 255, 112 (2025).
  17. A. J. Kemp, S. C. Wilks, and M. Tabak, Laser-to-proton conversion efficiency studies for proton fast ignition, Phys. Plasmas 31, 042709 (2024).
  18. S. Malko, W. Cayzac, V. Ospina-Bohórquez, K. Bhutwala, M. Bailly-Grandvaux, C. McGuffey, R. Fedosejevs, X. Vaisseau, A. Tauschwitz, J. I. Apiñaniz, et al., Proton stopping measurements at low velocity in warm dense carbon, Nat. Commun. 13, 2893 (2022).
  19. D. J. Hoarty, T. Guymer, S. F. James, E. Gumbrell, C. R. D. Brown, M. Hill, J. Morton, and H. Doyle, Equation of state studies of warm dense matter samples heated by laser produced proton beams, High Energy Density Phys. 8, 50 (2012).
  20. T. S. Bauer, Development, characterization, alignment and experimental validation of partial sphere target arrays for advanced proton acceleration studies, Ph.D. thesis, TU Darmstadt, 2025.
  21. M. Borghesi, A. J. Mackinnon, D. H. Campbell, D. G. Hicks, S. Kar, P. K. Patel, D. Price, L. Romagnani, A. Schiavi, and O. Willi, Multi-MeV proton source investigations in ultraintense laser-foil interactions, Phys. Rev. Lett. 92, 055003 (2004).
  22. M. E. Foord, T. Bartal, C. Bellei, M. Key, K. Flippo, R. B. Stephens, P. K. Patel, H. S. McLean, L. C. Jarrott, M. S. Wei, and F. N. Beg, Proton trajectories and electric fields in a laser-accelerated focused proton beam, Phys. Plasmas 19, 056702 (2012).
  23. C. Bellei, M. E. Foord, T. Bartal, M. H. Key, H. S. McLean, P. K. Patel, R. B. Stephens, and F. N. Beg, Electron and ion dynamics during the expansion of a laser-heated plasma under vacuum, Phys. Plasmas 19, 033109 (2012).
  24. K. Lezhnin, V. O. Bohorquez, K. A. Bhutwala, J. Griff-McMahon, X. Vaisseau, T. Bauer, W. Fox, and S. Malko, Laser ion acceleration from concave targets: Focusing, scaling, and robustness studies, Talk at the 66th Annual Meeting of the APS Division of Plasma Physics, Mini-Conference: Proton Transport in HED II: Proton Focusing (Session CM10.4) (2024).
  25. H. Ahmed, S. Kar, G. Cantono, G. Nersisyan, S. Brauckmann, D. Doria, D. Gwynne, A. Macchi, K. Naughton, O. Willi, C. Lewis, and M. Borghesi, Investigations of ultrafast charge dynamics in laser-irradiated targets by a self probing technique employing laser driven protons, Nucl. Instrum. Methods Phys. Res. Sect. A 829, 172 (2016).
  26. A. Poyé, J.-L. Dubois, F. Lubrano-Lavaderci, E. D’Humières, M. Bardon, S. Hulin, M. Bailly-Grandvaux, J. Ribolzi, D. Raffestin, J. J. Santos, P. Nicolaï, and V. Tikhonchuk, Dynamic model of target charging by short laser pulse interactions, Phys. Rev. E 92, 043107 (2015).

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Phys. Rev. Research 8, 013182– Published 19 February, 2026
  • Received 20 October 2025
  • Accepted 20 January 2026
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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.

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