- Open Access
Laser ion acceleration from concave targets by subpicosecond pulses
Phys. Rev. Research 8, 033219 – Published 24 August, 2026
DOI: https://doi.org/10.1103/rbwx-m6mb
Abstract
Laser-driven proton acceleration provides a powerful route for generating ultrashort, high-charge proton beams. Many applications, including secondary neutron sources and inertial fusion, benefit from tight proton beam focusing. Concave targets offer a robust solution, yet the scaling of proton focusing with laser and target parameters remains poorly understood. Here, we present a numerical study of laser-driven proton acceleration and focusing from hemispherical targets using the fully kinetic, relativistic Particle-In-Cell code EPOCH. We focus on the subpicosecond laser-pulse regime (duration fs), centering on the laser parameters of our recent experiment at the Colorado State University ALEPH laser facility. We investigate the proton acceleration mechanisms, characterize proton focusing, and assess how focal spot parameters scale with laser and target parameters. We identify Target Normal Sheath Acceleration as the dominant mechanism, supplemented by a secondary postacceleration stage near the geometrical center of the hemisphere. We demonstrate that both the proton focal spot size and focal plane position scale approximately linearly with the hemisphere radius, with the focal plane consistently located downstream of the geometrical center. The opening angle of the concave target mainly affects the proton beam waist. Energy-dependent proton focusing can be understood, in part, as arising from the evolving curvature of the accelerating structure, which departs from the target curvature. Evidence for self-similar proton focusing is found in the regime of nearly uniform target irradiation.
Physics Subject Headings (PhySH)
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References (65)
- A. Macchi, M. Borghesi, and M. Passoni, Ion acceleration by superintense laser-plasma interaction, Rev. Mod. Phys. 85, 751 (2013).
- H. Daido, M. Nishiuchi, and A. S. Pirozhkov, Review of laser-driven ion sources and their applications, Rep. Prog. Phys. 75, 056401 (2012).
- J. Schreiber, P. Bolton, and K. Parodi, Invited Review Article: “Hands-on” laser-driven ion acceleration: A primer for laser-driven source development and potential applications, Rev. Sci. Instrum. 87, 071101 (2016).
- S. Bulanov and V. Khoroshkov, Feasibility of using laser ion accelerators in proton therapy, Plasma Phys. Rep. 28, 453 (2002).
- S. V. Bulanov, J. J. Wilkens, T. Z. Esirkepov, G. Korn, G. Kraft, S. D. Kraft, M. Molls, and V. S. Khoroshkov, Laser ion acceleration for hadron therapy, Phys.-Usp. 57, 1149 (2014).
- M. Borghesi, A. Schiavi, D. Campbell, M. Haines, O. Willi, A. MacKinnon, L. Gizzi, M. Galimberti, R. Clarke, and H. Ruhl, Proton imaging: A diagnostic for inertial confinement fusion/fast ignitor studies, Plasma Phys. Controlled Fusion 43, A267 (2001).
- D. B. Schaeffer, Archie F. Bott, M. Borghesi, Kirk A. Flippo, W. Fox, J. Fuchs, C. Li, F. H. Séguin, H.-S. Park, P. Tzeferacos, et al., Proton imaging of high-energy-density laboratory plasmas, Rev. Mod. Phys. 95, 045007 (2023).
- J. Alvarez, J. Fernández-Tobias, K. Mima, S. Nakai, S. Kar, Y. Kato, and J. Perlado, Laser driven neutron sources: Characteristics, applications and prospects, Phys. Procedia 60, 29 (2014).
- A. Yogo, Y. Arikawa, Y. Abe, S. Mirfayzi, T. Hayakawa, K. Mima, and R. Kodama, Advances in laser-driven neutron sources and applications, Eur. Phys. J. A 59, 191 (2023).
- M. Roth, T. Cowan, M. Key, S. Hatchett, C. Brown, W. Fountain, J. Johnson, D. Pennington, R. Snavely, S. Wilks, et al., Fast ignition by intense laser-accelerated proton beams, Phys. Rev. Lett. 86, 436 (2001).
- S. Wilks, A. Langdon, T. E. Cowan, M. Roth, M. Singh, S. Hatchett, M. Key, D. Pennington, A. Mackinnon, and R. Snavely, Energetic proton generation in ultra-intense laser–solid interactions, Phys. Plasmas 8, 542 (2001).
- H. Ruhl, S. Bulanov, T. Cowan, T. Liseikina, P. Nickles, F. Pegoraro, M. Roth, and W. Sandner, Computer simulation of the three-dimensional regime of proton acceleration in the interaction of laser radiation with a thin spherical target, Plasma Phys. Rep. 27, 363 (2001).
- P. Patel, A. Mackinnon, M. Key, T. Cowan, M. Foord, M. Allen, D. Price, H. Ruhl, P. Springer, and R. Stephens, Isochoric heating of solid-density matter with an ultrafast proton beam, Phys. Rev. Lett. 91, 125004 (2003).
- T. Toncian, M. Borghesi, J. Fuchs, E. d'Humières, P. Antici, P. Audebert, E. Brambrink, C. A. Cecchetti, A. Pipahl, L. Romagnani, et al., Ultrafast laser-driven microlens to focus and energy-select mega-electron volt protons, Science 312, 410 (2006).
- M. Schollmeier, S. Becker, M. Geißel, K. Flippo, A. Blažević, S. Gaillard, D. Gautier, F. Grüner, K. Harres, M. Kimmel, et al., Controlled transport and focusing of laser-accelerated protons with miniature magnetic devices, Phys. Rev. Lett. 101, 055004 (2008).
- M. Key, R. Freeman, S. Hatchett, A. MacKinnon, P. Patel, R. Snavely, and R. Stephens, Proton fast ignition, Fusion Sci. Technol. 49, 440 (2006).
- T. Ditmire, M. Roth, P. Patel, D. Callahan, G. Cheriaux, P. Gibbon, D. Hammond, A. Hannasch, L. Jarrott, G. Schaumann, et al., Focused energy, a new approach towards inertial fusion energy, J. Fusion Energy 42, 27 (2023).
- D. T. Offermann, K. A. Flippo, J. Cobble, M. J. Schmitt, S. Gaillard, T. Bartal, D. Rose, D. 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).
- S. Kar, K. Markey, M. Borghesi, D. Carroll, P. McKenna, D. Neely, M. Quinn, and M. Zepf, Ballistic focusing of polyenergetic protons driven by petawatt laser pulses, Phys. Rev. Lett. 106, 225003 (2011).
- S. Chen, E. d'Humières, E. Lefebvre, L. Romagnani, T. Toncian, P. Antici, P. Audebert, E. Brambrink, C. Cecchetti, T. Kudyakov, et al., Focusing dynamics of high-energy density, laser-driven ion beams, Phys. Rev. Lett. 108, 055001 (2012).
- 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, et al., Focusing of short-pulse high-intensity laser-accelerated proton beams, Nat. Phys. 8, 139 (2012).
- C. McGuffey, J. Kim, M. Wei, P. Nilson, S. Chen, J. Fuchs, P. Fitzsimmons, M. Foord, D. Mariscal, H. McLean, et al., Focussing protons from a kilojoule laser for intense beam heating using proximal target structures, Sci. Rep. 10, 9415 (2020).
- A. Morace, Y. Abe, J. Honrubia, N. Iwata, Y. Arikawa, Y. Nakata, T. Johzaki, A. Yogo, Y. Sentoku, K. Mima, et al., Super-strong magnetic field-dominated ion beam dynamics in focusing plasma devices, Sci. Rep. 12, 6876 (2022).
- B. Shi, A. Yogo, K. Okamoto, D. Golovin, S. R. Mirfayzi, A. Morace, Y. Arikawa, K. Yamanoi, Y. Abe, M. Murakami, et al., Picosecond snapshot imaging of electric fields induced on a cone guide target designed for fast ignition scenario, J. Plasma Phys. 88, 905880404 (2022).
- J. Griff-McMahon, X. Vaisseau, W. Fox, K. Lezhnin, K. Bhutwala, R. Nedbailo, V. Ospina-Bohórquez, T. Karpowski, P. K. Patel, and S. Malko, Geometric scaling of laser-driven proton focusing from hemispherical foils, Phys. Rev. Res. 8, 013182 (2026).
- R. Snavely, B. Zhang, K. Akli, Z. Chen, R. Freeman, P. Gu, S. Hatchett, D. Hey, J. Hill, M. Key, et al., Laser generated proton beam focusing and high temperature isochoric heating of solid matter, Phys. Plasmas 14, 092703 (2007).
- M. Foord, T. Bartal, C. Bellei, M. Key, K. Flippo, R. Stephens, P. Patel, H. McLean, L. Jarrott, M. Wei, et al., Proton trajectories and electric fields in a laser-accelerated focused proton beam, Phys. Plasmas 19, 056702 (2012).
- D. Dorozhkina and V. Semenov, Exact solution of Vlasov equations for quasineutral expansion of plasma bunch into vacuum, Phys. Rev. Lett. 81, 2691 (1998).
- C. Bellei, M. Foord, T. Bartal, M. Key, H. McLean, P. Patel, R. Stephens, and F. Beg, Electron and ion dynamics during the expansion of a laser-heated plasma under vacuum, Phys. Plasmas 19, 033109 (2012).
- B. Qiao, M. Foord, M. Wei, R. Stephens, M. Key, H. McLean, P. Patel, and F. Beg, Dynamics of high-energy proton beam acceleration and focusing from hemisphere-cone targets by high-intensity lasers, Phys. Rev. E 87, 013108 (2013).
- M. Carrié and E. Lefebvre, Focusing of laser-accelerated proton beams using curved targets, and improved energy deposition, High Energy Density Phys. 7, 353 (2011).
- X. Jiang, D. Zou, M. Yu, N. Zhao, L. Hu, J. Ouyang, F. Shao, W. Tang, and T. Yu, High-flux angularly uniform proton beams from multiple laser interaction with wire-hemisphere targets, High Power Laser Sci. Eng. 12, e79 (2024).
- J. Kim, R. Rajawat, T. Wang, and G. Shvets, Acceleration and focusing of multispecies ion beam using a converging laser-driven shock, Phys. Rev. E 111, 025203 (2025).
- A. Kemp, S. Wilks, and M. Tabak, Laser-to-proton conversion efficiency studies for proton fast ignition, Phys. Plasmas 31, 042709 (2024).
- A. Kemp, S. Wilks, M. Tabak, and D. Higginson, On the role of self-generated magnetic fields in focused ion beams driven by intense picosecond laser pulses, Phys. Plasmas 32, 093102 (2025).
- D. Higginson, R. Simpson, A. Kemp, G. Kemp, D. Mariscal, W. Riedel, M. Tabak, S. Wilks, and S. MacLaren, Focusing of laser-accelerated ions with spherically curved targets, Phys. Plasmas 33, 013105 (2026).
- D. Rusby, A. Kemp, S. Wilks, K. Miller, M. Sherlock, H. Chen, R. Simpson, D. Mariscal, K. Swanson, B. Djordjević, et al., Review and meta-analysis of electron temperatures from high-intensity laser–solid interactions, Phys. Plasmas 31, 040503 (2024).
- P. Mora, Plasma expansion into a vacuum, Phys. Rev. Lett. 90, 185002 (2003).
- J. Fuchs, P. Antici, E. d'Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, et al., Laser-driven proton scaling laws and new paths towards energy increase, Nat. Phys. 2, 48 (2006).
- T. D. Arber, K. Bennett, C. S. Brady, A. Lawrence-Douglas, M. Ramsay, N. J. Sircombe, P. Gillies, R. G. Evans, H. Schmitz, A. R. Bell, et al., Contemporary particle-in-cell approach to laser-plasma modelling, Plasma Phys. Controlled Fusion 57, 113001 (2015).
- EPOCH code, https://epochpic.github.io, accessed 26 June 2026.
- O. Buneman, TRISTAN: The 3-D, EM particle code, in Computer Space Plasma Physics: Simulation Techniques and Software, edited by H. Matsumoto and Y. Omura (Terra Scientific Publishing Company, Tokyo, 1993), pp. 67–84.
- M. Allen, P. K. Patel, A. Mackinnon, D. Price, S. Wilks, and E. Morse, Direct experimental evidence of back-surface ion acceleration from laser-irradiated gold foils, Phys. Rev. Lett. 93, 265004 (2004).
- Y. Ping, R. Shepherd, B. F. Lasinski, M. Tabak, H. Chen, H. K. Chung, K. B. Fournier, S. B. Hansen, A. Kemp, D. A. Liedahl, K. Widmann, S. C. Wilks, W. Rozmus, and M. Sherlock, Absorption of short laser pulses on solid targets in the ultrarelativistic regime, Phys. Rev. Lett. 100, 085004 (2008).
- K. Xiao, C. Zhou, K. Jiang, Y. Yang, R. Li, H. Zhang, B. Qiao, T. Huang, J. Cao, T. Cai, et al., Multidimensional effects on proton acceleration using high-power intense laser pulses, Phys. Plasmas 25, 023103 (2018).
- T. Kluge, W. Enghardt, S. Kraft, U. Schramm, K. Zeil, T. Cowan, and M. Bussmann, Enhanced laser ion acceleration from mass-limited foils, Phys. Plasmas 17, 123103 (2010).
- A. Morace, C. Bellei, T. Bartal, L. Willingale, J. Kim, A. Maksimchuk, K. Krushelnick, M. Wei, P. Patel, D. Batani, et al., Improved laser-to-proton conversion efficiency in isolated reduced mass targets, Appl. Phys. Lett. 103, 054102 (2013).
- M. Borghesi, A. J. Mackinnon, D. H. Campbell, D. G. Hicks, S. Kar, P. K. Patel, D. Price, L. Romagnani, A. Schiavi, Multi-MeV proton source investigations in ultraintense laser-foil interactions, Phys. Rev. Lett. 92, 055003 (2004).
- A. Pukhov, Three-dimensional simulations of ion acceleration from a foil irradiated by a short-pulse laser, Phys. Rev. Lett. 86, 3562 (2001).
- G. Sarri, A. Macchi, C. A. Cecchetti, S. Kar, T. V. Liseykina, X. H. Yang, M. E. Dieckmann, J. Fuchs, M. Galimberti, L. Gizzi, et al., Dynamics of self-generated, large amplitude magnetic fields following high-intensity laser matter interaction, Phys. Rev. Lett. 109, 205002 (2012).
- M. Burza, A. Gonoskov, G. Genoud, A. Persson, K. Svensson, M. Quinn, P. McKenna, M. Marklund, and C.-G. Wahlström, Hollow microspheres as targets for staged laser-driven proton acceleration, New J. Phys. 13, 013030 (2011).
- M. King, A. Higginson, C. McGuffey, R. Wilson, G. Schaumann, T. Hodge, J. Ohland, S. Gales, M. Hill, S. Pitt, et al., Geometry effects on energy selective focusing of laser-driven protons with open and closed hemisphere-cone targets, Plasma Phys. Controlled Fusion 66, 015001 (2024).
- C. Caizergues, E. d'Humières, D. Raffestin, M. Tosca, L. Giuffrida, A. Morace, D. Batani, and P. D. Nicolaï, Enhanced proton–boron fusion yield with advanced target geometries under direct laser illumination, Phys. Plasmas 32, 123101 (2025).
- V. Ospina-Bohórquez and X. Vaisseau, Scaling and performance analysis of Smilei in hemispherical foil target simulations for inertial fusion energy, Procedia Comput. Sci. 255, 112 (2025).
- G. R. Lynch and O. I. Dahl, Approximations to multiple Coulomb scattering, Nucl. Instrum. Methods Phys. Res. Sect. B 58, 6 (1991).
- A. RE. Bell and R. J. Kingham, Resistive collimation of electron beams in laser-produced plasmas, Phys. Rev. Lett. 91, 035003 (2003).
- S. Kar, A. P. L. Robinson, D. C. Carroll, O. Lundh, K. Markey, P. McKenna, P. Norreys, and M. Zepf, Guiding of relativistic electron beams in solid targets by resistively controlled magnetic fields, Phys. Rev. Lett. 102, 055001 (2009).
- Z. Lécz, J. Budai, A. Andreev, and S. Ter-Avetisyan, Thickness of natural contaminant layers on metal surfaces and its effects on laser-driven ion acceleration, Phys. Plasmas 27, 013105 (2020).
- A. Sgattoni, P. Londrillo, A. Macchi, and M. Passoni, Laser ion acceleration using a solid target coupled with a low-density layer, Phys. Rev. E 85, 036405 (2012).
- J. Park, J. Bin, S. Steinke, Q. Ji, S. Bulanov, M. Thévenet, J.-L. Vay, T. Schenkel, C. Geddes, C. Schroeder, et al., Target normal sheath acceleration with a large laser focal diameter, Phys. Plasmas 27, 123104 (2020).
- G. Hoffmeister, C. Bellei, K. Harres, D. Ivanov, D. Kraus, A. Pelka, B. Rethfeld, G. Schaumann, and M. Roth, Influence of fs-laser desorption on target normal sheath accelerated ions, Phys. Rev. ST Accel. Beams 16, 041304 (2013).
- B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Lamb, P. MacNeice, R. Rosner, J. Truran, and H. Tufo, FLASH: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes, Astrophys. J. Suppl. Ser. 131, 273 (2000).
- P. Tzeferacos, M. Fatenejad, N. Flocke, C. Graziani, G. Gregori, D. Lamb, D. Lee, J. Meinecke, A. Scopatz, and K. Weide, FLASH MHD simulations of experiments that study shock-generated magnetic fields, High Energy Density Phys. 17, 24 (2015).
- L. A. Gizzi, E. Boella, L. Labate, F. Baffigi, P. J. Bilbao, F. Brandi, G. Cristoforetti, A. Fazzi, L. Fulgentini, D. Giove, et al., Enhanced laser-driven proton acceleration via improved fast electron heating in a controlled pre-plasma, Sci. Rep. 11, 13728 (2021).
- https://doi.org/10.34770/edd2-7q70.