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Shock compression of liquid helium to 360 GPa

M. Wadas1,2,*, S. Brygoo3, P. Loubeyre3, P. M. Celliers4, G. W. Collins5, J. H. Eggert4, R. Jeanloz6, E. Johnsen1, B. Militzer6 et al.

J. R. Rygg5 and M. Millot4

  • *Contact author: mwadas@umich.edu
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Phys. Rev. Research 8, 013335 – Published 27 March, 2026

DOI: https://doi.org/10.1103/87r3-tgy1

Abstract

Data for the shock equation of state of helium are obtained up to 360GPa, nearly doubling the pressure of previous experimental measurements. The helium samples are first precompressed to 0.35–0.42 gcm−3 in a diamond anvil cell prior to laser-driven shock compression at the Omega Laser Facility. Time-resolved Doppler velocimetry and pyrometry reveal significant reflectivity and greater compressibility compared to the predictions of existing broad-range tabular equation of state models, which may be caused by the onset of ionization. These experimental observations, however, are largely captured with molecular-dynamics simulations based on density functional theory, affirming the ability of first-principles techniques to capture complex physics, while enabling critical insight for the behavior of warm dense helium in Jovian interiors and white dwarf atmospheres.

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Corrections

18 May, 2026

Correction: Affiliation number 3 was presented incorrectly and has been fixed. The value given in the second sentence of the abstract has been fixed.

Article Text

References (66)

  1. P. J. Kortbeek and J. A. Schouten, Equation of state of fluid helium to very high pressure, Chem. Phys. 95, 4519 (1991).
  2. J. M. McMahon, M. A. Morales, C. Pierleoni, and D. M. Ceperley, The properties of hydrogen and helium under extreme conditions, Rev. Mod. Phys. 84, 1607 (2012).
  3. B. Militzer, F. Soubiran, S. M. Wahl, and W. Hubbard, Understanding Jupiter’s interior, J. Geophys. Res. Planets 121, 1552 (2016).
  4. G. Chabrier, S. Mazevet, and François Soubiran, A new equation of state for dense hydrogen–helium mixtures, Astrophys. J. 872, 51 (2019).
  5. D. Saumon, S. Blouin, and P.-E. Tremblay, Current challenges in the physics of white dwarf stars, Phys. Rep. 988, 1 (2022).
  6. B. Militzer, W. B. Hubbard, S. Wahl, J. I. Lunine, E. Galanti, Y. Kaspi, Y. Miguel, T. Guillot, K. M. Moore, M. Parisi, et al., Juno spacecraft measurements of Jupiter’s gravity imply a dilute core, Planet. Sci. J. 3, 185 (2022).
  7. B. Militzer, S. Wahl, and W. B. Hubbard, Models of Saturn’s interior constructed with an accelerated concentric Maclaurin spheroid method, Astrophys. J. 879, 78 (2019).
  8. L. Stixrude and R. Jeanloz, Fluid helium at conditions of giant planetary interiors, Proc. Natl. Acad. Sci. USA 105, 11071 (2008).
  9. F. Soubiran, S. Mazevet, C. Winisdoerffer, and G. Chabrier, Optical signature of hydrogen-helium demixing at extreme density-temperature conditions, Phys. Rev. B 87, 165114 (2013).
  10. J. Zheng, Q. F. Chen, Y. J. Gu, J. T. Li, Z. G. Li, C. J. Li, and Z. Y. Chen, Shock-adiabatic to quasi-isentropic compression of warm dense helium up to 150 GPa, Phys. Rev. B 95, 224104 (2017).
  11. S. Brygoo, P. Loubeyre, M. Millot, J. R. Rygg, P. M. Celliers, J. H. Eggert, R. Jeanloz, and G. W. Collins, Evidence of hydrogen- helium immiscibility at Jupiter-interior conditions, Nature (London) 593, 517 (2021).
  12. P. M. Celliers, P. Loubeyre, J. H. Eggert, S. Brygoo, R. S. McWilliams, D. G. Hicks, T. R. Boehly, R. Jeanloz, and G. W. Collins, Insulator-to-conducting transition in dense fluid helium, Phys. Rev. Lett. 104, 184503 (2010).
  13. F. Soubiran, S. Mazevet, C. Winisdoerffer, and G. Chabrier, Helium gap in the warm dense matter regime and experimental reflectivity measurements, Phys. Rev. B 86, 115102 (2012).
  14. C. R. Mankovich and J. J. Fortney, Evidence for a dichotomy in the interior structures of Jupiter and Saturn from helium phase separation, Astrophys. J. 889, 51 (2020).
  15. M. A. Morales, E. Schwegler, D. Ceperley, C. Pierleoni, S. Hamel, and K. Caspersen, Phase separation in hydrogen–helium mixtures at Mbar pressures, Proc. Natl. Acad. Sci. USA 106, 1324 (2009).
  16. S. A. Khairallah and B. Militzer, First-principles studies of the metallization and the equation of state of solid helium, Phys. Rev. Lett. 101, 106407 (2008).
  17. P. Bergeron, D. Saumon, and F. Wesemael, New model atmospheres for very cool white dwarfs with mixed H/He and pure He compositions, Astrophys. J. 443, 764 (1995).
  18. C. A. Iglesias, F. J. Rogers, and D. Saumon, Density effects on the opacity of cool helium white dwarf atmospheres, Astrophys. J. 569, L111 (2002).
  19. P. M. Kowalski, S. Mazevet, D. Saumon, and M. Challacombe, Equation of state and optical properties of warm dense helium, Phys. Rev. B 76, 075112 (2007).
  20. M. Preising and R. Redmer, Metallization of dense fluid helium from ab initio simulations, Phys. Rev. B 102, 224107 (2020).
  21. T. Dornheim, Z. A Moldabekov, K. Ramakrishna, P. Tolias, A. D Baczewski, D. Kraus, T. R. Preston, D. A. Chapman, M. P. Böhme, T. Döppner, et al., Electronic density response of warm dense matter, Phys. Plasmas 30, 032705 (2023).
  22. B. Militzer, First principles calculations of shock compressed fluid helium, Phys. Rev. Lett. 97, 175501 (2006).
  23. A. Kietzmann, B. Holst, R. Redmer, M. P. Desjarlais, and T. R. Mattsson, Quantum molecular dynamics simulations for the nonmetal-to-metal transition in fluid helium, Phys. Rev. Lett. 98, 190602 (2007).
  24. B. Militzer, Path integral Monte Carlo and density functional molecular dynamics simulations of hot, dense helium, Phys. Rev. B 79, 155105 (2009).
  25. B. Militzer, Correlations in hot dense helium, J. Phys. A: Math. Theor. 42, 214001 (2009).
  26. C. Winisdoerffer and G. Chabrier, Free-energy model for fluid helium at high density, Phys. Rev. E 71, 026402 (2005).
  27. N. Nettelmann, B. Holst, A. Kietzmann, M. French, R. Redmer, and D. Blaschke, Ab initio equation of state data for hydrogen, helium, and water and the internal structure of Jupiter, Astrophys. J. 683, 1217 (2008).
  28. M. Preising, W. Lorenzen, A. Becker, R. Redmer, M. D. Knudson, and M. P. Desjarlais, Equation of state and optical properties of warm dense helium, Phys. Plasmas 25, 012706 (2018).
  29. Z.-G. Li, Y. Cheng, Q.-F. Chen, and X.-R. Chen, Equation of state and transport properties of warm dense helium via quantum molecular dynamics simulations, Phys. Plasmas 23, 052701 (2016).
  30. M. Ross and D. A. Young, Helium at high density, Phys. Lett. A 118, 463 (1986).
  31. M. A. Mochalov, R. I. Il’kaev, V. E. Fortov, A. L. Mikhailov, V. A. Arinin, A. O. Blikov, S. E. Elfimov, V. A. Komrakov, V. A. Ogorodnikov, and A. V. Ryzhkov, Thermodynamic parameters of helium under shock-wave and quasi-isentropic compressions at pressures up to 4800 GPa and compression ratios up to 900, J. Exp. Theor. Phys. 125, 948 (2017).
  32. V. K. Gryaznov, I. L. Iosilevskiy, and V. E. Fortov, Thermodynamics of hydrogen and helium plasmas in megabar and multi-megabar pressure range under strong shock and isentropic compression, Plasma Phys. Control. Fusion 58, 014012 (2016).
  33. M. Preising and R. Redmer, Nonmetal-to-metal transition in dense fluid helium, Contrib. Plasma Phys. 61, e202100105 (2021).
  34. A. Förster, T. Kahlbaum, and W. Ebeling, Equation of state and the phase diagram of dense fluid helium in the region of partial ionization, Laser Part. Beams 10, 253 (1992).
  35. V. D. Urlin, Equations of state and the phase diagram of dielectric and metallic helium-4, J. Exp. Theor. Phys. 127, 121 (2018).
  36. R. M. More, K. H. Warren, D. A. Young, and G. B. Zimmerman, A new quotidian equation of state (QEOS) for hot dense matter, Phys. Fluids 31, 3059 (1988).
  37. S. P. Lyon, Sesame: The Los Alamos National Laboratory equation of state database, Los Alamos National Laboratory Report No. LA-UR-92-3407 (Los Alamos National Laboratory, LA,1992).
  38. A. Becker, W. Lorenzen, J. J. Fortney, N. Nettelmann, M. Schöttler, and R. Redmer, Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of brown dwarfs, Astrophys. J. Suppl. Ser. 215, 21 (2014).
  39. B. Militzer, F. González-Cataldo, S. Zhang, K. P. Driver, and F. Soubiran, First-principles equation of state database for warm dense matter computation, Phys. Rev. E 103, 013203 (2021).
  40. D. Saumon, Evaluation of helium equation of state tables, Technical Report No. LA-UR-20-25308, Los Alamos National Laboratory (LANL) (Los Alamos, NM, USA, 2020).
  41. J. Eggert, S. Brygoo, P. Loubeyre, R. S. McWilliams, P. M. Celliers, D. G. Hicks, T. R. Boehly, R. Jeanloz, and G. W. Collins, Hugoniot data for helium in the ionization regime, Phys. Rev. Lett. 100, 124503 (2008).
  42. S. Brygoo, M. Millot, P. Loubeyre, A. E. Lazicki, S. Hamel, T. Qi, et al., Analysis of laser shock experiments on precompressed samples using a quartz reference and application to warm dense hydrogen and helium, J. Appl. Phys. 118, 195901 (2015).
  43. P. Loubeyre, J. M. Besson, J. P. Pinceaux, and J. P. Hansen, High-pressure melting curve of He4, Phys. Rev. Lett. 49, 1172 (1982).
  44. R. Le Toullec, P. Loubeyre, and J.-P. Pinceaux, Refractive-index measurements of dense helium up to 16 GPa at T = 298 K: Analysis of its thermodynamic and electronic properties, Phys. Rev. B 40, 2368 (1989).
  45. P. Loubeyre, R. LeToullec, J. P. Pinceaux, H. K. Mao, J. Hu, and R. J. Hemley, Equation of state and phase diagram of solid He4 from single-crystal x-ray diffraction over a large P-T domain, Phys. Rev. Lett. 71, 2272 (1993).
  46. W. L. Vos, M. G. E. van Hinsberg, and J. A. Schouten, High-pressure triple point in helium: The melting line of helium up to 240 kbar, Phys. Rev. B 42, 6106 (1990).
  47. W. J. Nellis, N. C. Holmes, A. C. Mitchell, R. J. Trainor, G. K. Governo, M. Ross, and D. A. Young, Shock compression of liquid helium to 56 GPa (560 kbar), Phys. Rev. Lett. 53, 1248 (1984).
  48. A. C. Mitchell and W. J. Nellis, Diagnostic system of the Lawrence Livermore National Laboratory two-stage light-gas gun, Rev. Sci. Instrum. 52, 347 (1981).
  49. R. Jeanloz, P. M. Celliers, G. W. Collins, J. H. Eggert, K. M. Lee, R. S. McWilliams, S. Brygoo, and P. Loubeyre, Achieving high-density states through shock-wave loading of precompressed samples, Proc. Natl. Acad. Sci. USA 104, 9172 (2007).
  50. M. J. Wadas, G. Cearley, J. Eggert, E. Johnsen, and M. Millot, A theoretical approach for transient shock strengthening in high-energy-density laser compression experiments, Phys. Plasmas 28, 082708 (2021).
  51. M. Millot, S. Hamel, J. R. Rygg, P. M. Celliers, G. W. Collins, F. Coppari, D. E. Fratanduono, R. Jeanloz, D. C. Swift, and J. H. Eggert, Experimental evidence for superionic water ice using shock compression, Nat. Phys. 14, 297 (2018).
  52. J. C. Chervin, B. Canny, and M. Mancinelli, Ruby-spheres as pressure gauge for optically transparent high pressure cells, Int. J. High Pressure Res. 21, 305 (2001).
  53. E. Calderon, M. Gauthier, F. Decremps, G. Hamel, G. Syfosse, and A. Polian, Complete determination of the elastic moduli of α-quartz under hydrostatic pressure up to 1 GPa: An ultrasonic study, J. Phys.: Condens. Matter 19, 436228 (2007).
  54. G. Ghosh, Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals, Opt. Commun. 163, 95 (1999).
  55. A. Dewaele, J. H. Eggert, P. Loubeyre, and R. Le Toullec, Measurement of refractive index and equation of state in dense He, H2, H2O, and Ne under high pressure in a diamond anvil cell, Phys. Rev. B 67, 094112 (2003).
  56. P. M. Celliers, D. K. Bradley, G. W. Collins, D. G. Hicks, T. R. Boehly, and W. J. Armstrong, Line-imaging velocimeter for shock diagnostics at the OMEGA laser facility, Rev. Sci. Instrum. 75, 4916 (2004).
  57. P. M. Celliers and M. Millot, Imaging velocity interferometer system for any reflector (VISAR) diagnostics for high energy density sciences, Rev. Sci. Instrum. 94, 011101 (2023).
  58. M. D. Knudson and M. P. Desjarlais, Shock compression of quartz to 1.6 TPa: Redefining a pressure standard, Phys. Rev. Lett. 103, 225501 (2009).
  59. M. P. Desjarlais, M. D. Knudson, and K. R. Cochrane, Extension of the Hugoniot and analytical release model of α-quartz to 0.2–3 TPa, J. Appl. Phys. 122, 035903 (2017).
  60. Y.-J. Kim, B. Militzer, B. Boates, S. Bonev, P. Celliers, G. Collins, et al., Evidence for dissociation and ionization in shock compressed nitrogen to 800 GPa, Phys. Rev. Lett. 129, 015701 (2022).
  61. G. I. Kerley, An equation of state for helium, Kerley Technical Services report KTS04-2 (Kerley Technical Services, Appomattox, VA, 2004), arXiv:1306.6577.
  62. C. T. Seagle, W. D. Reinhart, A. J. Lopez, R. J. Hickman, T. F. Thornhill, High precision hugoniot measurements on statically pre-compressed fluid helium, J. Appl. Phys. 120, 125902 (2016).
  63. D. G. Hicks, T. R. Boehly, J. H. Eggert, J. E. Miller, P. M. Celliers, and G. W. Collins, Dissociation of liquid silica at high pressures and temperatures, Phys. Rev. Lett. 97, 025502 (2006).
  64. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  65. J. E. Miller, T. R. Boehly, A. Melchior, D. D. Meyerhofer, P. M. Celliers, J. H. Eggert, D. G. Hicks, C. M. Sorce, J. A. Oertel, and P. M. Emmel, Streaked optical pyrometer system for laser-driven shock-wave experiments on OMEGA, Rev. Sci. Instrum. 78, 034903 (2007).
  66. M. Millot, N. Dubrovinskaia, A. Černok, S. Blaha, L. Dubrovinsky, D. G. Braun, P. M. Celliers, G. W. Collins, J. H. Eggert, and R. Jeanloz, Shock compression of stishovite and melting of silica at planetary interior conditions, Science 347, 418 (2015).

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Phys. Rev. Research 8, 013335– Published 27 March, 2026
  • Received 11 April 2025
  • Accepted 10 February 2026
  • Corrected 18 May 2026
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