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Essay: Pushing the Frontiers of High Energy Density Science toward Unexplored States of Matter

Federica Coppari*

  • *Contact author: coppari1@llnl.gov

Phys. Rev. Lett. 137, 040001 – Published 20 July, 2026

DOI: https://doi.org/10.1103/1d8y-2cmz

Abstract

Recent breakthroughs in high energy density (HED) science, the study of materials at extreme conditions of pressure and temperature, are profoundly reshaping our understanding across multiple scientific fields. HED science encompasses extreme states of matter across plasma physics, warm dense matter, and condensed matter, bridging fields such as planetary science, materials science, and fusion energy research. Enabled by revolutionary technologies such as ultraintense laser-driven compression, novel insights are emerging from continuous developments. Historically anchored in plasma science, HED physics is evolving toward the understanding of new states of matter, following technological advances. In this Essay, I will present my view of HED science, with particular emphasis on a relatively new and unexplored area within the field that extends beyond plasma physics and warm dense matter, and includes condensed solid and liquid matter at extreme densities and (relatively) cold temperatures.

Part of a series of Essays which concisely present author visions for the future of their field.

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PRL Forward-Looking Essays

To welcome work from areas across the physical sciences and inspire the new generation of physicists, this series of forward-looking Essays is designed to envision future directions for a given topic .

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References (106)

  1. R. Drake, High-Energy-Density Physics: Fundamentals, Inertial Fusion, and Experimental Astrophysics, Shock Wave and High Pressure Phenomena (Springer, Berlin Heidelberg, 2006).
  2. J. Larsen, Foundations of High-Energy-Density Physics: Physical Processes of Matter at Extreme Conditions (Cambridge University Press, Cambridge, England, 2017).
  3. D. Saumon, The sesame 5267 equation of state of deuterium, Technical Report, LA-UR-13-20032, Los Alamos National Laboratory.
  4. C. J. Wu et al., Wide-ranged multiphase equation of state for iron and model variations addressing uncertainties in high-pressure melting, Phys. Rev. B 108, 014102 (2023).
  5. G. I. Kerley, Equations of state for Be, Ni, W, and Au, Technical Report, SAND 2003-3784, Sandia National Laboratories (2003).
  6. J. Colvin and J. Larsen, Extreme Physics (Cambridge University Press, Cambridge, England, 2013).
  7. D. T. Casey et al., Thermonuclear reactions probed at stellar-core conditions with laser-based inertial-confinement fusion, Nat. Phys. 13, 1227 (2017).
  8. O. A. Hurricane, P.  K. Patel, R. Betti, D.  H. Froula, S.  P. Regan, S.  A. Slutz, M.  R. Gomez, and M.  A. Sweeney, Physics principles of inertial confinement fusion and U.S. program overview, Rev. Mod. Phys. 95, 025005 (2023).
  9. D. Riley, Generation and characterisation of warm dense matter with intense lasers, Plasma Phys. Controlled Fusion 60, 014033 (2018).
  10. J. Vorberger et al., Roadmap for warm dense matter physics, Plasma Phys. Controlled Fusion 68, 073501 (2026).
  11. D. Saumon, S. Blouin, and Tremblay, P.-E. Current challenges in the physics of white dwarf stars, Phys. Rep. 988, 1 (2022).
  12. M. Bailly-Grandvaux et al., 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).
  13. A. Boujibar, P. Driscoll, and Y. Fei, Super-Earth internal structures and initial thermal states, J. Geophys. Res. 125, e2019JE006124 (2020).
  14. Fundamental Research in High Energy Density Science (The National Academies Press, Washington, DC, 2023).
  15. Y. Zel’dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic Press Inc., New York, 1966).
  16. L. Davison and R. Graham, Shock compression of solids, Phys. Rep. 55, 255 (1979).
  17. D. C. Swift and R. P. Johnson, Quasi-isentropic compression by ablative laser loading: Response of materials to dynamic loading on nanosecond time scales, Phys. Rev. E 71, 066401 (2005).
  18. It is important to point out that ramp compression of materials results in temperatures that are somewhat higher than the material’s isentrope. This is because the plastic work performed by the uniaxial compression at high strain rate is dissipated as heat [J. Mason, A. Rosakis, and G. Ravichandran, On the strain and strain rate dependence of the fraction of plastic work converted to heat: An experimental study using high speed infrared detectors and the Kolsky bar, Mech. Mater. 17, 135 (1994)].
  19. J. S. Wark, R. R. Whitlock, A. A. Hauer, J. E. Swain, and P. J. Solone, Subnanosecond x-ray diffraction from laser-shocked crystals, Phys. Rev. B 40, 5705 (1989).
  20. D. H. Kalantar et al., Multiple film plane diagnostic for shocked lattice measurements (invited), Rev. Sci. Instrum. 74, 1929 (2003).
  21. J. R. Rygg et al., Powder diffraction from solids in the terapascal regime, Rev. Sci. Instrum. 83, 113904 (2012).
  22. J. M. Foster et al., X-ray diffraction measurements of plasticity in shock-compressed vanadium in the region of 10–70 GPa, J. Appl. Phys. 122, 025117 (2017).
  23. J. R. Rygg et al., X-ray diffraction at the National Ignition Facility, Rev. Sci. Instrum. 91, 043902 (2020).
  24. A. Denoeud et al., X-ray powder diffraction in reflection geometry on multi-beam kJ-type laser facilities, Rev. Sci. Instrum. 92, 013902 (2021).
  25. T. Xi et al., Real-time x-ray diffraction measurement on laser shock-loaded hexanitrostilbene (HNS), Energetic Mater. Front. 5, 224 (2024).
  26. W. A. Bassett, Diamond anvil cell, 50th birthday, High Press. Res. 29, 163 (2009).
  27. M. I. Eremets, I. A. Trojan, P. Gwaze, J. Huth, R. Boehler, and V. D. Blank, The strength of diamond, Appl. Phys. Lett. 87, 141902 (2005).
  28. I. O’Bannon, F. Earl, Z. Jenei, H. Cynn, M. J. Lipp, and J. R. Jeffries, Contributed review: Culet diameter and the achievable pressure of a diamond anvil cell: Implications for the upper pressure limit of a diamond anvil cell, Rev. Sci. Instrum. 89, 111501 (2018).
  29. L. Dubrovinsky, N. Dubrovinskaia, V. B. Prakapenka, and A. M. Abakumov, Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar, Nat. Commun. 3, 1163 (2012).
  30. N. Dubrovinskaia et al., Terapascal static pressure generation with ultrahigh yield strength nanodiamond, Sci. Adv. 2, e1600341 (2016).
  31. A. Dewaele, P. Loubeyre, F. Occelli, O. Marie, and M. Mezouar, Toroidal diamond anvil cell for detailed measurements under extreme static pressures, Nat. Commun. 9, 2913 (2018).
  32. Z. Jenei, E. F. O’Bannon, S. T. Weir, H. Cynn, M. J. Lipp, and W. J. Evans, Single crystal toroidal diamond anvils for high pressure experiments beyond 5 megabar, Nat. Commun. 9, 3563 (2018).
  33. S. Pasternak, G. Aquilanti, S. Pascarelli, R. Poloni, B. Canny, M.-V. Coulet, and L. Zhang, A diamond anvil cell with resistive heating for high pressure and high temperature x-ray diffraction and absorption studies, Rev. Sci. Instrum. 79, 085103 (2008).
  34. A. F. Goncharov, J. A. Montoya, N. Subramanian, V. V. Struzhkin, A. Kolesnikov, M. Somayazulu, and R. J. Hemley, Laser heating in diamond anvil cells: Developments in pulsed and continuous techniques, J. Synchrotron Radiat. 16, 769 (2009).
  35. T. Ishikawa et al., A compact x-ray free-electron laser emitting in the sub-ångström region, Nat. Photonics 6, 540 (2012).
  36. J. Park et al., Design of a hard x-ray beamline and end-station for pump and probe experiments at Pohang Accelerator Laboratory X-ray Free Electron Laser facility, Nucl. Instrum. Methods Phys. Res., Sect. A 810, 74 (2016).
  37. 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).
  38. D. Milathianaki et al., Femtosecond visualization of lattice dynamics in shock-compressed matter, Science 342, 220 (2013).
  39. J. S. Wark, M. I. McMahon, and J. H. Eggert, Femtosecond diffraction and dynamic high pressure science, J. Appl. Phys. 132, 080902 (2022).
  40. W. J. Evans, C.-S. Yoo, G. W. Lee, H. Cynn, M. J. Lipp, and K. Visbeck, Dynamic diamond anvil cell (dDAC): A novel device for studying the dynamic-pressure properties of materials, Rev. Sci. Instrum. 78, 073904 (2007).
  41. B. Nagler et al., The matter in extreme conditions instrument at the linac coherent light source, J. Synchrotron Radiat. 22, 520 (2015).
  42. U. Zastrau et al., The high energy density scientific instrument at the European XFEL, J. Synchrotron Radiat. 28, 1393 (2021).
  43. P. Demontis, R. LeSar, and M. L. Klein, New high-pressure phases of ice, Phys. Rev. Lett. 60, 2284 (1988).
  44. C. Cavazzoni, Superionic and metallic states of water and ammonia at giant planet conditions, Science 283, 44 (1999).
  45. M. French and R. Redmer, Optical properties of water at high temperature, Phys. Plasmas 18, 043301 (2011).
  46. M. French, M. P. Desjarlais, and R. Redmer, Ab initio calculation of thermodynamic potentials and entropies for superionic water, Phys. Rev. E 93, 022140 (2016).
  47. H. F. Wilson, M. L. Wong, and B. Militzer, Superionic to Superionic Phase change in water: Consequences for the interiors of uranus and neptune, Phys. Rev. Lett. 110, 151102 (2013).
  48. J. A. Hernandez and R. Caracas, Superionic-superionic phase transitions in body-centered cubic H2 O Ice, Phys. Rev. Lett. 117, 135503 (2016).
  49. 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).
  50. M. Millot, F. Coppari, J. R. Rygg, A. C. Barrios, S. Hamel, D. C. Swift, and J. H. Eggert, Nanosecond x-ray diffraction of shock-compressed superionic water ice, Nature (London) 569, 251 (2019).
  51. J. Haldemann, Y. Alibert, C. Mordasini, and W. Benz, AQUA: A collection of H2O equations of state for planetary models, Astron. Astrophys. 643, A105 (2020).
  52. R. Redmer, T. R. Mattsson, N. Nettelmann, and M. French, The phase diagram of water and the magnetic fields of Uranus and Neptune, Icarus 211, 798 (2011).
  53. B. Militzer, Ab initio entropy calculations of water predict the interiors of uranus and neptune to be 15%–30% colder than previous models, Astrophys. J. 990, 20 (2025).
  54. J. A. Queyroux et al., Melting curve and isostructural solid transition in superionic ice, Phys. Rev. Lett. 125, 195501 (2020).
  55. V. B. Prakapenka, N. Holtgrewe, S. S. Lobanov, and A. F. Goncharov, Structure and properties of two superionic ice phases, Nat. Phys. 17, 1233 (2021).
  56. G. Weck, J.-A. Queyroux, S. Ninet, F. Datchi, M. Mezouar, and P. Loubeyre, Evidence and stability field of fcc superionic water ice using static compression, Phys. Rev. Lett. 128, 165701 (2022).
  57. M. Gorman et al., Shock compression experiments using the DiPOLE 100-X laser on the high energy density instrument at the European x-ray free electron laser: Quantitative structural analysis of liquid Sn, J. Appl. Phys. 135, 165902 (2022).
  58. G. Morard et al., Structural evolution of liquid silicates under conditions in Super-Earth interiors, Nat. Commun. 15, 8483 (2024).
  59. H. F. Swift, Light-Gas Gun Technology: A Historical Perspective (Springer, Berlin, Heidelberg, 2005), pp. 1–35.
  60. W. A. Stygar, M. E. Cuneo, D. I. Headley, H. C. Ives, R. J. Leeper, M. G. Mazarakis, C. L. Olson, J. L. Porter, T. C. Wagoner, and J. R. Woodworth, Architecture of petawatt-class z-pinch accelerators, Phys. Rev. ST Accel. Beams 10, 030401 (2007).
  61. F. Coppari, R. F. Smith, D. B. Thorn, J. R. Rygg, D. A. Liedahl, R. G. Kraus, A. Lazicki, M. Millot, and J. H. Eggert, Optimized x-ray sources for x-ray diffraction measurements at the Omega Laser Facility, Rev. Sci. Instrum. 90, 125113 (2019).
  62. D. Broege et al., The Dynamic Compression Sector laser: A 100-J UV laser for dynamic compression research, Rev. Sci. Instrum. 90, 053001 (2019).
  63. K. Tono et al., Beamline, experimental stations and photon beam diagnostics for the hard x-ray free electron laser of SACLA, New J. Phys. 15, 083035 (2013).
  64. A. Dewaele, M. Mezouar, N. Guignot, and P. Loubeyre, High melting points of tantalum in a laser-heated diamond anvil cell, Phys. Rev. Lett. 104, 255701 (2010).
  65. M. C. Akin, J. H. Nguyen, M. A. Beckwith, R. Chau, W. P. Ambrose, O. V. Fat’yanov, P. D. Asimow, and N. C. Holmes, Tantalum sound velocity under shock compression, J. Appl. Phys. 125, 145903 (2019).
  66. R. G. Kraus, F. Coppari, D.  E. Fratanduono, R.  F. Smith, A. Lazicki, C. Wehrenberg, J.  H. Eggert, J.  R. Rygg, and G.  W. Collins, Melting of tantalum at multimegabar pressures on the nanosecond timescale, Phys. Rev. Lett. 126, 255701 (2021).
  67. A. Lazicki et al., Metastability of diamond ramp-compressed to 2 TPa, Nature (London) 589, 532 (2021).
  68. M. T. Yin, Si-III (BC-8) crystal phase of Si and C: Structural properties, phase stabilities, and phase transitions, Phys. Rev. B 30, 1773 (1984).
  69. A. A. Correa, S. A. Bonev, and G. Galli, Carbon under extreme conditions: Phase boundaries and electronic properties from first-principles theory, Proc. Natl. Acad. Sci. U.S.A. 103, 1204 (2006).
  70. M. Martinez-Canales, C. J. Pickard, and R. J. Needs, Thermodynamically stable phases of carbon at multiterapascal pressures, Phys. Rev. Lett. 108, 045704 (2012).
  71. J. Sun, D. D. Klug, and Martoňák, R. Structural transformations in carbon under extreme pressure: Beyond diamond, J. Chem. Phys. 130, 194512 (2009).
  72. K. Nguyen-Cong et al., Extreme metastability of diamond and its transformation to the BC8 post-diamond phase of carbon, J. Phys. Chem. Lett. 15, 1152 (2024).
  73. R. J. Husband et al., Phase transition kinetics of superionic H2O ice phases revealed by Megahertz x-ray free-electron laser-heating experiments, Nat. Commun. 15, 8256 (2024).
  74. Y.-H. Lee et al., Multiple freezing–melting pathways of high-density ice through ice XXI phase at room temperature, Nat. Mater. 25, 302 (2025).
  75. J. B. Neaton and N. W. Ashcroft, On the constitution of sodium at higher densities, Phys. Rev. Lett. 86, 2830 (2001).
  76. Y. Ma, M. Eremets, A. R. Oganov, Y. Xie, I. Trojan, S. Medvedev, A. O. Lyakhov, M. Valle, and V. Prakapenka, Transparent dense sodium, Nature (London) 458, 182 (2009).
  77. C. V. Storm et al., Experimental signatures of interstitial electron density in transparent dense sodium, Commun. Mater. 6, 201 (2025).
  78. M.-S. Miao and R. Hoffmann, High pressure electrides: A predictive chemical and physical theory, Acc. Chem. Res. 47, 1311 (2014).
  79. C. J. Pickard and R. J. Needs, Aluminium at terapascal pressures, Nat. Mater. 9, 624 (2010).
  80. M. G. Gorman et al., Experimental observation of open structures in elemental magnesium at terapascal pressures, Nat. Phys. 18, 1307 (2022).
  81. J. B. Neaton and N. W. Ashcroft, Pairing in dense lithium, Nature (London) 400, 141 (1999).
  82. M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, New high-pressure phases of lithium, Nature (London) 408, 174 (2000).
  83. P. Li, G. Gao, Y. Wang, and Y. Ma, Crystal structures and exotic behavior of magnesium under pressure, J. Phys. Chem. C 114, 21745 (2010).
  84. X. Dong et al., A stable compound of helium and sodium at high pressure, Nat. Chem. 9, 440 (2017).
  85. H. Zong, V. N. Robinson, A. Hermann, L. Zhao, S. Scandolo, X. Ding, and G. J. Ackland, Free electron to electride transition in dense liquid potassium, Nat. Phys. 17, 955 (2021).
  86. S. Ahmed, F. González-Cataldo, V. N. Robinson, and B. Militzer, Electride behavior at high pressure in silicon and other elements in solid and liquid phases, Phys. Rev. B 112, 165111 (2025).
  87. T. Guillot, The interiors of giant planets: Models and outstanding questions, Annu. Rev. Earth Planet Sci. 33, 493 (2005).
  88. D. S. Spiegel, J. J. Fortney, and C. Sotin, Structure of exoplanets, Proc. Natl. Acad. Sci. U.S.A. 111, 12622 (2014).
  89. R. Helled, N. Nettelmann, and T. Guillot, Uranus and neptune: Origin, evolution and internal structure, Space Sci. Rev. 216, 38 (2020).
  90. S. Stanley and J. Bloxham, Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields, Nature (London) 428, 151 (2004).
  91. M. Bethkenhagen, D. Cebulla, R. Redmer, and S. Hamel, Superionic phases of the 1∶1 water-ammonia mixture, J. Phys. Chem. A 119, 10582 (2015).
  92. T. Thévenet et al., From methane to nanodiamond precursors in water: Superacid-like condensation pathways under extreme conditions, Angew. Chem., Int. Ed. Engl. 65, e20364 (2025).
  93. F. Coppari, R. F. Smith, J. H. Eggert, J. Wang, J. R. Rygg, A. Lazicki, J. A. Hawreliak, G. W. Collins, and T. S. Duffy, Experimental evidence for a phase transition in magnesium oxide at exoplanet pressures, Nat. Geosci. 6, 926 (2013).
  94. F. Coppari, R. F. Smith, J. Wang, M. Millot, D. Kim, J. R. Rygg, S. Hamel, J. H. Eggert, and T. S. Duffy, Implications of the iron oxide phase transition on the interiors of rocky exoplanets, Nat. Geosci. 14, 121 (2021).
  95. Z. Konôpková, R. S. McWilliams, N. Gómez-Pérez, and A. F. Goncharov, Direct measurement of thermal conductivity in solid iron at planetary core conditions, Nature (London) 534, 99 (2016).
  96. K. Ohta, Y. Kuwayama, K. Hirose, K. Shimizu, and Y. Ohishi, Experimental determination of the electrical resistivity of iron at Earth’s core conditions, Nature (London) 534, 95 (2016).
  97. 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).
  98. M. Guarguaglini, F. Soubiran, J.-A. Hernandez, A. Benuzzi-Mounaix, R. Bolis, E. Brambrink, T. Vinci, and A. Ravasio, Electrical conductivity of warm dense silica from double-shock experiments, Nat. Commun. 12, 840 (2021).
  99. A. W. Ashley, M. Mookherjee, M. Xu, T. Yu, G. Manthilake, and Y. Wang, Viscosity measurements at high pressures: A critical appraisal of corrections to stokes’ law, J. Geophys. Res. 129, e2023JB028489 (2024).
  100. Anjeli Paola P. Estrada Alvarez et al., Viscous motion of particles in shock-compressed epoxy, Abstract submitted to the 65th Annual Meeting of the APS Division of Plasma Physics, 2023, https://meetings-archive.aps.org/dpp/2023/cp11/64/.
  101. P. W. Hatfield et al., The data-driven future of high-energy-density physics, Nature (London) 593, 351 (2021).
  102. S. Jiang et al., Thermal transport in warm dense matter revealed by refraction-enhanced x-ray radiography with a deep-neural-network analysis, Commun. Phys. 6, 98 (2023).
  103. M. J. Guardalben, L. N. Goduguluri, A. Mathur, J. Wang, and R. Yadav, Prediction of laser beam spatial profiles in a high-energy laser facility by use of deep learning, Opt. Express 32, 42692 (2024).
  104. L. Fiedler, K. Shah, M. Bussmann, and A. Cangi, Deep dive into machine learning density functional theory for materials science and chemistry, Phys. Rev. Mater. 6, 040301 (2022).
  105. B. Huang, G. F. von Rudorff, and O. A. von Lilienfeld, The central role of density functional theory in the AI age, Science 381, 170 (2023).
  106. Foundation Models for Scientific Discovery and Innovation: Opportunities Across the Department of Energy and the Scientific Enterprise (The National Academies Press, Washington, DC, 2025).

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