A Review of Equation-of-State Models for Inertial Confinement Fusion Materials

Gaffney, J. A.; Hu, S. X.; Arnault, P.; Becker, A.; Benedict, L. X.; Boehly, T. R.; Celliers, P. M.; Ceperley, D. M.; Čertík, O.; Clérouin, J.; Collins, G. W.; Collins, L. A.; Danel, J. -F.; Desbiens, N.; Dharma-wardana, M. W. C.; Ding, Y. H.; Fernandez-Pañella, A.; Gregor, M. C.; Grabowski, P. E.; Hamel, S.; Hansen, S. B.; Harbour, L.; He, X. T.; Johnson, D. D.; Kang, W.; Karasiev, V. V.; Kazandjian, L.; Knudson, M. D.; Ogitsu, T.; Pierleoni, C.; Piron, R.; Redmer, R.; Robert, G.; Saumon, D.; Shamp, A.; Sjostrom, T.; Smirnov, A. V.; Starrett, C. E.; Sterne, P. A.; Wardlow, A.; Whitley, H. D.; Wilson, B.; Zhang, P.; Zurek, E.

doi:10.1016/j.hedp.2018.08.001

A Review of Equation-of-State Models for Inertial Confinement Fusion Materials

Journal Article · Sat Aug 18 00:00:00 UTC 2018 · High Energy Density Physics

DOI:https://doi.org/10.1016/j.hedp.2018.08.001· OSTI ID:1476340

Gaffney, J. A. ^[1]; Hu, S. X. ^[2]; Arnault, P. ^[3]; Becker, A. ^[4]; Benedict, L. X. ^[5]; Boehly, T. R. ^[2]; ^[5]; Ceperley, D. M. ^[6]; ^[7]; ^[3]; Collins, G. W. ^[2]; Collins, L. A. ^[7]; Danel, J. -F. ^[3]; Desbiens, N. ^[3]; Dharma-wardana, M. W. C. ^[8]; Ding, Y. H. ^[2]; Fernandez-Pañella, A. ^[5]; Gregor, M. C. ^[5]; Grabowski, P. E. ^[5]; Hamel, S. ^[5] more »

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Laboratory for Laser Energetics, University of Rochester
Univ. of Rochester, NY (United States). Lab. for Laser Energetics
Alternative Energies and Atomic Energy Commission (CEA), Arpajon (France)
Univ. Rostock, Rostock (Germany). Inst. für Physik
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Physics
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
National Research Council of Canada, Ottawa (Canada)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of Montreal, Quebec (Canada)
Peking Univ., Beijing (China). Center for Applied Physics and Technology, HEDPS; Inst. of Applied Physics and Computational Mathematics, Beijing (China)
Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Materials Science & Engineering
Peking Univ., Beijing (China). Center for Applied Physics and Technology, HEDPS; Peking Univ., Beijing (China). College of Engineering
Washington State Univ., Pullman, WA (United States)
Univ. of L’Aquila (Italy).Dept. of Physical and Chemical Sciences; Univ. Paris-Sud, Orsay (France); Univ. Paris-Saclay, Gif-sur-Yvette (France). Maison de la Simulation
State Univ. of New York at Buffalo (SUNY), Buffalo, NY (United States). Dept. of Chemistry
Ames Lab. and Iowa State Univ., Ames, IA (United States)
AWE Aldermaston, Reading, Berkshire (United Kingdom)

Material equation-of-state (EOS) models, generally providing the pressure and internal energy for a given density and temperature, are required to close the equations of hydrodynamics. As a result they are an essential piece of physics used to simulate inertial con nement fusion (ICF) implosions. Historically, EOS models based on different physical/chemical pictures of matter have been developed for ICF relevant materials such as the deuterium (D2) or deuterium-tritium (DT) fuel, as well as candidate ablator materials such as polystyrene (CH), glow-discharge polymer (GDP), Berylium (Be), Carbon (C), and boron carbide (B₄C). The accuracy of these EOS models can directly affect the reliability of ICF target design and understanding, as shock timing and material compressibility are essentially determined by what EOS models are used in ICF simulations. Systematic comparisons of current EOS models, benchmarking with experiments, not only help us to understand what model differences are and why they occur, but also to identify the state-of-the-art EOS models for ICF target designers to use. For this purpose, the first Equation of- State Workshop, supported by the US Department of Energy's ICF program, was held at the Laboratory for Laser Energetics (LLE), University of Rochester on 31 May - 2nd June, 2017. Finally, this paper presents a detailed review on the findings from this workshop: (1) 5-10% model-model variations exist throughout the relevant parameter space, and can be much larger in regions where ionization and dissociation are occurring, (2) the D₂ EOS is particularly uncertain, with no single model able to match the available experimental data, and this drives similar uncertainties in the CH EOS, and (3) new experimental capabilities such as Hugoniot measurements around 100 Mbar and high-quality temperature measurements are essential to reducing EOS uncertainty.

View Accepted Manuscript (DOE)

Research Organization:: Ames Laboratory (AMES), Ames, IA (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Univ. of Rochester, NY (United States). Lab. for Laser Energetics

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001; AC02-07CH11358; AC04-94AL85000; AC52-06NA25396; AC52-07NA27344; NA0001944; NA0002006; NA0003525; SC0002139

OSTI ID:: 1476340

Alternate ID(s):: OSTI ID: 1703957
OSTI ID: 23071540
OSTI ID: 1483369
OSTI ID: 1489960
OSTI ID: 1496980
OSTI ID: 1497265

Report Number(s):: 1--437; 2018--156; IS-J--9757; LA-UR--18-25070; LLNL-JRNL--750338; SAND--2018-9706J; 2018-156, 1437, 2395

Journal Information:: High Energy Density Physics, Journal Name: High Energy Density Physics Journal Issue: C Vol. 28; ISSN 1574-1818

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (151)

Properties of Hot Dense Plasmas by Orbital-Free Molecular Dynamics Lambert, F.; Clérouin, J.; Mazevet, S. Contributions to Plasma Physics, Vol. 47, Issue 4-5 https://doi.org/10.1002/ctpp.200710037	journal	July 2007
Fermion nodes Ceperley, D. M. Journal of Statistical Physics, Vol. 63, Issue 5-6 https://doi.org/10.1007/BF01030009	journal	June 1991
Inferno: A better model of atoms in dense plasmas Liberman, David A. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 27, Issue 3 https://doi.org/10.1016/0022-4073(82)90125-X	journal	March 1982
On the calculation of the energy of a Bloch wave in a metal Korringa, J. Physica, Vol. 13, Issue 6-7 https://doi.org/10.1016/0031-8914(47)90013-X	journal	August 1947
New method for the calculation of the pair correlation function. I van Leeuwen, J. M. J.; Groeneveld, J.; de Boer, J. Physica, Vol. 25, Issue 7-12 https://doi.org/10.1016/0031-8914(59)90004-7	journal	January 1959
Equation of state and phase diagram of dense hydrogen Kerley, Gerald I. Physics of the Earth and Planetary Interiors, Vol. 6, Issue 1-3 https://doi.org/10.1016/0031-9201(72)90036-2	journal	January 1972
Statistical mechanics of simple coulomb systems Baus, M. Physics Reports, Vol. 59, Issue 1 https://doi.org/10.1016/0370-1573(80)90022-8	journal	March 1980
Density functional formalism at finite temperatures with some applications Gupta, Uday; Rajagopal, A. K. Physics Reports, Vol. 87, Issue 6 https://doi.org/10.1016/0370-1573(82)90077-1	journal	July 1982
Review of the NLTE emissivities code comparison virtual workshop Bowen, C.; Decoster, A.; Fontes, C. J. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 81, Issue 1-4 https://doi.org/10.1016/S0022-4073(03)00061-X	journal	September 2003
WorkOp-IV summary: lessons from iron opacities Serduke, Franklin J. D.; Minguez, Emilio; Davidson, Steven J. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 65, Issue 1-3 https://doi.org/10.1016/S0022-4073(99)00094-1	journal	April 2000
Finite-temperature orbital-free DFT molecular dynamics: Coupling Profess and Quantum Espresso Karasiev, Valentin V.; Sjostrom, Travis; Trickey, S. B. Computer Physics Communications, Vol. 185, Issue 12 https://doi.org/10.1016/j.cpc.2014.08.023	journal	December 2014
High-mode Rayleigh-Taylor growth in NIF ignition capsules Hammel, B. A.; Haan, S. W.; Clark, D. S. High Energy Density Physics, Vol. 6, Issue 2 https://doi.org/10.1016/j.hedp.2009.12.005	journal	June 2010
Multi-center electronic structure calculations for plasma equation of state Wilson, B. G.; Johnson, D. D.; Alam, A. High Energy Density Physics, Vol. 7, Issue 2 https://doi.org/10.1016/j.hedp.2011.01.002	journal	June 2011
Large-scale molecular dynamics simulations of dense plasmas: The Cimarron Project Graziani, Frank R.; Batista, Victor S.; Benedict, Lorin X. High Energy Density Physics, Vol. 8, Issue 1 https://doi.org/10.1016/j.hedp.2011.06.010	journal	March 2012
Ab initio calculations of the equation of state of hydrogen in a regime relevant for inertial fusion applications Morales, Miguel A.; Benedict, Lorin X.; Clark, Daniel S. High Energy Density Physics, Vol. 8, Issue 1 https://doi.org/10.1016/j.hedp.2011.09.002	journal	March 2012
A simple method for determining the ionic structure of warm dense matter Starrett, C. E.; Saumon, D. High Energy Density Physics, Vol. 10 https://doi.org/10.1016/j.hedp.2013.12.001	journal	March 2014
Comparing plasma population kinetics codes: Review of the NLTE-3 Kinetics Workshop Bowen, C.; Lee, R. W.; Ralchenko, Yu. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 99, Issue 1-3 https://doi.org/10.1016/j.jqsrt.2005.05.008	journal	May 2006
Purgatorio—a new implementation of the Inferno algorithm Wilson, B.; Sonnad, V.; Sterne, P. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 99, Issue 1-3 https://doi.org/10.1016/j.jqsrt.2005.05.053	journal	May 2006
Shock compression of diamond crystal Kondo, Ken-ichi; Ahrens, Thomas J. Geophysical Research Letters, Vol. 10, Issue 4 https://doi.org/10.1029/GL010i004p00281	journal	April 1983
Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications Nuckolls, John; Wood, Lowell; Thiessen, Albert Nature, Vol. 239, Issue 5368, p. 139-142 https://doi.org/10.1038/239139a0	journal	September 1972
The ice layer in Uranus and Neptune—diamonds in the sky? Ross, Marvin Nature, Vol. 292, Issue 5822 https://doi.org/10.1038/292435a0	journal	July 1981
Fuel gain exceeding unity in an inertially confined fusion implosion Hurricane, O. A.; Callahan, D. A.; Casey, D. T. Nature, Vol. 506, Issue 7488 https://doi.org/10.1038/nature13008	journal	February 2014
Ramp compression of diamond to five terapascals Smith, R. F.; Eggert, J. H.; Jeanloz, R. Nature, Vol. 511, Issue 7509 https://doi.org/10.1038/nature13526	journal	July 2014
Laser-shock compression of diamond and evidence of a negative-slope melting curve Brygoo, Stéphanie; Henry, Emeric; Loubeyre, Paul Nature Materials, Vol. 6, Issue 4 https://doi.org/10.1038/nmat1863	journal	March 2007
Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions Kraus, D.; Vorberger, J.; Pak, A. Nature Astronomy, Vol. 1, Issue 9 https://doi.org/10.1038/s41550-017-0219-9	journal	August 2017
Reflected shock experiments on the equation-of-state properties of liquid deuterium at 100–600 GPa (1–6 Mbar) Mostovych, A. N.; Chan, Y.; Lehecha, T. Physics of Plasmas, Vol. 8, Issue 5 https://doi.org/10.1063/1.1359444	journal	May 2001
Electrical conductivities of methane, benzene, and polybutene shock compressed to 60 GPa (600 kbar) Nellis, W. J.; Hamilton, D. C.; Mitchell, A. C. The Journal of Chemical Physics, Vol. 115, Issue 2 https://doi.org/10.1063/1.1379537	journal	July 2001
Effective Potentials between the Components of a Hydrogeneous Plasma Barker, A. A. The Journal of Chemical Physics, Vol. 55, Issue 4 https://doi.org/10.1063/1.1676306	journal	August 1971
Properties of fluid deuterium under double-shock compression to several Mbar Boehly, T. R.; Hicks, D. G.; Celliers, P. M. Physics of Plasmas, Vol. 11, Issue 9 https://doi.org/10.1063/1.1778164	journal	September 2004
Equation-of-state measurements for polystyrene at multi-TPa pressures in laser direct-drive experiments Ozaki, N.; Ono, T.; Takamatsu, K. Physics of Plasmas, Vol. 12, Issue 12 https://doi.org/10.1063/1.2149310	journal	December 2005
Early stage of implosion in inertial confinement fusion: Shock timing and perturbation evolution Goncharov, V. N.; Gotchev, O. V.; Vianello, E. Physics of Plasmas, Vol. 13, Issue 1 https://doi.org/10.1063/1.2162803	journal	January 2006
Hugoniot measurement of diamond under laser shock compression up to 2TPa Nagao, H.; Nakamura, K. G.; Kondo, K. Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2205194	journal	May 2006
Demonstration of the shock-timing technique for ignition targets on the National Ignition Facility Boehly, T. R.; Munro, D.; Celliers, P. M. Physics of Plasmas, Vol. 16, Issue 5 https://doi.org/10.1063/1.3078422	journal	May 2009
Shock Hugoniot and temperature data for polystyrene obtained with quartz standard Ozaki, N.; Sano, T.; Ikoma, M. Physics of Plasmas, Vol. 16, Issue 6 https://doi.org/10.1063/1.3152287	journal	June 2009
Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field Slutz, S. A.; Herrmann, M. C.; Vesey, R. A. Physics of Plasmas, Vol. 17, Issue 5 https://doi.org/10.1063/1.3333505	journal	May 2010
High-precision measurements of the equation of state of hydrocarbons at 1–10 Mbar using laser-driven shock waves Barrios, M. A.; Hicks, D. G.; Boehly, T. R. Physics of Plasmas, Vol. 17, Issue 5 https://doi.org/10.1063/1.3358144	journal	May 2010
Plastic ablator ignition capsule design for the National Ignition Facility Clark, Daniel S.; Haan, Steven W.; Hammel, Bruce A. Physics of Plasmas, Vol. 17, Issue 5 https://doi.org/10.1063/1.3403293	journal	May 2010
X-ray ablation rates in inertial confinement fusion capsule materials Olson, R. E.; Rochau, G. A.; Landen, O. L. Physics of Plasmas, Vol. 18, Issue 3 https://doi.org/10.1063/1.3566009	journal	March 2011
Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility Haan, S. W.; Lindl, J. D.; Callahan, D. A. Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3592169	journal	May 2011
A new global equation of state model for hot, dense matter Young, David A.; Corey, Ellen M. Journal of Applied Physics, Vol. 78, Issue 6 https://doi.org/10.1063/1.359955	journal	September 1995
Equation of state of beryllium at shock pressures of 0.4–1.1 TPa (4–11 Mbar) Nellis, W. J.; Moriarty, J. A.; Mitchell, A. C. Journal of Applied Physics, Vol. 82, Issue 5 https://doi.org/10.1063/1.366029	journal	September 1997
Shock timing experiments on the National Ignition Facility: Initial results and comparison with simulation Robey, H. F.; Boehly, T. R.; Celliers, P. M. Physics of Plasmas, Vol. 19, Issue 4 https://doi.org/10.1063/1.3694122	journal	April 2012
Systematics of high-pressure and high-temperature behavior of hydrocarbons Ree, Francis H. The Journal of Chemical Physics, Vol. 70, Issue 2 https://doi.org/10.1063/1.437487	journal	January 1979
Equation‐of‐state data for molecular hydrogen and deuterium at shock pressures in the range 2–76 GPa (20–760 kbar) ^a) Nellis, W. J.; Mitchell, A. C.; van Thiel, M. The Journal of Chemical Physics, Vol. 79, Issue 3 https://doi.org/10.1063/1.445938	journal	August 1983
Equation of state and optical luminosity of benzene, polybutene, and polyethylene shocked to 210 GPa (2.1 Mbar) Nellis, W. J.; Ree, F. H.; Trainor, R. J. The Journal of Chemical Physics, Vol. 80, Issue 6 https://doi.org/10.1063/1.447027	journal	March 1984
Precision equation-of-state measurements on National Ignition Facility ablator materials from 1 to 12 Mbar using laser-driven shock waves Barrios, M. A.; Boehly, T. R.; Hicks, D. G. Journal of Applied Physics, Vol. 111, Issue 9 https://doi.org/10.1063/1.4712050	journal	May 2012
Equation of state of dense plasmas by ab initio simulations: Bridging the gap between quantum molecular dynamics and orbital-free molecular dynamics at high temperature Danel, J. -F.; Kazandjian, L.; Zérah, G. Physics of Plasmas, Vol. 19, Issue 12 https://doi.org/10.1063/1.4773191	journal	December 2012
High-density carbon ablator experiments on the National Ignition Facility MacKinnon, A. J.; Meezan, N. B.; Ross, J. S. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4876611	journal	May 2014
Equation of state of dense plasmas: Orbital-free molecular dynamics as the limit of quantum molecular dynamics for high- Z elements Danel, J. -F.; Blottiau, P.; Kazandjian, L. Physics of Plasmas, Vol. 21, Issue 10 https://doi.org/10.1063/1.4897190	journal	October 2014
Impact of first-principles properties of deuterium–tritium on inertial confinement fusion target designs Hu, S. X.; Goncharov, V. N.; Boehly, T. R. Physics of Plasmas, Vol. 22, Issue 5 https://doi.org/10.1063/1.4917477	journal	April 2015
Direct-drive inertial confinement fusion: A review Craxton, R. S.; Anderson, K. S.; Boehly, T. R. Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4934714	journal	November 2015
Extended application of Kohn-Sham first-principles molecular dynamics method with plane wave approximation at high energy—From cold materials to hot dense plasmas Zhang, Shen; Wang, Hongwei; Kang, Wei Physics of Plasmas, Vol. 23, Issue 4 https://doi.org/10.1063/1.4947212	journal	April 2016
First beryllium capsule implosions on the National Ignition Facility Kline, J. L.; Yi, S. A.; Simakov, A. N. Physics of Plasmas, Vol. 23, Issue 5 https://doi.org/10.1063/1.4948277	journal	May 2016
Symmetry control of an indirectly driven high-density-carbon implosion at high convergence and high velocity Divol, L.; Pak, A.; Berzak Hopkins, L. F. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982215	journal	May 2017
Performance of beryllium targets with full-scale capsules in low-fill 6.72-mm hohlraums on the National Ignition Facility Simakov, A. N.; Wilson, D. C.; Yi, S. A. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4983141	journal	May 2017
First-principles equation-of-state table of beryllium based on density-functional theory calculations Ding, Y. H. Physics of Plasmas, Vol. 24, Issue 6 https://doi.org/10.1063/1.4984780	journal	June 2017
Extension of the Hugoniot and analytical release model of α -quartz to 0.2–3 TPa Desjarlais, M. P.; Knudson, M. D.; Cochrane, K. R. Journal of Applied Physics, Vol. 122, Issue 3 https://doi.org/10.1063/1.4991814	journal	July 2017
A review on ab initio studies of static, transport, and optical properties of polystyrene under extreme conditions for inertial confinement fusion applications Collins, L. A.; Boehly, T. R.; Ding, Y. H. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5017970	journal	May 2018
A new quotidian equation of state (QEOS) for hot dense matter More, R. M.; Warren, K. H.; Young, D. A. Physics of Fluids, Vol. 31, Issue 10 https://doi.org/10.1063/1.866963	journal	January 1988
Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain Lindl, John Physics of Plasmas, Vol. 2, Issue 11 https://doi.org/10.1063/1.871025	journal	November 1995
Absolute measurements of the equations of state of low-Z materials in the multi-Mbar regime using laser-driven shocks Cauble, R.; Da Silva, L. B.; Perry, T. S. Physics of Plasmas, Vol. 4, Issue 5 https://doi.org/10.1063/1.872362	journal	May 1997
The development and advantages of beryllium capsules for the National Ignition Facility Wilson, Douglas C.; Bradley, Paul A.; Hoffman, Nelson M. Physics of Plasmas, Vol. 5, Issue 5 https://doi.org/10.1063/1.872865	journal	May 1998
A generic model for the ionic contribution to the equation of state Johnson, J. D. High Pressure Research, Vol. 6, Issue 5 https://doi.org/10.1080/08957959108203212	journal	December 1991
An Equation of State for Low-Mass Stars and Giant Planets Saumon, D.; Chabrier, G.; van Horn, H. M. The Astrophysical Journal Supplement Series, Vol. 99 https://doi.org/10.1086/192204	journal	July 1995
Testing White Dwarf Crystallization Theory with Asteroseismology of the Massive Pulsating DA Star BPM 37093 Metcalfe, T. S.; Montgomery, M. H.; Kanaan, A. The Astrophysical Journal, Vol. 605, Issue 2 https://doi.org/10.1086/420884	journal	March 2004
Shock Compression of Deuterium and the Interiors of Jupiter and Saturn Saumon, D.; Guillot, T. The Astrophysical Journal, Vol. 609, Issue 2 https://doi.org/10.1086/421257	journal	July 2004
Explicit local exchange-correlation potentials Hedin, L.; Lundqvist, B. I. Journal of Physics C: Solid State Physics, Vol. 4, Issue 14 https://doi.org/10.1088/0022-3719/4/14/022	journal	October 1971
A selfconsistent calculation of the rigid neutral atom density according to the auxiliary neutral atom model Dagens, L. Journal of Physics C: Solid State Physics, Vol. 5, Issue 17 https://doi.org/10.1088/0022-3719/5/17/011	journal	September 1972
AB INITIO EQUATIONS OF STATE FOR HYDROGEN (H-REOS.3) AND HELIUM (He-REOS.3) AND THEIR IMPLICATIONS FOR THE INTERIOR OF BROWN DWARFS Becker, Andreas; Lorenzen, Winfried; Fortney, Jonathan J. The Astrophysical Journal Supplement Series, Vol. 215, Issue 2 https://doi.org/10.1088/0067-0049/215/2/21	journal	January 2014
National direct-drive program on OMEGA and the National Ignition Facility Goncharov, V. N.; Regan, S. P.; Campbell, E. M. Plasma Physics and Controlled Fusion, Vol. 59, Issue 1 https://doi.org/10.1088/0741-3335/59/1/014008	journal	October 2016
Indirect drive ignition at the National Ignition Facility Meezan, N. B.; Edwards, M. J.; Hurricane, O. A. Plasma Physics and Controlled Fusion, Vol. 59, Issue 1 https://doi.org/10.1088/0741-3335/59/1/014021	journal	October 2016
A POSSIBLE CARBON-RICH INTERIOR IN SUPER-EARTH 55 Cancri e Madhusudhan, Nikku; Lee, Kanani K. M.; Mousis, Olivier The Astrophysical Journal, Vol. 759, Issue 2 https://doi.org/10.1088/2041-8205/759/2/L40	journal	October 2012
Extension of the Thomas-Fermi-Dirac Statistical Theory of the Atom to Finite Temperatures Cowan, R. D.; Ashkin, J. Physical Review, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRev.105.144	journal	January 1957
Shock-Wave Compressions of Twenty-Seven Metals. Equations of State of Metals Walsh, John M.; Rice, Melvin H.; McQueen, Robert G. Physical Review, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRev.108.196	journal	October 1957
Thermal Properties of the Inhomogeneous Electron Gas Mermin, N. David Physical Review, Vol. 137, Issue 5A https://doi.org/10.1103/PhysRev.137.A1441	journal	March 1965
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Equations of State of Elements Based on the Generalized Fermi-Thomas Theory Feynman, R. P.; Metropolis, N.; Teller, E. Physical Review, Vol. 75, Issue 10 https://doi.org/10.1103/PhysRev.75.1561	journal	May 1949
Solution of the Schrödinger Equation in Periodic Lattices with an Application to Metallic Lithium Kohn, W.; Rostoker, N. Physical Review, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRev.94.1111	journal	June 1954
Statistical mechanics of Coulomb gases of arbitrary charge Rogers, F. J. Physical Review A, Vol. 10, Issue 6 https://doi.org/10.1103/PhysRevA.10.2441	journal	December 1974
Formation of composites in equilibrium plasmas Rogers, F. J. Physical Review A, Vol. 19, Issue 1 https://doi.org/10.1103/PhysRevA.19.375	journal	January 1979
Gradient correction to the statistical electronic free energy at nonzero temperatures: Application to equation-of-state calculations Perrot, F. Physical Review A, Vol. 20, Issue 2 https://doi.org/10.1103/PhysRevA.20.586	journal	August 1979
Equation of state of dense, partially degenerate, reacting plasmas Rogers, F. J. Physical Review A, Vol. 24, Issue 3 https://doi.org/10.1103/PhysRevA.24.1531	journal	September 1981
Shock compression measurements at 1 to 7 TPa Ragan, Charles E. Physical Review A, Vol. 25, Issue 6 https://doi.org/10.1103/PhysRevA.25.3360	journal	June 1982
Statistical Mechanics of Reacting Coulomb Gases Rogers, F. J.; DeWitt, H. E. Physical Review A, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevA.8.1061	journal	August 1973
Self-consistent field model for condensed matter Liberman, David A. Physical Review B, Vol. 20, Issue 12 https://doi.org/10.1103/PhysRevB.20.4981	journal	December 1979
Temperature measurements and dissociation of shock-compressed liquid deuterium and hydrogen Holmes, N. C.; Ross, M.; Nellis, W. J. Physical Review B, Vol. 52, Issue 22 https://doi.org/10.1103/PhysRevB.52.15835	journal	December 1995
Equation of state and the Hugoniot of laser shock-compressed deuterium: Demonstration of a basis-function-free method for quantum calculations Dharma-wardana, M. W. C.; Perrot, François Physical Review B, Vol. 66, Issue 1 https://doi.org/10.1103/PhysRevB.66.014110	journal	July 2002
Principal Hugoniot, reverberating wave, and mechanical reshock measurements of liquid deuterium to 400 GPa using plate impact techniques Knudson, M. D.; Hanson, D. L.; Bailey, J. E. Physical Review B, Vol. 69, Issue 14 https://doi.org/10.1103/PhysRevB.69.144209	journal	April 2004
Shock compression of liquid deuterium up to 109 GPa Boriskov, G. V.; Bykov, A. I.; Il’kaev, R. I. Physical Review B, Vol. 71, Issue 9 https://doi.org/10.1103/PhysRevB.71.092104	journal	March 2005
High-precision measurements of the diamond Hugoniot in and above the melt region Hicks, D. G.; Boehly, T. R.; Celliers, P. M. Physical Review B, Vol. 78, Issue 17 https://doi.org/10.1103/PhysRevB.78.174102	journal	November 2008
Laser-driven single shock compression of fluid deuterium from 45 to 220 GPa Hicks, D. G.; Boehly, T. R.; Celliers, P. M. Physical Review B, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevB.79.014112	journal	January 2009
Strength effects in diamond under shock compression from 0.1 to 1 TPa McWilliams, R. S.; Eggert, J. H.; Hicks, D. G. Physical Review B, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevB.81.014111	journal	January 2010
First-principles equation-of-state table of deuterium for inertial confinement fusion applications Hu, S. X.; Militzer, B.; Goncharov, V. N. Physical Review B, Vol. 84, Issue 22 https://doi.org/10.1103/PhysRevB.84.224109	journal	December 2011
Equation of state of CH 1.36 : First-principles molecular dynamics simulations and shock-and-release wave speed measurements Hamel, Sebastien; Benedict, Lorin X.; Celliers, Peter M. Physical Review B, Vol. 86, Issue 9 https://doi.org/10.1103/PhysRevB.86.094113	journal	September 2012
Extended data set for the equation of state of warm dense hydrogen isotopes Loubeyre, P.; Brygoo, S.; Eggert, J. Physical Review B, Vol. 86, Issue 14 https://doi.org/10.1103/PhysRevB.86.144115	journal	October 2012
High-pressure–temperature phase diagram and the equation of state of beryllium Lazicki, Amy; Dewaele, Agnès; Loubeyre, Paul Physical Review B, Vol. 86, Issue 17 https://doi.org/10.1103/PhysRevB.86.174118	journal	November 2012
Isentropic compression of hydrogen: Probing conditions deep in planetary interiors Becker, Andreas; Nettelmann, Nadine; Holst, Bastian Physical Review B, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevB.88.045122	journal	July 2013
Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations Karasiev, Valentin V.; Chakraborty, Debajit; Shukruto, Olga A. Physical Review B, Vol. 88, Issue 16 https://doi.org/10.1103/PhysRevB.88.161108	journal	October 2013
Adiabatic release measurements in α -quartz between 300 and 1200 GPa: Characterization of α -quartz as a shock standard in the multimegabar regime Knudson, M. D.; Desjarlais, M. P. Physical Review B, Vol. 88, Issue 18 https://doi.org/10.1103/PhysRevB.88.184107	journal	November 2013
Multiphase equation of state for carbon addressing high pressures and temperatures Benedict, Lorin X.; Driver, Kevin P.; Hamel, Sebastien Physical Review B, Vol. 89, Issue 22 https://doi.org/10.1103/PhysRevB.89.224109	journal	June 2014
Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide Sjostrom, Travis; Crockett, Scott Physical Review B, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevB.92.115104	journal	September 2015
Equation of state, adiabatic sound speed, and Grüneisen coefficient of boron carbide along the principal Hugoniot to 700 GPa Fratanduono, D. E.; Celliers, P. M.; Braun, D. G. Physical Review B, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevB.94.184107	journal	November 2016
Validity boundary of orbital-free molecular dynamics method corresponding to thermal ionization of shell structure Gao, Chang; Zhang, Shen; Kang, Wei Physical Review B, Vol. 94, Issue 20 https://doi.org/10.1103/PhysRevB.94.205115	journal	November 2016
Hugoniot and release measurements in diamond shocked up to 26 Mbar Gregor, M. C.; Fratanduono, D. E.; McCoy, C. A. Physical Review B, Vol. 95, Issue 14 https://doi.org/10.1103/PhysRevB.95.144114	journal	April 2017
Properties of B 4 C in the shocked state for pressures up to 1.5 TPa Shamp, Andrew; Zurek, Eva; Ogitsu, Tadashi Physical Review B, Vol. 95, Issue 18 https://doi.org/10.1103/PhysRevB.95.184111	journal	May 2017
Measuring the shock impedance mismatch between high-density carbon and deuterium at the National Ignition Facility Millot, M.; Celliers, P. M.; Sterne, P. A. Physical Review B, Vol. 97, Issue 14 https://doi.org/10.1103/PhysRevB.97.144108	journal	April 2018
Ion-ion interaction and equation of state of a dense plasma: Application to beryllium Perrot, F. Physical Review E, Vol. 47, Issue 1 https://doi.org/10.1103/PhysRevE.47.570	journal	January 1993
Validation of the activity expansion method with ultrahigh pressure shock equations of state Rogers, Forrest J.; Young, David A. Physical Review E, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevE.56.5876	journal	November 1997
Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas Benedict, Lorin X.; Surh, Michael P.; Castor, John I. Physical Review E, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevE.86.046406	journal	October 2012
Electronic and ionic structures of warm and hot dense matter Starrett, C. E.; Saumon, D. Physical Review E, Vol. 87, Issue 1 https://doi.org/10.1103/PhysRevE.87.013104	journal	January 2013
Classical representation of a quantum system at equilibrium: Theory Dufty, James; Dutta, Sandipan Physical Review E, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevE.87.032101	journal	March 2013
Thomas-Fermi Z -scaling laws and coupling stabilization for plasmas Arnault, Philippe; Clérouin, Jean; Robert, Gregory Physical Review E, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevE.88.063106	journal	December 2013
Combining Kohn-Sham and orbital-free density-functional theory for Hugoniot calculations to extreme pressures Sheppard, Daniel; Kress, Joel D.; Crockett, Scott Physical Review E, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevE.90.063314	journal	December 2014
Pseudoatom molecular dynamics Starrett, C. E.; Daligault, J.; Saumon, D. Physical Review E, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevE.91.013104	journal	January 2015
High-density carbon capsule experiments on the national ignition facility Ross, J. S.; Ho, D.; Milovich, J. Physical Review E, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevE.91.021101	journal	February 2015
First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions Hu, S. X.; Collins, L. A.; Goncharov, V. N. Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.043104	journal	October 2015
Equation of state of warm dense deuterium and its isotopes from density-functional theory molecular dynamics Danel, J. -F.; Kazandjian, L.; Piron, R. Physical Review E, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevE.93.043210	journal	April 2016
Equation of state of dense plasmas with pseudoatom molecular dynamics Starrett, C. E.; Saumon, D. Physical Review E, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevE.93.063206	journal	June 2016
Dissociation along the principal Hugoniot of the Laser Mégajoule ablator material Colin-Lalu, P.; Recoules, V.; Salin, G. Physical Review E, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevE.94.023204	journal	August 2016
Equation of state, phonons, and lattice stability of ultrafast warm dense matter Harbour, L.; Dharma-wardana, M. W. C.; Klug, D. D. Physical Review E, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevE.95.043201	journal	April 2017
First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations Hu, S. X.; Gao, R.; Ding, Y. Physical Review E, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevE.95.043210	journal	April 2017
High-temperature electronic structure with the Korringa-Kohn-Rostoker Green's function method Starrett, C. E. Physical Review E, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevE.97.053205	journal	May 2018
Studies of Plastic-Ablator Compressibility for Direct-Drive Inertial Confinement Fusion on Omega Hu, S. X.; Smalyuk, V. A.; Goncharov, V. N. Physical Review Letters, Vol. 100, Issue 18 https://doi.org/10.1103/PhysRevLett.100.185003	journal	May 2008
Diamond at 800 GPa Bradley, D. K.; Eggert, J. H.; Smith, R. F. Physical Review Letters, Vol. 102, Issue 7 https://doi.org/10.1103/PhysRevLett.102.075503	journal	February 2009
Shock Compression of Quartz to 1.6 TPa: Redefining a Pressure Standard Knudson, M. D.; Desjarlais, M. P. Physical Review Letters, Vol. 103, Issue 22 https://doi.org/10.1103/PhysRevLett.103.225501	journal	November 2009
Velocity and Timing of Multiple Spherically Converging Shock Waves in Liquid Deuterium Boehly, T. R.; Goncharov, V. N.; Seka, W. Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.195005	journal	May 2011
High-Gain Magnetized Inertial Fusion Slutz, Stephen A.; Vesey, Roger A. Physical Review Letters, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevLett.108.025003	journal	January 2012
Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations Karasiev, Valentin V.; Sjostrom, Travis; Dufty, James Physical Review Letters, Vol. 112, Issue 7 https://doi.org/10.1103/PhysRevLett.112.076403	journal	February 2014
Experimental Demonstration of Fusion-Relevant Conditions in Magnetized Liner Inertial Fusion Gomez, M. R.; Slutz, S. A.; Sefkow, A. B. Physical Review Letters, Vol. 113, Issue 15 https://doi.org/10.1103/PhysRevLett.113.155003	journal	October 2014
Fast and Accurate Quantum Molecular Dynamics of Dense Plasmas Across Temperature Regimes Sjostrom, Travis; Daligault, Jérôme Physical Review Letters, Vol. 113, Issue 15 https://doi.org/10.1103/PhysRevLett.113.155006	journal	October 2014
Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations Tubman, Norm M.; Liberatore, Elisa; Pierleoni, Carlo Physical Review Letters, Vol. 115, Issue 4 https://doi.org/10.1103/PhysRevLett.115.045301	journal	July 2015
Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements Militzer, Burkhard; Driver, Kevin P. Physical Review Letters, Vol. 115, Issue 17 https://doi.org/10.1103/PhysRevLett.115.176403	journal	October 2015
High-Precision Shock Wave Measurements of Deuterium: Evaluation of Exchange-Correlation Functionals at the Molecular-to-Atomic Transition Knudson, M. D.; Desjarlais, M. P. Physical Review Letters, Vol. 118, Issue 3 https://doi.org/10.1103/PhysRevLett.118.035501	journal	January 2017
Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B. Physical Review Letters, Vol. 120, Issue 7 https://doi.org/10.1103/PhysRevLett.120.076401	journal	February 2018
Fusion Energy Output Greater than the Kinetic Energy of an Imploding Shell at the National Ignition Facility Le Pape, S.; Berzak Hopkins, L. F.; Divol, L. Physical Review Letters, Vol. 120, Issue 24 https://doi.org/10.1103/PhysRevLett.120.245003	journal	June 2018
Unified Approach for Molecular Dynamics and Density-Functional Theory Car, R.; Parrinello, M. Physical Review Letters, Vol. 55, Issue 22 https://doi.org/10.1103/PhysRevLett.55.2471	journal	November 1985
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Absolute Equation of State Measurements on Shocked Liquid Deuterium up to 200 GPa (2 Mbar) Da Silva, L. B.; Celliers, P.; Collins, G. W. Physical Review Letters, Vol. 78, Issue 3 https://doi.org/10.1103/PhysRevLett.78.483	journal	January 1997
Simple Classical Mapping of the Spin-Polarized Quantum Electron Gas: Distribution Functions and Local-Field Corrections Dharma-wardana, M. W. C.; Perrot, F. Physical Review Letters, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevLett.84.959	journal	January 2000
2D Electron Gas at Arbitrary Spin Polarizations and Coupling Strengths: Exchange-Correlation Energies, Distribution Functions, and Spin-Polarized Phases Perrot, François; Dharma-wardana, M. W. C. Physical Review Letters, Vol. 87, Issue 20 https://doi.org/10.1103/PhysRevLett.87.206404	journal	October 2001
Equation of State Measurements in Liquid Deuterium to 70 GPa Knudson, M. D.; Hanson, D. L.; Bailey, J. E. Physical Review Letters, Vol. 87, Issue 22 https://doi.org/10.1103/PhysRevLett.87.225501	journal	November 2001
Use of a Wave Reverberation Technique to Infer the Density Compression of Shocked Liquid Deuterium to 75 GPa Knudson, M. D.; Hanson, D. L.; Bailey, J. E. Physical Review Letters, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevLett.90.035505	journal	January 2003
Path integrals in the theory of condensed helium Ceperley, D. M. Reviews of Modern Physics, Vol. 67, Issue 2 https://doi.org/10.1103/RevModPhys.67.279	journal	April 1995
Shock-Wave Exploration of the High-Pressure Phases of Carbon Knudson, M. D.; Desjarlais, M. P.; Dolan, D. H. Science, Vol. 322, Issue 5909 https://doi.org/10.1126/science.1165278	journal	December 2008
Astrophysical Opacity Rogers, F. J.; Iglesias, C. A. Science, Vol. 263, Issue 5143 https://doi.org/10.1126/science.263.5143.50	journal	January 1994
Measurements of the Equation of State of Deuterium at the Fluid Insulator-Metal Transition Collins, G. W. Science, Vol. 281, Issue 5380 https://doi.org/10.1126/science.281.5380.1178	journal	August 1998
Temperature measurements of shock-compressed liquid hydrogen: implications for the interior of Jupiter Nellis, W.; Ross, M.; Holmes, N. Science, Vol. 269, Issue 5228 https://doi.org/10.1126/science.7652570	journal	September 1995
Shock compression of solid deuterium Belov, S. I.; Boriskov, G. V.; Bykov, A. I. Journal of Experimental and Theoretical Physics Letters, Vol. 76, Issue 7 https://doi.org/10.1134/1.1528696	journal	October 2002
Shock-wave compression of solid deuterium at a pressure of 120 GPa Boriskov, G. V.; Bykov, A. I.; Il’kaev, R. I. Doklady Physics, Vol. 48, Issue 10 https://doi.org/10.1134/1.1623535	journal	October 2003
Experimental measurements of the compressibility, temperature, and light absorption in dense shock-compressed gaseous deuterium Grishechkin, S. K.; Gruzdev, S. K.; Gryaznov, V. K. Journal of Experimental and Theoretical Physics Letters, Vol. 80, Issue 6 https://doi.org/10.1134/1.1830656	journal	September 2004
Measuring high pressure equation of state of polystyrene using laser driven shock wave Shu, Hua; Huang, Xiuguang; Ye, Junjian The European Physical Journal D, Vol. 69, Issue 11 https://doi.org/10.1140/epjd/e2015-60378-x	journal	November 2015

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