Citation: | Kang Dongdong, Hou Yong, Zeng Qiyu, Dai Jiayu. Unified first-principles equations of state of deuterium-tritium mixtures in the global inertial confinement fusion region[J]. Matter and Radiation at Extremes, 2020, 5(5): 055401. doi: 10.1063/5.0008231 |
[1] |
E. M. Campbell, V. N. Goncharov, T. C. Sangster, S. P. Regan, P. B. Radha et al., “Laser-direct-drive program: Promise, challenge, and path forward,” Matter Radiat. Extremes 2, 37 (2017).10.1016/j.mre.2017.03.001 doi: 10.1016/j.mre.2017.03.001
|
[2] |
Z. Li, Z. Wang, R. Xu, J. Yang, F. Ye et al., “Experimental investigation of Z-pinch radiation source for indirect drive inertial confinement fusion,” Matter Radiat. Extremes 4, 046201 (2019).10.1063/1.5099088 doi: 10.1063/1.5099088
|
[3] |
J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2, 3933 (1995).10.1063/1.871025 doi: 10.1063/1.871025
|
[4] |
L. Caillabet, S. Mazevet, and P. Loubeyre, “Multiphase equation of state of hydrogen from ab initio calculations in the range 0.2 to 5 g/cc up to 10 eV,” Phys. Rev. B 83, 094101 (2011).10.1103/physrevb.83.094101 doi: 10.1103/physrevb.83.094101
|
[5] |
L. Caillabet, B. Canaud, G. Salin, S. Mazevet, and P. Loubeyre, “Change in inertial confinement fusion implosions upon using an ab initio multiphase DT equation of state,” Phys. Rev. Lett. 107, 115004 (2011).10.1103/physrevlett.107.115004 doi: 10.1103/physrevlett.107.115004
|
[6] |
S. X. Hu, B. Militzer, V. N. Goncharov, and S. Skupsky, “First-principles equation-of-state table of deuterium for inertial confinement fusion applications,” Phys. Rev. B 84, 224109 (2011).10.1103/physrevb.84.224109 doi: 10.1103/physrevb.84.224109
|
[7] |
S. X. Hu, L. A. Collins, V. N. Goncharov, J. D. Kress, T. R. Boehly et al., “First-principles studies on the equation of state, thermal conductivity, and opacity of deuterium-tritium (DT) and polystyrene (CH) for inertial confinement fusion applications,” J. Phys.: Conf. Ser. 717, 012064 (2016).10.1088/1742-6596/717/1/012064 doi: 10.1088/1742-6596/717/1/012064
|
[8] |
J. Danel, L. Kazandjian, and R. Piron, “Equation of state of warm dense deuterium and its isotopes from density-functional theory molecular dynamics,” Phys. Rev. E 93, 043210 (2016).10.1103/physreve.93.043210 doi: 10.1103/physreve.93.043210
|
[9] |
C. Wang and P. Zhang, “Wide range equation of state for fluid hydrogen from density functional theory,” Phys. Plasmas 20, 092703 (2013).10.1063/1.4821839 doi: 10.1063/1.4821839
|
[10] |
M. A. Morales, L. X. Benedict, D. S. Clark, E. Schwegler, I. Tamblyn et al., “Ab initio calculations of the equation of state of hydrogen in a regime relevant for inertial fusion applications,” High Energy Density Phys. 8, 5 (2012).10.1016/j.hedp.2011.09.002 doi: 10.1016/j.hedp.2011.09.002
|
[11] |
H. Liu, G. Zhang, Q. Zhang, H. Song, Q. Li et al., “Progress on equation of state of hydrogen and deuterium,” Chin. J. High Pressure Phys. 32, 050101 (2018).10.11858/gywlxb.20180587 doi: 10.11858/gywlxb.20180587
|
[12] |
J. A. Gaffney, S. X. Hu, P. Arnault, A. Becker, L. X. Benedict et al., “A review of equation-of-state models for inertial confinement fusion materials,” High Energy Density Phys. 28, 7 (2018).10.1016/j.hedp.2018.08.001 doi: 10.1016/j.hedp.2018.08.001
|
[13] |
S. Faik, A. Tauschwitz, and I. Iosilevskiy, “The equation of state package FEOS for high energy density matter,” Comput. Phys. Commun. 227, 117 (2018).10.1016/j.cpc.2018.01.008 doi: 10.1016/j.cpc.2018.01.008
|
[14] |
W. J. Nellis, “Dynamic compression of materials: Metallization of fluid hydrogen at high pressures,” Rep. Prog. Phys. 69, 1479 (2006).10.1088/0034-4885/69/5/r05 doi: 10.1088/0034-4885/69/5/r05
|
[15] |
G. V. Boriskov, A. I. Bykov, R. Ilkaev, V. D. Selemir, G. V. Simakov et al., “Shock compression of liquid deuterium up to 109 GPa,” Phys. Rev. B 71, 092104 (2005).10.1103/physrevb.71.092104 doi: 10.1103/physrevb.71.092104
|
[16] |
D. G. Hicks, T. R. Boehly, P. M. Celliers, J. H. Eggert, S. J. Moon et al., “Laser-driven single shock compression of fluid deuterium from 45 to 220 GPa,” Phys. Rev. B 79, 014112 (2009).10.1103/physrevb.79.014112 doi: 10.1103/physrevb.79.014112
|
[17] |
R. Nora, W. Theobald, R. Betti, F. J. Marshall, D. T. Michel et al., “Gigabar spherical shock generation on the OMEGA laser,” Phys. Rev. Lett. 114, 045001 (2015).10.1103/physrevlett.114.045001 doi: 10.1103/physrevlett.114.045001
|
[18] |
A. Fernandez-Pañella, M. Millot, D. E. Fratanduono, M. P. Desjarlais, S. Hamel et al., “Shock compression of liquid deuterium up to 1 TPa,” Phys. Rev. Lett. 122, 255702 (2019).10.1103/physrevlett.122.255702 doi: 10.1103/physrevlett.122.255702
|
[19] |
M. D. Knudson, D. L. Hanson, J. E. Bailey, C. A. Hall, J. R. Asay et al., “Principal hugoniot, reverberating wave, and mechanical reshock measurements of liquid deuterium to 400 GPa using plate impact techniques,” Phys. Rev. B 69, 144209 (2004).10.1103/physrevb.69.144209 doi: 10.1103/physrevb.69.144209
|
[20] |
M. D. Knudson, M. P. Desjarlais, A. Becker, R. W. Lemke, K. R. Cochrance et al., “Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium,” Science 348, 1455 (2015).10.1126/science.aaa7471 doi: 10.1126/science.aaa7471
|
[21] |
D. Saumon and G. Chabrier, “Fluid hydrogen at high density: Pressure ionization,” Phys. Rev. A 46, 2084 (1992).10.1103/physreva.46.2084 doi: 10.1103/physreva.46.2084
|
[22] |
F. J. Rogers, “New activity expansion calculations for warm dense deuterium,” Contrib. Plasma Phys. 41, 179 (2001).10.1002/1521-3986(200103)41:2/3<179::aid-ctpp179>3.0.co;2-h doi: 10.1002/1521-3986(200103)41:2/3<179::aid-ctpp179>3.0.co;2-h
|
[23] |
H. Juranek, R. Redmer, and Y. Rosenfeld, “Fluid variational theory for pressure dissociation in dense hydrogen: Multicomponent reference system and nonadditivity effects,” J. Chem. Phys. 117, 1768 (2002).10.1063/1.1486210 doi: 10.1063/1.1486210
|
[24] |
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. Controlled Fusion 58, 014012 (2016).10.1088/0741-3335/58/1/014012 doi: 10.1088/0741-3335/58/1/014012
|
[25] |
G. I. Kerley, “Equation of state and phase diagram of dense hydrogen,” Phys. Earth Planet. Inter. 6, 78 (1972).10.1016/0031-9201(72)90036-2 doi: 10.1016/0031-9201(72)90036-2
|
[26] |
G. I. Kerley, Technical Report No. SAND2003-3613, Sandia National Laboratory, Albuquerque, NM, 2003.
|
[27] |
Y. Hou, F. Jin, and J. Yuan, “Influence of the electronic energy level broadening on the ionization of atoms in hot and dense plasmas: An average atom model demonstration,” Phys. Plasmas 13, 093301 (2006).10.1063/1.2338023 doi: 10.1063/1.2338023
|
[28] |
J. Chihara, “Average atom model based on quantum hyper-netted chain method,” High Energy Density Phys. 19, 38 (2016).10.1016/j.hedp.2016.03.002 doi: 10.1016/j.hedp.2016.03.002
|
[29] |
Y. Hou and J. Yuan, “Alternative ion-ion pair-potential model applied to molecular dynamics simulations of hot and dense plasmas: Al and Fe as examples,” Phys. Rev. E 79, 016402 (2009).10.1103/physreve.79.016402 doi: 10.1103/physreve.79.016402
|
[30] |
S. X. Hu, B. Militzer, V. N. Goncharov, and S. Skupsky, “Strong coupling and degeneracy effects in inertial confinement fusion implosions,” Phys. Rev. Lett. 104, 235003 (2010).10.1103/physrevlett.104.235003 doi: 10.1103/physrevlett.104.235003
|
[31] |
P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Phys. Rev. 136, B864 (1964).10.1103/physrev.136.b864 doi: 10.1103/physrev.136.b864
|
[32] |
W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133 (1965).10.1103/physrev.140.a1133 doi: 10.1103/physrev.140.a1133
|
[33] |
N. D. Mermin, “Thermal properties of the inhomogeneous electron gas,” Phys. Rev. 137, A1441 (1965).10.1103/physrev.137.a1441 doi: 10.1103/physrev.137.a1441
|
[34] |
T. J. Lenosky, S. R. Bickham, J. D. Kress, and L. A. Collins, “Density-functional calculation of the Hugoniot of shocked liquid deuterium,” Phys. Rev. B 61, 1 (2000).10.1103/physrevb.61.1 doi: 10.1103/physrevb.61.1
|
[35] |
M. P. Desjarlais, “Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing,” Phys. Rev. B 68, 064204 (2003).10.1103/physrevb.68.064204 doi: 10.1103/physrevb.68.064204
|
[36] |
B. Holst, R. Redmer, and M. P. Desjarlais, “Thermophysical properties of warm dense hydrogen using quantum molecular dynamics simulations,” Phys. Rev. B 77, 184201 (2008).10.1103/physrevb.77.184201 doi: 10.1103/physrevb.77.184201
|
[37] |
B. Militzer and D. M. Ceperley, “Path integral Monte Carlo calculation of the deuterium Hugoniot,” Phys. Rev. Lett. 85, 1890 (2000).10.1103/physrevlett.85.1890 doi: 10.1103/physrevlett.85.1890
|
[38] |
K. P. Driver and B. Militzer, “All-electron path integral Monte Carlo simulations of warm dense matter: Application to water and carbon plasmas,” Phys. Rev. Lett. 108, 115502 (2012).10.1103/physrevlett.108.115502 doi: 10.1103/physrevlett.108.115502
|
[39] |
C. Pierleoni, D. M. Ceperley, and M. Holzmann, “Coupled electron-ion Monte Carlo calculations of dense metallic hydrogen,” Phys. Rev. Lett. 93, 146402 (2004).10.1103/physrevlett.93.146402 doi: 10.1103/physrevlett.93.146402
|
[40] |
M. A. Morales, C. Pierleoni, and D. M. Ceperley, “Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations,” Phys. Rev. E 81, 021202 (2010).10.1103/physreve.81.021202 doi: 10.1103/physreve.81.021202
|
[41] |
R. C. Clay III, M. P. Desjarlais, and L. Shulenburger, “Deuterium Hugoniot: Pitfalls of thermodynamic sampling beyond density functional theory,” Phys. Rev. B 100, 075103 (2019).10.1103/physrevb.100.075103 doi: 10.1103/physrevb.100.075103
|
[42] |
F. Lambert, J. Clérouin, and G. Zérah, “Very-high-temperature molecular dynamics,” Phys. Rev. E 73, 016403 (2006).10.1103/physreve.73.016403 doi: 10.1103/physreve.73.016403
|
[43] |
V. V. Karasiev, T. Sjostrom, and S. B. Trickey, “Generalized-gradient-approximation noninteracting free-energy functionals for orbital-free density functional calculations,” Phys. Rev. B 86, 115101 (2012).10.1103/physrevb.86.115101 doi: 10.1103/physrevb.86.115101
|
[44] |
H. Y. Sun, D. Kang, Y. Hou, and J. Y. Dai, “Transport properties of warm and hot dense iron from orbital free and corrected Yukawa potential molecular dynamics,” Matter Radiat. Extremes 2, 287 (2017).10.1016/j.mre.2017.09.001 doi: 10.1016/j.mre.2017.09.001
|
[45] |
S. Zhang, H. Wang, W. Kang, P. Zhang, and X. T. He, “Extended application of Kohn–Sham first-principles molecular dynamics method with plane wave approximation at high energyąłFrom cold materials to hot dense plasmas,” Phys. Plasmas 23, 042707 (2016).10.1063/1.4947212 doi: 10.1063/1.4947212
|
[46] |
J. Dai, Y. Hou, and J. Yuan, “Unified first principles description from warm dense matter to ideal ionized gas plasma: Electron-ion collisions induced friction,” Phys. Rev. Lett. 104, 245001 (2010).10.1103/physrevlett.104.245001 doi: 10.1103/physrevlett.104.245001
|
[47] |
J. Dai and J. Yuan, “Large-scale efficient Langevin dynamics, and why it works,” Europhys. Lett. 88, 20001 (2009).10.1209/0295-5075/88/20001 doi: 10.1209/0295-5075/88/20001
|
[48] |
J. Dai, Y. Hou, and J. Yuan, “Quantum Langevin molecular dynamic determination of the solar-interior equation of state,” Astrophys. J. 721, 1158 (2010).10.1088/0004-637x/721/2/1158 doi: 10.1088/0004-637x/721/2/1158
|
[49] |
J. Dai, Y. Hou, and J. Yuan, “Influence of ordered structures on electrical conductivity and XANES from warm to hot dense matter,” High Energy Density Phys. 7, 84 (2011).10.1016/j.hedp.2011.02.002 doi: 10.1016/j.hedp.2011.02.002
|
[50] |
J. Dai, D. Kang, Z. Zhao, Y. Wu, and J. Yuan, “Dynamic ionic clusters with flowing electron bubbles from warm to hot dense iron along the Hugoniot curve,” Phys. Rev. Lett. 109, 175701 (2012).10.1103/physrevlett.109.175701 doi: 10.1103/physrevlett.109.175701
|
[51] |
J. Dai, Y. Hou, D. Kang, H. Sun, J. Wu et al., “Structure, equation of state, diffusion and viscosity of warm dense Fe under the conditions of a giant planet core,” New J. Phys. 15, 045003 (2013).10.1088/1367-2630/15/4/045003 doi: 10.1088/1367-2630/15/4/045003
|
[52] |
D. Kang and J. Dai, “Dynamic electron–cion collisions and nuclear quantum effects in quantum simulation of warm dense matter,” J. Phys.: Condens. Matter 30, 073002 (2018).10.1088/1361-648x/aa9e29 doi: 10.1088/1361-648x/aa9e29
|
[53] |
A. V. Plyukhin, “Generalized Fokker-Planck equation, Brownian motion, and ergodicity,” Phys. Rev. E 77, 061136 (2008).10.1103/physreve.77.061136 doi: 10.1103/physreve.77.061136
|
[54] |
R. G. Gordon and Y. S. Kim, “Theory for the forces between closed-shell atoms and molecules,” J. Chem. Phys. 56, 3122 (1972).10.1063/1.1677649 doi: 10.1063/1.1677649
|
[55] |
S. Ichimaru, “Strongly coupled plasmas: High-density classical plasmas and degenerate electron liquids,” Rev. Mod. Phys. 54, 1017 (1982).10.1103/revmodphys.54.1017 doi: 10.1103/revmodphys.54.1017
|
[56] |
P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli et al., “Advanced capabilities for materials modelling with quantum ESPRESSO,” J. Phys.: Condens. Matter 29, 465901 (2017).10.1088/1361-648x/aa8f79 doi: 10.1088/1361-648x/aa8f79
|
[57] |
J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865 (1996).10.1103/physrevlett.77.3865 doi: 10.1103/physrevlett.77.3865
|
[58] |
R. P. Feynman, N. Metropolis, and E. Teller, “Equations of state of elements based on the generalized Fermi-Thomas theory,” Phys. Rev. 75, 1561 (1949).10.1103/physrev.75.1561 doi: 10.1103/physrev.75.1561
|
[59] |
F. Perrot, “Gradient correction to the statistical electronic free energy at nonzero temperatures: Application to equation-of-state calculations,” Phys. Rev. A 20, 586 (1979).10.1103/physreva.20.586 doi: 10.1103/physreva.20.586
|
[60] |
M. Chen, X. C. Huang, J. M. Dieterich, L. Hung, I. Shin et al., “Introducing PROFESS 3.0: An advanced program for orbital-free density functional theory molecular dynamics simulations,” Comput. Phys. Commun. 190, 228 (2015).10.1016/j.cpc.2014.12.021 doi: 10.1016/j.cpc.2014.12.021
|
[61] |
K. Luo, V. V. Karasiev, and S. B. Trickey, “A simple generalized gradient approximation for the noninteracting kinetic energy density functional,” Phys. Rev. B 98, 041111(R) (2018).10.1103/physrevb.98.041111 doi: 10.1103/physrevb.98.041111
|
[62] |
K. Luo, V. V. Karasiev, and S. B. Trickey, “Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional,” Phys. Rev. B 101, 075116 (2020).10.1103/physrevb.101.075116 doi: 10.1103/physrevb.101.075116
|
[63] |
V. A. Baturin, W. Däppen, A. V. Oreshina, S. V. Ayukov, and A. B. Gorshkov, “Interpolation of equation-of-state data,” Astron. Astrophys. 626, A108 (2019).10.1051/0004-6361/201935669 doi: 10.1051/0004-6361/201935669
|
[64] |
D. Kang, H. Sun, J. Dai, W. Chen, Z. Zhao et al., “Nuclear quantum dynamics in dense hydrogen,” Sci. Rep. 4, 5484 (2014).10.1038/srep05484 doi: 10.1038/srep05484
|
[65] |
B. Lu, D. Kang, D. Wang, T. Gao, and J. Dai, “Towards the same line of liquid-liquid phase transition of dense hydrogen from various theoretical predictions,” Chin. Phys. Lett. 36, 103102 (2019).10.1088/0256-307x/36/10/103102 doi: 10.1088/0256-307x/36/10/103102
|
[66] |