1
|
Karasiev VV, Hinz J, Goshadze RMN. Framework for Laplacian-Level Noninteracting Free-Energy Density Functionals. J Phys Chem Lett 2024; 15:8272-8279. [PMID: 39106051 PMCID: PMC11331511 DOI: 10.1021/acs.jpclett.4c01521] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2024] [Revised: 07/30/2024] [Accepted: 07/31/2024] [Indexed: 08/07/2024]
Abstract
A framework for orbital-free Laplacian-level meta-generalized-gradient approximation (meta-GGA) for the noninteracting free-energy-density functionals based upon analysis of the fourth-order gradient expansion is developed. The framework presented here provides a new tool for developing advanced orbital-free thermal functionals at the meta-GGA level of theory. A nonempirical meta-GGA functional, which in the slowly varying density limit correctly reduces to the finite-temperature fourth-order gradient expansion for the noninteracting free energy, is constructed. Application to warm dense helium demonstrates that the developed meta-GGA functional drastically increases the accuracy of orbital-free-density functional theory simulations at temperatures below 40 eV as compared to the lower Thomas-Fermi and GGA rungs.
Collapse
Affiliation(s)
- Valentin V. Karasiev
- Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York 14623-1299 United States
| | - Joshua Hinz
- Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York 14623-1299 United States
| | - R. M. N. Goshadze
- Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York 14623-1299 United States
| |
Collapse
|
2
|
White TG, Dai J, Riley D. Dynamic and transient processes in warm dense matter. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220223. [PMID: 37393937 PMCID: PMC10315215 DOI: 10.1098/rsta.2022.0223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 05/22/2023] [Indexed: 07/04/2023]
Abstract
In this paper, we discuss some of the key challenges in the study of time-dependent processes and non-equilibrium behaviour in warm dense matter. We outline some of the basic physics concepts that have underpinned the definition of warm dense matter as a subject area in its own right and then cover, in a selective, non-comprehensive manner, some of the current challenges, pointing along the way to topics covered by the papers presented in this volume. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
Collapse
Affiliation(s)
- Thomas G. White
- Department of Physics, University of Nevada, Reno, NV 89557, USA
| | - Jiayu Dai
- College of Science, National University of Defense Technology, Changsha 410073, People’s Republic of China
| | - David Riley
- School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK
| |
Collapse
|
3
|
Schoelmerich MO, Döppner T, Allen CH, Divol L, Oliver M, Haden D, Biener M, Crippen J, Delora-Ellefson J, Ferguson B, Gericke DO, Goldman A, Haid A, Heinbockel C, Kalantar D, Karmiol Z, Kemp G, Kroll J, Landen OL, Masters N, Ping Y, Spindloe C, Theobald W, White TG. Developing a platform for Fresnel diffractive radiography with 1 μm spatial resolution at the National Ignition Facility. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:013104. [PMID: 36725556 DOI: 10.1063/5.0101890] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
An x-ray Fresnel diffractive radiography platform was designed for use at the National Ignition Facility. It will enable measurements of micron-scale changes in the density gradients across an interface between isochorically heated warm dense matter materials, the evolution of which is driven primarily through thermal conductivity and mutual diffusion. We use 4.75 keV Ti K-shell x-ray emission to heat a 1000 μm diameter plastic cylinder, with a central 30 μm diameter channel filled with liquid D2, up to 8 eV. This leads to a cylindrical implosion of the liquid D2 column, compressing it to ∼2.3 g/cm3. After pressure equilibration, the location of the D2/plastic interface remains steady for several nanoseconds, which enables us to track density gradient changes across the material interface with high precision. For radiography, we use Cu He-α x rays at 8.3 keV. Using a slit aperture of only 1 μm width increases the spatial coherence of the source, giving rise to significant diffraction features in the radiography signal, in addition to the refraction enhancement, which further increases its sensitivity to density scale length changes at the D2/plastic interface.
Collapse
Affiliation(s)
- M O Schoelmerich
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - T Döppner
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - C H Allen
- Department of Physics, University of Nevada, Reno, 1664 N Virginia St., Reno, Nevada 89557, USA
| | - L Divol
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - M Oliver
- Central Laser Facility, STFC Rutherford-Appleton Laboratory, Chilton OX11 0QX, United Kingdom
| | - D Haden
- Department of Physics, University of Nevada, Reno, 1664 N Virginia St., Reno, Nevada 89557, USA
| | - M Biener
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - J Crippen
- General Atomics, P.O. Box 85608, San Diego, California 92186-5608, USA
| | - J Delora-Ellefson
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - B Ferguson
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - D O Gericke
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - A Goldman
- Department of Physics, University of Nevada, Reno, 1664 N Virginia St., Reno, Nevada 89557, USA
| | - A Haid
- General Atomics, P.O. Box 85608, San Diego, California 92186-5608, USA
| | - C Heinbockel
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - D Kalantar
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - Z Karmiol
- Department of Physics, University of Nevada, Reno, 1664 N Virginia St., Reno, Nevada 89557, USA
| | - G Kemp
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - J Kroll
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - O L Landen
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - N Masters
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - Y Ping
- Lawrence Livermore National Laboratory, L-493, 7000 East Avenue, Livermore, California 94550, USA
| | - C Spindloe
- Central Laser Facility, STFC Rutherford-Appleton Laboratory, Chilton OX11 0QX, United Kingdom
| | - W Theobald
- Laboratory for Laser Energetics, 250 E River Rd., Rochester, New York 14623, USA
| | - T G White
- Department of Physics, University of Nevada, Reno, 1664 N Virginia St., Reno, Nevada 89557, USA
| |
Collapse
|
4
|
Wang ZQ, Tang J, Hou Y, Chen QF, Chen XR, Dai JY, Meng XJ, Gu YJ, Liu L, Li GJ, Lan YS, Li ZG. Benchmarking the effective one-component plasma model for warm dense neon and krypton within quantum molecular dynamics simulation. Phys Rev E 2020; 101:023302. [PMID: 32168678 DOI: 10.1103/physreve.101.023302] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Accepted: 01/15/2020] [Indexed: 11/07/2022]
Abstract
The effective one-component plasma (EOCP) model has provided an efficient approach to obtaining many important thermophysical parameters of hot dense matter [J. Clérouin, et al., Phys. Rev. Lett. 116, 115003 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.115003]. In this paper, we perform extensive quantum molecular dynamics (QMD) simulations to determine the equations of state, ionic structures, and ionic transport properties of neon and krypton within the warm dense matter (WDM) regime where the density (ρ) is up to 12 g/cm^{3} and the temperature (T) is up to 100 kK. The simulated data are then used as a benchmark to explicitly evaluate the EOCP and Yukawa models. It is found that, within present ρ-T regime, the EOCP model can excellently reproduce the diffusion and viscosity coefficients of neon and krypton due to the fact that this model defines a system which nearly reproduces the actual physical states of WDM. Therefore, the EOCP model may be a promising alternative approach to reasonably predicting the transport behaviors of matter in WDM regime at lower QMD computational cost. The evaluation of Yukawa model shows that the consideration of the energy level broadening effect in the average atom model is necessary. Finally, with the help of EOCP model, the Stokes-Einstein relationships about neon and krypton are discussed, and fruitful plasma parameters as well as a practical ρ-T-dependent formula of the effective coupling parameter are obtained. These results not only provide valuable information for future theoretical and experimental studies on dense neon and krypton but also reveal the applicability of the EOCP model and the limitation of the Yukawa model in WDM regime and further support the continuing search for a unified description of ionic transport in dense plasma.
Collapse
Affiliation(s)
- Zhao-Qi Wang
- College of Physics, Sichuan University, Chengdu 610065, People's Republic of China.,National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Jun Tang
- Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621908, People's Republic of China
| | - Yong Hou
- Department of Physics, National University of Defense Technology, Changsha 410073, People's Republic of China
| | - Qi-Feng Chen
- National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Xiang-Rong Chen
- College of Physics, Sichuan University, Chengdu 610065, People's Republic of China
| | - Jia-Yu Dai
- Department of Physics, National University of Defense Technology, Changsha 410073, People's Republic of China
| | - Xu-Jun Meng
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, People's Republic of China
| | - Yun-Jun Gu
- National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Lei Liu
- College of Physics, Sichuan University, Chengdu 610065, People's Republic of China.,National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Guo-Jun Li
- College of Physics, Sichuan University, Chengdu 610065, People's Republic of China.,National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Yang-Shun Lan
- College of Physics, Sichuan University, Chengdu 610065, People's Republic of China.,National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Zhi-Guo Li
- National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| |
Collapse
|
5
|
White AJ, Ticknor C, Meyer ER, Kress JD, Collins LA. Multicomponent mutual diffusion in the warm, dense matter regime. Phys Rev E 2019; 100:033213. [PMID: 31639979 DOI: 10.1103/physreve.100.033213] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Indexed: 11/07/2022]
Abstract
We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.
Collapse
Affiliation(s)
- A J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Ticknor
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - E R Meyer
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - L A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
6
|
Zhang S, Militzer B, Gregor MC, Caspersen K, Yang LH, Gaffney J, Ogitsu T, Swift D, Lazicki A, Erskine D, London RA, Celliers PM, Nilsen J, Sterne PA, Whitley HD. Theoretical and experimental investigation of the equation of state of boron plasmas. Phys Rev E 2018; 98:023205. [PMID: 30253522 DOI: 10.1103/physreve.98.023205] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2018] [Indexed: 06/08/2023]
Abstract
We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures (5.1×10^{4}-5.2×10^{8} K) and densities (0.25-49 g/cm^{3}) and experimental shock Hugoniot data at unprecedented high pressures (5608±118 GPa). The calculations are performed with first-principles methods combining path-integral Monte Carlo (PIMC) at high temperatures and density-functional-theory molecular-dynamics (DFT-MD) methods at lower temperatures. PIMC and DFT-MD cross-validate each other by providing coherent EOS (difference <1.5 Hartree/boron in energy and <5% in pressure) at 5.1×10^{5} K. The Hugoniot measurement is conducted at the National Ignition Facility using a planar shock platform. The pressure-density relation found in our shock experiment is on top of the shock Hugoniot profile predicted with our first-principles EOS and a semiempirical EOS table (LEOS 50). We investigate the self-diffusivity and the effect of thermal and pressure-driven ionization on the EOS and shock compression behavior in high-pressure and -temperature conditions. We also study the sensitivity of a polar direct-drive exploding pusher platform to pressure variations based on applying pressure multipliers to LEOS 50 and by utilizing a new EOS model based on our ab initio simulations via one-dimensional radiation-hydrodynamic calculations. The results are valuable for future theoretical and experimental studies and engineering design in high-energy density research.
Collapse
Affiliation(s)
- Shuai Zhang
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Department of Astronomy, University of California, Berkeley, California 94720, USA
| | - Michelle C Gregor
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Kyle Caspersen
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Lin H Yang
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Jim Gaffney
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Tadashi Ogitsu
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Damian Swift
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Amy Lazicki
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - D Erskine
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Richard A London
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - P M Celliers
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Joseph Nilsen
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Philip A Sterne
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Heather D Whitley
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| |
Collapse
|
7
|
Liu L, Li ZG, Dai JY, Chen QF, Chen XR. Quantum molecular dynamics study on the proton exchange, ionic structures, and transport properties of warm dense hydrogen-deuterium mixtures. Phys Rev E 2018; 97:063204. [PMID: 30011461 DOI: 10.1103/physreve.97.063204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2018] [Indexed: 06/08/2023]
Abstract
Comprehensive knowledge of physical properties such as equation of state (EOS), proton exchange, dynamic structures, diffusion coefficients, and viscosities of hydrogen-deuterium mixtures with densities from 0.1 to 5 g/cm^{3} and temperatures from 1 to 50 kK has been presented via quantum molecular dynamics (QMD) simulations. The existing multi-shock experimental EOS provides an important benchmark to evaluate exchange-correlation functionals. The comparison of simulations with experiments indicates that a nonlocal van der Waals density functional (vdW-DF1) produces excellent results. Fraction analysis of molecules using a weighted integral over pair distribution functions was performed. A dissociation diagram together with a boundary where the proton exchange (H_{2}+D_{2}⇌2HD) occurs was generated, which shows evidence that the HD molecules form as the H_{2} and D_{2} molecules are almost 50% dissociated. The mechanism of proton exchange can be interpreted as a process of dissociation followed by recombination. The ionic structures at extreme conditions were analyzed by the effective coordination number model. High-order cluster, circle, and chain structures can be founded in the strongly coupled warm dense regime. The present QMD diffusion coefficient and viscosity can be used to benchmark two analytical one-component plasma (OCP) models: the Coulomb and Yukawa OCP models.
Collapse
Affiliation(s)
- Lei Liu
- Institute of Atomic and Molecular Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610064, People's Republic of China
- National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Zhi-Guo Li
- National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Jia-Yu Dai
- Department of Physics, National University of Defense Technology, Changsha 410073, People's Republic of China
| | - Qi-Feng Chen
- National Key Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, People's Republic of China
| | - Xiang-Rong Chen
- Institute of Atomic and Molecular Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610064, People's Republic of China
| |
Collapse
|
8
|
Kang D, Dai J. Dynamic electron-ion collisions and nuclear quantum effects in quantum simulation of warm dense matter. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:073002. [PMID: 29186001 DOI: 10.1088/1361-648x/aa9e29] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The structural, thermodynamic and transport properties of warm dense matter (WDM) are crucial to the fields of astrophysics and planet science, as well as inertial confinement fusion. WDM refers to the states of matter in a regime of temperature and density between cold condensed matter and hot ideal plasmas, where the density is from near-solid up to ten times solid density, and the temperature between 0.1 and 100 eV. In the WDM regime, matter exhibits moderately or strongly coupled, partially degenerate properties. Therefore, the methods used to deal with condensed matter and isolated atoms need to be properly validated for WDM. It is therefore a big challenge to understand WDM within a unified theoretical description with reliable accuracy. Here, we review the progress in the theoretical study of WDM with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics. The related applications for WDM are also included.
Collapse
Affiliation(s)
- Dongdong Kang
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
| | | |
Collapse
|
9
|
White AJ, Collins LA, Kress JD, Ticknor C, Clérouin J, Arnault P, Desbiens N. Correlation and transport properties for mixtures at constant pressure and temperature. Phys Rev E 2017; 95:063202. [PMID: 28709340 DOI: 10.1103/physreve.95.063202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Indexed: 06/07/2023]
Abstract
Transport properties of mixtures of elements in the dense plasma regime play an important role in natural astrophysical and experimental systems, e.g., inertial confinement fusion. We present a series of orbital-free molecular dynamics simulations on dense plasma mixtures with comparison to a global pseudo ion in jellium model. Hydrogen is mixed with elements of increasingly high atomic number (lithium, carbon, aluminum, copper, and silver) at a fixed temperature of 100 eV and constant pressure set by pure hydrogen at 2g/cm^{3}, namely, 370 Mbars. We compute ionic transport coefficients, such as self-diffusion, mutual diffusion, and viscosity for various concentrations. Small concentrations of the heavy atoms significantly change the density of the plasma and decrease the transport coefficients. The structure of the mixture evidences a strong Coulomb coupling between heavy ions and the appearance of a broad correlation peak at short distances between hydrogen atoms. The concept of an effective one component plasma is used to quantify the overcorrelation of the light element induced by the admixture of a heavy element.
Collapse
Affiliation(s)
- Alexander J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Christopher Ticknor
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | |
Collapse
|
10
|
Benedict LX, Surh MP, Stanton LG, Scullard CR, Correa AA, Castor JI, Graziani FR, Collins LA, Čertík O, Kress JD, Murillo MS. Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime. Phys Rev E 2017; 95:043202. [PMID: 28505713 DOI: 10.1103/physreve.95.043202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2016] [Indexed: 06/07/2023]
Abstract
We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K<T_{e}<10^{9}K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealing to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.
Collapse
Affiliation(s)
- Lorin X Benedict
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Michael P Surh
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Liam G Stanton
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | | | - Alfredo A Correa
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - John I Castor
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Frank R Graziani
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Lee A Collins
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ondřej Čertík
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Michael S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| |
Collapse
|
11
|
Pribram-Jones A, Grabowski PE, Burke K. Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem. PHYSICAL REVIEW LETTERS 2016; 116:233001. [PMID: 27341227 DOI: 10.1103/physrevlett.116.233001] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2015] [Indexed: 06/06/2023]
Abstract
The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation approximations.
Collapse
Affiliation(s)
- Aurora Pribram-Jones
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Paul E Grabowski
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Kieron Burke
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
- Department of Chemistry, University of California, Irvine, California 92697, USA
| |
Collapse
|
12
|
Ticknor C, Kress JD, Collins LA, Clérouin J, Arnault P, Decoster A. Transport properties of an asymmetric mixture in the dense plasma regime. Phys Rev E 2016; 93:063208. [PMID: 27415378 DOI: 10.1103/physreve.93.063208] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Indexed: 06/06/2023]
Abstract
We study how concentration changes ionic transport properties along isobars-isotherms for a mixture of hydrogen and silver, representative of turbulent layers relevant to inertial confinement fusion and astrophysics. Hydrogen will typically be fully ionized while silver will be only partially ionized but can have a large effective charge. This will lead to very different physical conditions for the H and Ag. Large first principles orbital free molecular dynamics simulations are performed and the resulting transport properties are analyzed. Comparisons are made with transport theory in the kinetic regime and in the coupled regime. The addition of a small amount of heavy element in a light material has a dramatic effect on viscosity and diffusion of the mixture. This effect is explained through kinetic theory as a manifestation of a crossover between classical diffusion and Lorentz diffusion.
Collapse
Affiliation(s)
- Christopher Ticknor
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | |
Collapse
|
13
|
Clérouin J, Arnault P, Ticknor C, Kress JD, Collins LA. Unified Concept of Effective One Component Plasma for Hot Dense Plasmas. PHYSICAL REVIEW LETTERS 2016; 116:115003. [PMID: 27035306 DOI: 10.1103/physrevlett.116.115003] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Indexed: 06/05/2023]
Abstract
Orbital-free molecular dynamics simulations are used to benchmark two popular models for hot dense plasmas: the one component plasma (OCP) and the Yukawa model. A unified concept emerges where an effective OCP (EOCP) is constructed from the short-range structure of the plasma. An unambiguous ionization and the screening length can be defined and used for a Yukawa system, which reproduces the long-range structure with finite compressibility. Similarly, the dispersion relation of longitudinal waves is consistent with the screened model at vanishing wave number but merges with the OCP at high wave number. Additionally, the EOCP reproduces the overall relaxation time scales of the correlation functions associated with ionic motion. In the hot dense regime, this unified concept of EOCP can be fruitfully applied to deduce properties such as the equation of state, ionic transport coefficients, and the ion feature in x-ray Thomson scattering experiments.
Collapse
Affiliation(s)
| | | | - Christopher Ticknor
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
14
|
Daligault J, Baalrud SD, Starrett CE, Saumon D, Sjostrom T. Ionic Transport Coefficients of Dense Plasmas without Molecular Dynamics. PHYSICAL REVIEW LETTERS 2016; 116:075002. [PMID: 26943540 DOI: 10.1103/physrevlett.116.075002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Indexed: 06/05/2023]
Abstract
We present a theoretical model that allows a fast and accurate evaluation of ionic transport properties of realistic plasmas spanning from warm and dense to hot and dilute conditions, including mixtures. This is achieved by combining a recent kinetic theory based on effective interaction potentials with a model for the equilibrium radial density distribution based on an average atom model and the integral equations theory of fluids. The model should find broad use in applications where nonideal plasma conditions are traversed, including inertial confinement fusion, compact astrophysical objects, solar and extrasolar planets, and numerous present-day high energy density laboratory experiments.
Collapse
Affiliation(s)
- Jérôme Daligault
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Scott D Baalrud
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
| | | | - Didier Saumon
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Travis Sjostrom
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
15
|
Haxhimali T, Rudd RE, Cabot WH, Graziani FR. Shear viscosity for dense plasmas by equilibrium molecular dynamics in asymmetric Yukawa ionic mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:053110. [PMID: 26651805 DOI: 10.1103/physreve.92.053110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Indexed: 06/05/2023]
Abstract
We present molecular dynamics (MD) calculations of shear viscosity for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100-500 eV and a number density of 10^{25} ions/cc. The motion of 30,000-120,000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. Shear viscosity is calculated using the Green-Kubo approach with an integral of the shear stress autocorrelation function, a quantity calculated in the equilibrium MD simulations. We systematically study different mixtures through a series of simulations with increasing fraction of the minority high-Z element (Ar) in the D-Ar plasma mixture. In the more weakly coupled plasmas, at 500 eV and low Ar fractions, results from MD compare very well with Chapman-Enskog kinetic results. In the more strongly coupled plasmas, the kinetic theory does not agree well with the MD results. We develop a simple model that interpolates between classical kinetic theories at weak coupling and the Murillo Yukawa viscosity model at higher coupling. This hybrid kinetics-MD viscosity model agrees well with the MD results over the conditions simulated, ranging from moderately weakly coupled to moderately strongly coupled asymmetric plasma mixtures.
Collapse
Affiliation(s)
- Tomorr Haxhimali
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Robert E Rudd
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - William H Cabot
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Frank R Graziani
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| |
Collapse
|
16
|
Ticknor C, Collins LA, Kress JD. Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:023101. [PMID: 26382529 DOI: 10.1103/physreve.92.023101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2015] [Indexed: 06/05/2023]
Abstract
We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5-200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.
Collapse
Affiliation(s)
- Christopher Ticknor
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
17
|
Gill NM, Heinonen RA, Starrett CE, Saumon D. Ion-ion dynamic structure factor of warm dense mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:063109. [PMID: 26172810 DOI: 10.1103/physreve.91.063109] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2015] [Indexed: 06/04/2023]
Abstract
The ion-ion dynamic structure factor of warm dense matter is determined using the recently developed pseudoatom molecular dynamics method [Starrett et al., Phys. Rev. E 91, 013104 (2015)]. The method uses density functional theory to determine ion-ion pair interaction potentials that have no free parameters. These potentials are used in classical molecular dynamics simulations. This constitutes a computationally efficient and realistic model of dense plasmas. Comparison with recently published simulations of the ion-ion dynamic structure factor and sound speed of warm dense aluminum finds good to reasonable agreement. Using this method, we make predictions of the ion-ion dynamical structure factor and sound speed of a warm dense mixture-equimolar carbon-hydrogen. This material is commonly used as an ablator in inertial confinement fusion capsules, and our results are amenable to direct experimental measurement.
Collapse
Affiliation(s)
- N M Gill
- 206 Allison Laboratory, Auburn University, Auburn, Alabama 36849, USA
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - R A Heinonen
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - C E Starrett
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - D Saumon
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
18
|
|
19
|
Haxhimali T, Rudd RE, Cabot WH, Graziani FR. Diffusivity in asymmetric Yukawa ionic mixtures in dense plasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:023104. [PMID: 25215836 DOI: 10.1103/physreve.90.023104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2014] [Indexed: 06/03/2023]
Abstract
In this paper we present molecular dynamics (MD) calculations of the interdiffusion coefficient for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100-500 eV and a number density ∼10(25) ions/cm(3). The motion of 30,000-120,000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. The species diffusivity is then calculated using the Green-Kubo approach using an integral of the interdiffusion current autocorrelation function, a quantity calculated in the equilibrium MD simulations. Our MD simulation results show that a widely used expression relating the interdiffusion coefficient with the concentration-weighted sum of self-diffusion coefficients overestimates the interdiffusion coefficient. We argue that this effect due to cross-correlation terms in velocities is characteristic of asymmetric mixed plasmas. Comparison of the MD results with predictions of kinetic theories also shows a discrepancy with MD giving effectively a larger Coulomb logarithm.
Collapse
Affiliation(s)
- Tomorr Haxhimali
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Robert E Rudd
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - William H Cabot
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Frank R Graziani
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| |
Collapse
|
20
|
Hu SX, Collins LA, Boehly TR, Kress JD, Goncharov VN, Skupsky S. First-principles thermal conductivity of warm-dense deuterium plasmas for inertial confinement fusion applications. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:043105. [PMID: 24827353 DOI: 10.1103/physreve.89.043105] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2013] [Indexed: 06/03/2023]
Abstract
Thermal conductivity (κ) of both the ablator materials and deuterium-tritium (DT) fuel plays an important role in understanding and designing inertial confinement fusion (ICF) implosions. The extensively used Spitzer model for thermal conduction in ideal plasmas breaks down for high-density, low-temperature shells that are compressed by shocks and spherical convergence in imploding targets. A variety of thermal-conductivity models have been proposed for ICF hydrodynamic simulations of such coupled and degenerate plasmas. The accuracy of these κ models for DT plasmas has recently been tested against first-principles calculations using the quantum molecular-dynamics (QMD) method; although mainly for high densities (ρ > 100 g/cm3), large discrepancies in κ have been identified for the peak-compression conditions in ICF. To cover the wide range of density-temperature conditions undergone by ICF imploding fuel shells, we have performed QMD calculations of κ for a variety of deuterium densities of ρ = 1.0 to 673.518 g/cm3, at temperatures varying from T = 5 × 103 K to T = 8 × 106 K. The resulting κQMD of deuterium is fitted with a polynomial function of the coupling and degeneracy parameters Γ and θ, which can then be used in hydrodynamic simulation codes. Compared with the "hybrid" Spitzer-Lee-More model currently adopted in our hydrocode lilac, the hydrosimulations using the fitted κQMD have shown up to ∼20% variations in predicting target performance for different ICF implosions on OMEGA and direct-drive-ignition designs for the National Ignition Facility (NIF). The lower the adiabat of an imploding shell, the more variations in predicting target performance using κQMD. Moreover, the use of κQMD also modifies the shock conditions and the density-temperature profiles of the imploding shell at early implosion stage, which predominantly affects the final target performance. This is in contrast to the previous speculation that κQMD changes mainly the inside ablation process during the hot-spot formation of an ICF implosion.
Collapse
Affiliation(s)
- S X Hu
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - L A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - T R Boehly
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - J D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - V N Goncharov
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - S Skupsky
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| |
Collapse
|
21
|
Ticknor C, Herring SD, Lambert F, Collins LA, Kress JD. First principles nonequilibrium plasma mixing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:013108. [PMID: 24580347 DOI: 10.1103/physreve.89.013108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2013] [Indexed: 06/03/2023]
Abstract
We have performed nonequilibrium classical and quantum-mechanical molecular dynamics simulations that follow the interpenetration of deuterium-tritium (DT) and carbon (C) components through an interface initially in hydrostatic and thermal equilibrium. We concentrate on the warm, dense matter regime with initial densities of 2.5-5.5 g/cm3 and temperatures from 10 to 100 eV. The classical treatment employs a Yukawa pair-potential with the parameters adjusted to the plasma conditions, and the quantum treatment rests on an orbital-free density functional theory at the Thomas-Fermi-Dirac level. For times greater than about a picosecond, the component concentrations evolve in accordance with Fick's law for a classically diffusing fluid with the motion, though, described by the mutual diffusion coefficient of the mixed system rather than the self-diffusion of the individual components. For shorter times, microscopic processes control the clearly non-Fickian dynamics and require a detailed representation of the electron probability density in space and time.
Collapse
Affiliation(s)
- C Ticknor
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - S D Herring
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - F Lambert
- CEA, DAM, DIF, F-91297 Arpajon, France
| | - L A Collins
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J D Kress
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
22
|
Wang C, He XT, Zhang P. Thermophysical properties of hydrogen-helium mixtures: re-examination of the mixing rules via quantum molecular dynamics simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:033106. [PMID: 24125370 DOI: 10.1103/physreve.88.033106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2013] [Indexed: 06/02/2023]
Abstract
Thermophysical properties of hydrogen, helium, and hydrogen-helium mixtures have been investigated in the warm dense matter regime at electron number densities ranging from 6.02 × 10^{29} ∼ 2.41 × 10^{30} m^{-3} and temperatures from 4000 to 20000 K via quantum molecular dynamics simulations. We focus on the dynamical properties such as the equation of states, diffusion coefficients, and viscosity. Mixing rules (density matching, pressure matching, and binary ionic mixing rules) have been validated by checking composite properties of pure species against that of the fully interacting mixture derived from quantum molecular dynamics simulations. These mixing rules reproduce pressures within 10% accuracy, while it is 75% and 50% for the diffusion and viscosity, respectively. The binary ionic mixing rule moves the results into better agreement. Predictions from one component plasma model are also provided and discussed.
Collapse
Affiliation(s)
- Cong Wang
- Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, People's Republic of China and Center for Applied Physics and Technology, Peking University, Beijing 100871, People's Republic of China
| | | | | |
Collapse
|
23
|
Wang C, Long Y, He XT, Wu JF, Ye WH, Zhang P. Transport properties of dense deuterium-tritium plasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:013106. [PMID: 23944567 DOI: 10.1103/physreve.88.013106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2012] [Revised: 06/06/2013] [Indexed: 06/02/2023]
Abstract
Consistent descriptions of the equation of states and information about the transport coefficients of the deuterium-tritium mixture are demonstrated through quantum molecular dynamic (QMD) simulations (up to a density of 600 g/cm(3) and a temperature of 10(4) eV). Diffusion coefficients and viscosity are compared to the one-component plasma model in different regimes from the strong coupled to the kinetic one. Electronic and radiative transport coefficients, which are compared to models currently used in hydrodynamic simulations of inertial confinement fusion, are evaluated up to 800 eV. The Lorentz number is discussed from the highly degenerate to the intermediate region. One-dimensional hydrodynamic simulation results indicate that different temperature and density distributions are observed during the target implosion process by using the Spitzer model and ab initio transport coefficients.
Collapse
Affiliation(s)
- Cong Wang
- Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, People's Republic of China
| | | | | | | | | | | |
Collapse
|
24
|
Clérouin J, Robert G, Arnault P, Kress JD, Collins LA. Behavior of the coupling parameter under isochoric heating in a high-Z plasma. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:061101. [PMID: 23848620 DOI: 10.1103/physreve.87.061101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2013] [Indexed: 06/02/2023]
Abstract
The ion-ion coupling parameter Γ is estimated for tungsten along the ρ=40 g/cm(3) isochore corresponding to twice the normal density with temperatures ranging from 10 eV to 5 keV. Using a variety of approaches from a spherical Thomas-Fermi ion to a full three-dimensional orbital-free method, we show that along an isochore the effective ionic coupling parameter is almost constant over a wide range of temperatures (in our case Γ~/=20) due to the competition between rising temperatures and increased ionization. This Γ-plateau effect depends on the chosen density and is well delineated at normal density but almost disappears at five times the normal density. This effect could be used to obtain well-defined and predictable experimental conditions.
Collapse
|
25
|
Burakovsky L, Ticknor C, Kress JD, Collins LA, Lambert F. Transport properties of lithium hydride at extreme conditions from orbital-free molecular dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:023104. [PMID: 23496628 DOI: 10.1103/physreve.87.023104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2012] [Revised: 11/26/2012] [Indexed: 06/01/2023]
Abstract
We have performed a systematic study of lithium hydride (LiH), using orbital-free molecular dynamics, with a focus on mass transport properties such as diffusion and viscosity by extending our previous studies at the lower end of the warm, dense matter regime to cover a span of densities from ambient to 10-fold compressed and temperatures from 10 eV to 10 keV. We determine analytic formulas for self- and mutual-diffusion coefficients, and viscosity, which are in excellent agreement with our molecular dynamics results, and interpolate smoothly between liquid and dense plasma regimes. In addition, we find the orbital-free calculations begin to agree with the Brinzinskii-Landau formula above about 250 eV at which point the medium becomes fully ionized. A binary-ion model based on a bare Coulomb interaction within a neutralizing background with the effective charges determined from a regularization prescription shows good agreement above about 100 eV with the orbital-free results. Finally, we demonstrate the validity of a pressure-based mixing rule in determining the transport properties from the pure-species quantities.
Collapse
Affiliation(s)
- L Burakovsky
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | |
Collapse
|
26
|
Zhang Y, Wang C, Zheng F, Zhang P. Quantum molecular dynamics simulations of thermophysical properties of fluid ethane. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061111. [PMID: 23367897 DOI: 10.1103/physreve.86.061111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2012] [Indexed: 06/01/2023]
Abstract
We have performed first-principles molecular-dynamics simulations based on density-functional theory to study the thermophysical properties of ethane under extreme conditions. We present results for the equation of state of fluid ethane in the warm dense region. The optical conductivity is calculated via the Kubo-Greenwood formula from which the dc conductivity and optical reflectivity are derived. The close correlation between the nonmetal-metal transition of ethane and its decomposition, that ethane dissociates significantly into molecular and/or atomic hydrogen and some long alkane chains, has been systematically studied by analyzing the optical conductivity spectra, pair correlation functions, electronic density of states, and charge density distribution of fluid ethane.
Collapse
Affiliation(s)
- Yujuan Zhang
- LCP, Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, People's Republic of China
| | | | | | | |
Collapse
|
27
|
Lambert F, Recoules V. Plastic ablator and hydrodynamic instabilities: a first-principles set of microscopic coefficients. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:026405. [PMID: 23005867 DOI: 10.1103/physreve.86.026405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2012] [Indexed: 06/01/2023]
Abstract
We have performed orbital-free and quantum molecular dynamics simulations on plastic ablator along two isochores, namely 7 and 9 g cm(-3), from 5 to 40 eV. These thermodynamic conditions correspond to those encountered during inertial confinement fusion capsule implosion when hydrodynamic instabilities can take place. The coupling between orbital-free and quantum approaches allowed us to compute an exhaustive set of microscopic coefficients, i.e., equation-of-state, ionic diffusion coefficients, thermal and electrical conductivities, spanning phenomena that can mitigate the growth of classical Rayleigh-Taylor instability. Comparisons to widely used models in hydrodynamics codes are developed.
Collapse
|
28
|
Danel JF, Kazandjian L, Zérah G. Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:066701. [PMID: 23005237 DOI: 10.1103/physreve.85.066701] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2012] [Indexed: 06/01/2023]
Abstract
Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.
Collapse
Affiliation(s)
- J-F Danel
- CEA, DAM, DIF, F-91297 Arpajon, France
| | | | | |
Collapse
|
29
|
Kress JD, Cohen JS, Kilcrease DP, Horner DA, Collins LA. Quantum molecular dynamics simulations of transport properties in liquid and dense-plasma plutonium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:026404. [PMID: 21405915 DOI: 10.1103/physreve.83.026404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2010] [Indexed: 05/30/2023]
Abstract
We have calculated the viscosity and self-diffusion coefficients of plutonium in the liquid phase using quantum molecular dynamics (QMD) and in the dense-plasma phase using orbital-free molecular dynamics (OFMD), as well as in the intermediate warm dense matter regime with both methods. Our liquid metal results for viscosity are about 40% lower than measured experimentally, whereas a previous calculation using an empirical interatomic potential (modified embedded-atom method) obtained results 3-4 times larger than the experiment. The QMD and OFMD results agree well at the intermediate temperatures. The calculations in the dense-plasma regime for temperatures from 50 to 5000 eV and densities about 1-5 times ambient are compared with the one-component plasma (OCP) model, using effective charges given by the average-atom code INFERNO. The INFERNO-OCP model results agree with the OFMD to within about a factor of 2, except for the viscosity at temperatures less than about 100 eV, where the disagreement is greater. A Stokes-Einstein relationship of the viscosities and diffusion coefficients is found to hold fairly well separately in both the liquid and dense-plasma regimes.
Collapse
Affiliation(s)
- J D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | |
Collapse
|