1
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Wetta N, Pain JC. Average-atom approach for transport properties of shocked argon in the presence of a magnetic field. Phys Rev E 2024; 110:015202. [PMID: 39160962 DOI: 10.1103/physreve.110.015202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2024] [Accepted: 06/12/2024] [Indexed: 08/21/2024]
Abstract
We present electron transport calculations of shocked argon based on an average-atom modeling of the plasma and compare them with measurements, involving both incident and reflected shock waves. Since the corresponding experiments are subject to a 5 T magnetic field, the impact of the latter on the Rankine-Hugoniot equations is taken into account, starting from the magnetoresistive hydrodynamics, and the resistivity tensor is deduced from the Boltzmann equation. The resistivity tensor yields the electrical and Hall resistivities. Our average-atom code Paradisio provides the quantities required for the calculation of electrical resistivity within the Ziman-Evans formalism, as well as for the Hall resistivity. We obtain good agreement between calculated conductivities and experimental values, both for the incident and reflected shocks. Our values of the Hall constant are compared to experimental values derived from Hall voltage measurements, as well as to theoretical ones based on the quantum statistical linear-relaxation-time approach.
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2
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Ziaja B, Bekx JJ, Masek M, Medvedev N, Lipp V, Saxena V, Stransky M. Application of Boltzmann kinetic equations to model X-ray-created warm dense matter and plasma. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220216. [PMID: 37393933 PMCID: PMC10876064 DOI: 10.1098/rsta.2022.0216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Accepted: 03/28/2023] [Indexed: 07/04/2023]
Abstract
In this review, we describe the application of Boltzmann kinetic equations for modelling warm dense matter and plasma formed after irradiation of solid materials with intense femtosecond X-ray pulses. Classical Boltzmann kinetic equations are derived from the reduced N-particle Liouville equations. They include only single-particle densities of ions and free electrons present in the sample. The first version of the Boltzmann kinetic equation solver was completed in 2006. It could model non-equilibrium evolution of X-ray-irradiated finite-size atomic systems. In 2016, the code was adapted to study plasma created from X-ray-irradiated materials. Additional extension of the code was then also performed, enabling simulations in the hard X-ray irradiation regime. In order to avoid treatment of a very high number of active atomic configurations involved in the excitation and relaxation of X-ray-irradiated materials, an approach called 'predominant excitation and relaxation path' (PERP) was introduced. It limited the number of active atomic configurations by following the sample evolution only along most PERPs. The performance of the Boltzmann code is illustrated in the examples of X-ray-heated solid carbon and gold. Actual model limitations and further model developments are discussed. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Beata Ziaja
- Center for Free-Electron Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
- Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krakow, Poland
| | - John Jasper Bekx
- Center for Free-Electron Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
| | - Martin Masek
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2,182 21 Prague 8, Czech Republic
| | - Nikita Medvedev
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2,182 21 Prague 8, Czech Republic
- Institute of Plasma Physics, Czech Academy of Sciences, Za Slovankou 3, 182 00 Prague 8, Czech Republic
| | - Vladimir Lipp
- Center for Free-Electron Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
- Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krakow, Poland
| | - Vikrant Saxena
- Center for Free-Electron Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
- Department of Physics, Indian Institute of Technology Delhi,New Delhi 110016, India
| | - Michal Stransky
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2,182 21 Prague 8, Czech Republic
- European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany
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3
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Liang JH, Hu TX, Wu D, Sheng ZM. Kinetic studies of exchange-correlation effect on the collective excitations of warm dense plasmas. Phys Rev E 2022; 105:045206. [PMID: 35590614 DOI: 10.1103/physreve.105.045206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
The exchange-correlation of electrons, as a fundamental effect in quantum mechanics, plays an important role in the collective motions of electrons in warm dense matter. We derive the quantum kinetic equations based on the time-dependent Kohn-Sham equation. By using a temperature-dependent functional for the exchange correlation, the excitations of electrostatic waves are analyzed under the adiabatic local density approximation (ALDA). We find that the influences of the exchange-correlation effect on the group velocity of electrostatic waves can be as high as 10% when both the density and temperature are low. Moreover, we also compare the results obtained by using ALDA-based kinetic theory, exchange kinetic theory, and quantum hydrodynamics, and discuss the differences among them.
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Affiliation(s)
- Jiong-Hang Liang
- Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, 310027 Hangzhou, People's Republic of China
| | - Tian-Xing Hu
- Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, 310027 Hangzhou, People's Republic of China
| | - D Wu
- Key Laboratory for Laser Plasmas, School of Physics and Astronomy, and Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, 200240 Shanghai, People's Republic of China
| | - Zheng-Mao Sheng
- Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, 310027 Hangzhou, People's Republic of China
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4
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Xu Q, Jing X, Zhang B, Pask J, Suryanarayana P. Real-space density kernel method for Kohn-Sham density functional theory calculations at high temperature. J Chem Phys 2022; 156:094105. [DOI: 10.1063/5.0082523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Qimen Xu
- Georgia Institute of Technology, United States of America
| | - Xin Jing
- School of Computational Science and Engineering, Georgia Institute of Technology, United States of America
| | - Boqin Zhang
- Georgia Institute of Technology, United States of America
| | - John Pask
- Physics, LLNL, United States of America
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5
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Hunger K, Schoof T, Dornheim T, Bonitz M, Filinov A. Momentum distribution function and short-range correlations of the warm dense electron gas: Ab initio quantum Monte Carlo results. Phys Rev E 2021; 103:053204. [PMID: 34134307 DOI: 10.1103/physreve.103.053204] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2021] [Accepted: 03/19/2021] [Indexed: 01/22/2023]
Abstract
In a classical plasma the momentum distribution, n(k), decays exponentially, for large k, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay, n_{∞}(k)∼k^{-8} has been predicted. This is of relevance for cross sections and threshold processes in dense plasmas that depend on the number of energetic particles. Here we present extensive ab initio results for the momentum distribution of the nonideal uniform electron gas at warm dense matter conditions. Our results are based on first principle fermionic path integral Monte Carlo (CPIMC) simulations and clearly confirm the k^{-8} asymptotic. This asymptotic behavior is directly linked to short-range correlations which are analyzed via the on-top pair distribution function (on-top PDF), i.e., the PDF of electrons with opposite spin. We present extensive results for the density and temperature dependence of the on-top PDF and for the momentum distribution in the entire momentum range.
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Affiliation(s)
- Kai Hunger
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - Tim Schoof
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany.,Deutsches Elektronen Synchotron (DESY), Hamburg, Germany
| | - Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany.,Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - Alexey Filinov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany.,Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13, Moscow 125412, Russia
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6
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Ultrafast multi-cycle terahertz measurements of the electrical conductivity in strongly excited solids. Nat Commun 2021; 12:1638. [PMID: 33712576 PMCID: PMC7977037 DOI: 10.1038/s41467-021-21756-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 02/10/2021] [Indexed: 11/10/2022] Open
Abstract
Key insights in materials at extreme temperatures and pressures can be gained by accurate measurements that determine the electrical conductivity. Free-electron laser pulses can ionize and excite matter out of equilibrium on femtosecond time scales, modifying the electronic and ionic structures and enhancing electronic scattering properties. The transient evolution of the conductivity manifests the energy coupling from high temperature electrons to low temperature ions. Here we combine accelerator-based, high-brightness multi-cycle terahertz radiation with a single-shot electro-optic sampling technique to probe the evolution of DC electrical conductivity using terahertz transmission measurements on sub-picosecond time scales with a multi-undulator free electron laser. Our results allow the direct determination of the electron-electron and electron-ion scattering frequencies that are the major contributors of the electrical resistivity. The electrical conductivity is critical to understand warm dense matter, but the accurate measurement is extremely challenging. Here the authors use multi-cycle THz pulses to measure the conductivity of gold foils strongly heated by free-electron laser, determining the individual contributions of electron-electron and electron-ion scattering.
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7
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Sharma A, Hamel S, Bethkenhagen M, Pask JE, Suryanarayana P. Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations. J Chem Phys 2020; 153:034112. [PMID: 32716199 DOI: 10.1063/5.0016783] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an accurate and efficient real-space formulation of the Hellmann-Feynman stress tensor for O(N) Kohn-Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi-Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. We employ the new formulation to compute the viscosity of hydrogen at 106 K from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.
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Affiliation(s)
- Abhiraj Sharma
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Sebastien Hamel
- Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Mandy Bethkenhagen
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USAPhysics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USACNRS, École Normale Supérieure de Lyon, Laboratoire de Géologie de Lyon LGLTPE UMR5276, Centre Blaise Pascal, 46 Allée D'Italie, Lyon 69364, France
| | - John E Pask
- Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Phanish Suryanarayana
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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8
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Larder B, Gericke DO, Richardson S, Mabey P, White TG, Gregori G. Fast nonadiabatic dynamics of many-body quantum systems. SCIENCE ADVANCES 2019; 5:eaaw1634. [PMID: 31803829 PMCID: PMC6874487 DOI: 10.1126/sciadv.aaw1634] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2018] [Accepted: 09/25/2019] [Indexed: 06/10/2023]
Abstract
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of applicability. However, there remain many problems that are intractable for existing methods. In particular, many approaches face a huge computational barrier when modeling large numbers of coupled electrons and ions at finite temperature. Here, we address this shortfall with a new approach to modeling many-body quantum systems. On the basis of the Bohmian trajectory formalism, our new method treats the full particle dynamics with a considerable increase in computational speed. As a result, we are able to perform large-scale simulations of coupled electron-ion systems without using the adiabatic Born-Oppenheimer approximation.
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Affiliation(s)
- B. Larder
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - D. O. Gericke
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, UK
| | - S. Richardson
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- AWE, Aldermaston, Reading, Berkshire RG7 4PR, UK
| | - P. Mabey
- LULI–CNRS, Ecole Polytechnique, CEA, Université Paris-Saclay, F-91128 Palaiseau Cedex, France
| | - T. G. White
- Department of Physics, University of Nevada, Reno, NV 89557, USA
| | - G. Gregori
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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9
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Magnetized fast isochoric laser heating for efficient creation of ultra-high-energy-density states. Nat Commun 2018; 9:3937. [PMID: 30258053 PMCID: PMC6158241 DOI: 10.1038/s41467-018-06173-6] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2018] [Accepted: 08/22/2018] [Indexed: 11/08/2022] Open
Abstract
Fast isochoric heating of a pre-compressed plasma core with a high-intensity short-pulse laser is an attractive and alternative approach to create ultra-high-energy-density states like those found in inertial confinement fusion (ICF) ignition sparks. Laser-produced relativistic electron beam (REB) deposits a part of kinetic energy in the core, and then the heated region becomes the hot spark to trigger the ignition. However, due to the inherent large angular spread of the produced REB, only a small portion of the REB collides with the core. Here, we demonstrate a factor-of-two enhancement of laser-to-core energy coupling with the magnetized fast isochoric heating. The method employs a magnetic field of hundreds of Tesla that is applied to the transport region from the REB generation zone to the core which results in guiding the REB along the magnetic field lines to the core. This scheme may provide more efficient energy coupling compared to the conventional ICF scheme.
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10
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Harbour L, Förster GD, Dharma-Wardana MWC, Lewis LJ. Ion-ion dynamic structure factor, acoustic modes, and equation of state of two-temperature warm dense aluminum. Phys Rev E 2018; 97:043210. [PMID: 29758670 DOI: 10.1103/physreve.97.043210] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Indexed: 11/07/2022]
Abstract
The ion-ion dynamical structure factor and the equation of state of warm dense aluminum in a two-temperature quasiequilibrium state, with the electron temperature higher than the ion temperature, are investigated using molecular-dynamics simulations based on ion-ion pair potentials constructed from a neutral pseudoatom model. Such pair potentials based on density functional theory are parameter-free and depend directly on the electron temperature and indirectly on the ion temperature, enabling efficient computation of two-temperature properties. Comparison with ab initio simulations and with other average-atom calculations for equilibrium aluminum shows good agreement, justifying a study of quasiequilibrium situations. Analyzing the van Hove function, we find that ion-ion correlations vanish in a time significantly smaller than the electron-ion relaxation time so that dynamical properties have a physical meaning for the quasiequilibrium state. A significant increase in the speed of sound is predicted from the modification of the dispersion relation of the ion acoustic mode as the electron temperature is increased. The two-temperature equation of state including the free energy, internal energy, and pressure is also presented.
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Affiliation(s)
- L Harbour
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7
| | - G D Förster
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7
| | | | - Laurent J Lewis
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7
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11
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Dharma-Wardana MWC, Klug DD, Harbour L, Lewis LJ. Isochoric, isobaric, and ultrafast conductivities of aluminum, lithium, and carbon in the warm dense matter regime. Phys Rev E 2017; 96:053206. [PMID: 29347759 DOI: 10.1103/physreve.96.053206] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2017] [Indexed: 06/07/2023]
Abstract
We study the conductivities σ of (i) the equilibrium isochoric state σ_{is}, (ii) the equilibrium isobaric state σ_{ib}, and also the (iii) nonequilibrium ultrafast matter state σ_{uf} with the ion temperature T_{i} less than the electron temperature T_{e}. Aluminum, lithium, and carbon are considered, being increasingly complex warm dense matter systems, with carbon having transient covalent bonds. First-principles calculations, i.e., neutral-pseudoatom (NPA) calculations and density-functional theory (DFT) with molecular-dynamics (MD) simulations, are compared where possible with experimental data to characterize σ_{ic}, σ_{ib}, and σ_{uf}. The NPA σ_{ib} is closest to the available experimental data when compared to results from DFT with MD simulations, where simulations of about 64-125 atoms are typically used. The published conductivities for Li are reviewed and the value at a temperature of 4.5 eV is examined using supporting x-ray Thomson-scattering calculations. A physical picture of the variations of σ with temperature and density applicable to these materials is given. The insensitivity of σ to T_{e} below 10 eV for carbon, compared to Al and Li, is clarified.
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Affiliation(s)
| | - D D Klug
- National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6
| | - L Harbour
- Département de Physique, Université de Montréal, Montréal, Québec, Canada H3T 1J4
| | - Laurent J Lewis
- Département de Physique, Université de Montréal, Montréal, Québec, Canada H3T 1J4
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12
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Ng A, Sterne P, Hansen S, Recoules V, Chen Z, Tsui YY, Wilson B. dc conductivity of two-temperature warm dense gold. Phys Rev E 2016; 94:033213. [PMID: 27739824 DOI: 10.1103/physreve.94.033213] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2015] [Indexed: 06/06/2023]
Abstract
Using recently obtained ac conductivity data we have derived dc conductivity together with free electron density and electron momentum relaxation time in two-temperature warm dense gold with energy density up to 4.1 MJ/kg (0.8×10^{11}J/m^{3}). The derivation is based on a Drude interpretation of the dielectric function that takes into account contributions of intraband and interband transitions as well as atomic polarizability. The results provide valuable benchmarks for assessing the extended Ziman formula for electrical resistivity and an accompanying average atom model.
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Affiliation(s)
- A Ng
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
| | - P Sterne
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - S Hansen
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - V Recoules
- CEA, DAM, DIF, 91297 Arpajon Cedex, France
| | - Z Chen
- Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 1H9
| | - Y Y Tsui
- Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 1H9
| | - B Wilson
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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13
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Sasaki T, Takahashi T, Ohuchi T, Kawaguchi Y, Takahashi K, Kikuchi T, Aso T, Harada N, Horioka K, Nagatomo H, Fujioka S. Evaluation of Transport Properties in Warm Dense Matter Generated by Pulsed-power Discharge for Nuclear Fusion Systems. ACTA ACUST UNITED AC 2015. [DOI: 10.1016/j.egypro.2014.11.878] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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14
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Reinholz H, Röpke G, Rosmej S, Redmer R. Conductivity of warm dense matter including electron-electron collisions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:043105. [PMID: 25974600 DOI: 10.1103/physreve.91.043105] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/04/2023]
Abstract
We present an approach that can resolve the controversy with respect to the role of electron-electron collisions in calculating the dynamic conductivity of dense plasmas. In particular, the dc conductivity is analyzed in the low-density, nondegenerate limit where the Spitzer theory is valid and electron-electron collisions lead to the well-known reduction in comparison to the result considering only electron-ion collisions (Lorentz model). With increasing degeneracy, the contribution of electron-electron collisions to the dc conductivity is decreasing and can be neglected for the liquid metal domain where the Ziman theory is applicable. We give expressions for the effect of electron-electron collisions in calculating the conductivity in the warm dense matter region, i.e., for strongly coupled Coulomb systems at arbitrary degeneracy.
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Affiliation(s)
- H Reinholz
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany and University of Western Australia School of Physics, WA 6009 Crawley, Australia
| | - G Röpke
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
| | - S Rosmej
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
| | - R Redmer
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
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15
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Murillo MS, Weisheit J, Hansen SB, Dharma-wardana MWC. Partial ionization in dense plasmas: comparisons among average-atom density functional models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063113. [PMID: 23848795 DOI: 10.1103/physreve.87.063113] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2013] [Indexed: 06/02/2023]
Abstract
Nuclei interacting with electrons in dense plasmas acquire electronic bound states, modify continuum states, generate resonances and hopping electron states, and generate short-range ionic order. The mean ionization state (MIS), i.e, the mean charge Z of an average ion in such plasmas, is a valuable concept: Pseudopotentials, pair-distribution functions, equations of state, transport properties, energy-relaxation rates, opacity, radiative processes, etc., can all be formulated using the MIS of the plasma more concisely than with an all-electron description. However, the MIS does not have a unique definition and is used and defined differently in different statistical models of plasmas. Here, using the MIS formulations of several average-atom models based on density functional theory, we compare numerical results for Be, Al, and Cu plasmas for conditions inclusive of incomplete atomic ionization and partial electron degeneracy. By contrasting modern orbital-based models with orbital-free Thomas-Fermi models, we quantify the effects of shell structure, continuum resonances, the role of exchange and correlation, and the effects of different choices of the fundamental cell and boundary conditions. Finally, the role of the MIS in plasma applications is illustrated in the context of x-ray Thomson scattering in warm dense matter.
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Affiliation(s)
- Michael S Murillo
- Computational Physics and Methods Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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16
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Dong QL, Yang J, Jiang ZT, Sheng ZM, Zhang J. The energy band structures of the warm dense plasmas with micro-structures inherited from original carbon nanotubes. EPJ WEB OF CONFERENCES 2013. [DOI: 10.1051/epjconf/20135916003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Dharma-wardana MWC. Electron-ion and ion-ion potentials for modeling warm dense matter: Applications to laser-heated or shock-compressed Al and Si. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036407. [PMID: 23031034 DOI: 10.1103/physreve.86.036407] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2012] [Revised: 07/24/2012] [Indexed: 06/01/2023]
Abstract
The pair interactions Uij(r) determine the thermodynamics and linear transport properties of matter via the pair-distribution functions (PDFs), i.e., gij(r). Great simplicity is achieved if Uij(r) could be directly used to predict material properties via classical simulations, avoiding many-body wave functions. Warm dense matter (WDM) is encountered in quasiequilibria where the electron temperature Te differs from the ion temperature Ti, as in laser-heated or in shock-compressed matter. The electron PDFs gee(r) as perturbed by the ions are used to evaluate fully nonlocal exchange-correlation corrections to the free energy, using hydrogen as an example. Electron-ion potentials for ions with a bound core are discussed with Al and Si as examples, for WDM with Te≠Ti, and valid for times shorter than the electron-ion relaxation time. In some cases the potentials develop attractive regions and then become repulsive and "Yukawa-like" for higher Te. These results clarify the origin of initial phonon hardening and rapid release. Pair potentials for shock-heated WDM show that phonon hardening would not occur in most such systems. Defining meaningful quasiequilibrium static transport coefficients consistent with the dynamic values is addressed. There seems to be no meaningful "static conductivity" obtainable by extrapolating experimental or theoretical σ(ω,Ti,Te) to ω→0, unless Ti→Te as well. Illustrative calculations of quasistatic resistivities R(Ti,Te) of laser-heated as well as shock-heated aluminum and silicon are presented using our pseudopotentials, pair potentials, and classical integral equations. The quasistatic resistivities display clear differences in their temperature evolutions, but are not the strict ω→0 limits of the dynamic values.
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Amano Y, Miki Y, Takahashi T, Sasaki T, Kikuchi T, Harada N. Isochoric heating of foamed metal using pulsed power discharge as a making technique of warm dense matter. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2012; 83:085107. [PMID: 22938332 DOI: 10.1063/1.4742986] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
To generate well-defined warm dense state for evaluating electrical conductivity by using pulsed-power discharge, we have proposed an isochoric heating of foamed metal. Isochoric heating can be achieved by surrounding the foamed metal with a rigid-walled sapphire capillary. We evaluate the temperature and electrical conductivity of the foam∕plasma based on the line-pair method of the foam∕plasma emission and on the voltage-current waveforms. The electrical conductivity observed agrees with previous experiments and predictions. Thus, the proposed technique yields the electrical conductivity of warm dense matter with a well-defined temperature.
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Affiliation(s)
- Yusuke Amano
- Department of Electrical Engineering, Nagaoka University of Technology, Kamitomioka 1603-1, Nagaoka, Niigata 940-2188, Japan
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Reinholz H, Röpke G. Dielectric function beyond the random-phase approximation: kinetic theory versus linear response theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036401. [PMID: 22587190 DOI: 10.1103/physreve.85.036401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2011] [Indexed: 05/31/2023]
Abstract
Calculating the frequency-dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we give a proof that the Kohler variational principle can be extended to arbitrary frequencies. It is shown to be a special case of the Zubarev method for the construction of a nonequilibrium statistical operator from the principle of the extremum of entropy production. Within kinetic theory, the commonly used energy-dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.
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Affiliation(s)
- H Reinholz
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany.
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Apfelbaum EM. Calculation of electronic transport coefficients of Ag and Au plasma. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:066403. [PMID: 22304204 DOI: 10.1103/physreve.84.066403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2011] [Revised: 10/21/2011] [Indexed: 05/31/2023]
Abstract
The thermoelectric transport coefficients of silver and gold plasma have been calculated within the relaxation-time approximation. We considered temperatures of 10-100 kK and densities of ρ </~ 1 g/cm(3). The plasma composition was calculated using a corresponding system of coupled mass action laws, including the atom ionization up to +4. For momentum cross sections of electron-atom scattering we used the most accurate expressions available. The results of our modeling have been compared with other researchers' data whenever possible.
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Affiliation(s)
- E M Apfelbaum
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya Street 13, Building 2, Moscow 125412, Russia.
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Zhang M, Drabold DA. The work done by an external electromagnetic field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:085801. [PMID: 21411902 DOI: 10.1088/0953-8984/23/8/085801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Ehrenfest's theorem is used to derive the rate of change of kinetic energy induced by an external field. The expression for the power is valid for any electromagnetic field in arbitrary gauge. We discuss the applicable conditions for the Mott-Davis and Moseley-Lukes form of the Kubo-Greenwood formula (KGF) for the electrical conductivity which has been implemented in ab initio codes. We show that the conventional KGF does not satisfy gauge invariance, and is suitable only for computing the ac conductivity at sufficiently high frequency and when the gradient of the carrier density is small.
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Affiliation(s)
- Mingliang Zhang
- Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA.
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Dharma-wardana MWC, Murillo MS. Pair-distribution functions of two-temperature two-mass systems: comparison of molecular dynamics, classical-map hypernetted chain, quantum Monte Carlo, and Kohn-Sham calculations for dense hydrogen. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:026401. [PMID: 18352127 DOI: 10.1103/physreve.77.026401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2007] [Indexed: 05/26/2023]
Abstract
Two-temperature, two-mass quasiequilibrium plasmas may occur in electron-ion plasmas, nuclear-matter, as well as in electron-hole condensed-matter systems. Dense two-temperature hydrogen plasmas straddle the difficult partially degenerate regime of electron densities and temperatures which are important in astrophysics, in inertial-confinement fusion research, and other areas of warm dense-matter physics. Results from quantum Monte Carlo (QMC) are used to benchmark the procedures used in classical molecular-dynamics simulations and hypernetted chain (HNC) and classical-map HNC (CHNC) methods to derive electron-electron and electron-proton pair-distribution functions. Where QMC is not available, we used Kohn-Sham results as the reference calculation. Then, nonequilibrium molecular dynamics for two-temperature, two-mass plasmas are used to obtain pair distribution functions without specifying the interspecies cross temperature. Using these results, the correct HNC and CHNC procedures for the evaluation of pair-distribution functions in two-temperature two-mass two-component charged fluids are established and results for a mass ratio of 1:5, typical of electron-hole fluids, are presented.
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Blenski T, Cichocki B. Variational theory of average-atom and superconfigurations in quantum plasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:056402. [PMID: 17677177 DOI: 10.1103/physreve.75.056402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2006] [Revised: 02/26/2007] [Indexed: 05/16/2023]
Abstract
Models of screened ions in equilibrium plasmas with all quantum electrons are important in opacity and equation of state calculations. Although such models have to be derived from variational principles, up to now existing models have not been fully variational. In this paper a fully variational theory respecting virial theorem is proposed-all variables are variational except the parameters defining the equilibrium, i.e., the temperature T, the ion density ni and the atomic number Z. The theory is applied to the quasiclassical Thomas-Fermi (TF) atom, the quantum average atom (QAA), and the superconfigurations (SC) in plasmas. Both the self-consistent-field (SCF) equations for the electronic structure and the condition for the mean ionization Z* are found from minimization of a thermodynamic potential. This potential is constructed using the cluster expansion of the plasma free energy from which the zero and the first-order terms are retained. In the zero order the free energy per ion is that of the quantum homogeneous plasma of an unknown free-electron density n0 = Z* ni occupying the volume 1/ni. In the first order, ions submerged in this plasma are considered and local neutrality is assumed. These ions are considered in the infinite space without imposing the neutrality of the Wigner-Seitz (WS) cell. As in the Inferno model, a central cavity of a radius R is introduced, however, the value of R is unknown a priori. The charge density due to noncentral ions is zero inside the cavity and equals en0 outside. The first-order contribution to free energy per ion is the difference between the free energy of the system "central ion+infinite plasma" and the free energy of the system "infinite plasma." An important part of the approach is an "ionization model" (IM), which is a relation between the mean ionization charge Z* and the first-order structure variables. Both the IM and the local neutrality are respected in the minimization procedure. The correct IM in the TF case is found to be Z-Z*= integral d3 r[n(r)-n0], where n(r) is the first-order electron density. It is shown that in the QAA case the same IM has to be used and that other IMs lead to unphysical solutions. With this IM R becomes in both cases (TF and QAA) equal to the WS radius and the variational calculation leads to SCF equations in an infinite plasma while n0 (or equivalently Z*) is to be found from the condition integral d3r theta(r-R)Vel(r)=0, where theta denotes Heaviside function and Vel(r) is the SCF electrostatic potential. In the SC case results are similar except that averages over all superconfigurations appear. In the TF case the condition for n0 gives the neutrality of the WS sphere and one gets the classical TF ion-in-cell average atom. The situation is different in the QAA and in the SC cases in which the cavity is not neutral and the SCF potential Vel(r) is not zero outside the cavity. Due to the fully variational character of our approach the expression for the thermodynamic pressure in all cases does not require any numerical differentiation and is consistent with the virial theorem.
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Affiliation(s)
- T Blenski
- CEA, Centre d'Etudes de Saclay, DSM/DRECAM/SPAM, Bâtiment 522, F91191 Gif-sur-Yvette Cedex, France.
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