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Ovechkin AA, Loboda PA, Popova VV, Akulinina EY, Berezovskaya ME, Korolev AS, Kolchugin SV. Plasma ionization balance in chemical-picture and average-atom models. Phys Rev E 2023; 108:015207. [PMID: 37583194 DOI: 10.1103/physreve.108.015207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 07/02/2023] [Indexed: 08/17/2023]
Abstract
We propose an approximate method to calculate ion partition functions in the context of the chemical-picture representation of plasmas as an interacting mixture of various ions and free electrons under the local-thermodynamic-equilibrium conditions. The method uses the superconfiguration approach and implies that the first-order corrections to the energies of excited electron configurations due to the electron-electron interaction may be replaced by a similar first-order correction to the energy of the basic configuration of an ion with the same number of bound electrons. The method enables one to significantly speed up the calculations and generally provides quite accurate results. Using the method proposed, plasma ionization balance and average ion charges calculated on the base of the chemical-picture representation show a good agreement with the relevant average-atom data. For the case of weak electron-ion nonideality, we provide approximate relations between the chemical-picture and average-atom values of the average ion charge, chemical potential, and plasma-density depression of ionization potential.
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Affiliation(s)
- A A Ovechkin
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - P A Loboda
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
- National Research Nuclear University-Moscow Engineering Physics Institute (MEPhI), 31, Kashirskoe sh., Moscow 115409, Russia
| | - V V Popova
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - E Yu Akulinina
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - M E Berezovskaya
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - A S Korolev
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - S V Kolchugin
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
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Lv M, Li K, Wang C, Hu R, Zhao Y, Dai J. Bound electron screening effect on ion-ion potential of warm and hot dense matter. Phys Rev E 2021; 103:L051203. [PMID: 34134302 DOI: 10.1103/physreve.103.l051203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 05/04/2021] [Indexed: 11/07/2022]
Abstract
The effects of bound electron screening in warm and hot dense matter are investigated analytically and a theoretical description of screened short-range repulsion is given meanwhile. An empirical ion-ion potential including the classic charge screening and chemical bond attraction at various temperatures and densities is proposed. By solving hypernetted chain equations and comparing the obtained radial distribution function (RDF) with ab initio simulations, the proposed ion-ion potential is found to be promising over a wide range of temperatures and densities for warm dense aluminum and iron. The elastic scattering amplitude and the x-ray absorption near the edge structure of warm dense aluminum calculated from the obtained RDF are in good agreement with experiment results.
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Affiliation(s)
- Meng Lv
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Ke Li
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Chuan Wang
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Ronghao Hu
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Yang Zhao
- Research Center of Laser Fusion, China Academy of Engineering Physics, P. O. Box 919-986, Mianyang 621900, People's Republic of China
| | - Jiayu Dai
- Department of Physics, College of Science, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
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Ovechkin AA, Loboda PA, Falkov AL, Sapozhnikov PA. Equation of state modeling with pseudoatom molecular dynamics. Phys Rev E 2021; 103:053206. [PMID: 34134221 DOI: 10.1103/physreve.103.053206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
Using a modified version of the pseudoatom molecular-dynamics approach, the silicon and oxygen equations of state were generated and then employed to construct the equation of state of silicon dioxide. The results are supported by the close agreement with ab initio simulations of the silicon pressure and experimental shock Hugoniot of silicon dioxide. Ion thermal contributions to thermodynamic functions provided by the PAMD simulations are compared to their counterparts obtained with the one-component plasma and charged-hard-sphere approximations.
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Affiliation(s)
- A A Ovechkin
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia
| | - P A Loboda
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia.,National Research Nuclear University, Moscow Engineering Physics Institute (MEPhI), Moscow 115409, Russia
| | - A L Falkov
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia
| | - P A Sapozhnikov
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia
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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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Clérouin J, Desbiens N, Dubois V, Arnault P. Bayesian inference of x-ray diffraction spectra from warm dense matter with the one-component-plasma model. Phys Rev E 2017; 94:061202. [PMID: 28085351 DOI: 10.1103/physreve.94.061202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2016] [Indexed: 11/07/2022]
Abstract
We show that the Bayesian inference of recently measured x-ray diffraction spectra from laser-shocked aluminum [L. B. Fletcher et al., Nat. Photon. 9, 274 (2015)10.1038/nphoton.2015.41] with the one-component-plasma (OCP) model performs remarkably well at estimating the ionic density and temperature. This statistical approach requires many evaluations of the OCP static structure factor, which were done using a recently derived analytic fit. The atomic form factor is approximated by an exponential function in the diffraction window of the first peak. The electronic temperature is then estimated from a comparison of this approximated form factor with the electronic structure of an average atom model. Out-of-equilibrium states, with electrons hotter than ions, are diagnosed for the spectra obtained early after the pump, whereas at a late time delay the plasma is at thermal equilibrium. Apart from the present findings, this OCP-based modeling of warm dense matter has an important role to play in the interpretation of x-ray Thomson scattering measurements currently performed at large laser facilities.
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Harbour L, Dharma-Wardana MWC, Klug DD, Lewis LJ. Pair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium. Phys Rev E 2016; 94:053211. [PMID: 27967139 DOI: 10.1103/physreve.94.053211] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Indexed: 06/06/2023]
Abstract
Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) "Yukawa screening" and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.
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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
| | | | - D D Klug
- National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6
| | - L 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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Starrett CE, Saumon D. Equation of state of dense plasmas with pseudoatom molecular dynamics. Phys Rev E 2016; 93:063206. [PMID: 27415376 DOI: 10.1103/physreve.93.063206] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2016] [Indexed: 06/06/2023]
Abstract
We present an approximation for calculating the equation of state (EOS) of warm and hot dense matter that is built on the previously published pseudoatom molecular dynamics (PAMD) model of dense plasmas [Starrett et al., Phys. Rev. E 91, 013104 (2015)PLEEE81539-375510.1103/PhysRevE.91.013104]. While the EOS calculation with PAMD was previously limited to orbital-free density functional theory (DFT), the new approximation presented here allows a Kohn-Sham DFT treatment of the electrons. The resulting EOS thus includes a quantum mechanical treatment of the electrons with a self-consistent model of the ionic structure, while remaining tractable at high temperatures. The method is validated by comparisons with pressures from ab initio simulations of Be, Al, Si, and Fe. The EOS in the Thomas-Fermi approximation shows remarkable thermodynamic consistency over a wide range of temperatures for aluminum. We calculate the principal Hugoniots of aluminum and silicon up to 500 eV. We find that the ionic structure of the plasma has a modest effect that peaks at temperatures of a few eV and that the features arising from the electronic structure agree well with ab initio simulations.
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Affiliation(s)
- 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
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Current Issues in Finite-T Density-Functional Theory and Warm-Correlated Matter †. COMPUTATION 2016. [DOI: 10.3390/computation4020016] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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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.
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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
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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.
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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
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