1
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Dornheim T, Döppner T, Baczewski AD, Tolias P, Böhme MP, Moldabekov ZA, Gawne T, Ranjan D, Chapman DA, MacDonald MJ, Preston TR, Kraus D, Vorberger J. X-ray Thomson scattering absolute intensity from the f-sum rule in the imaginary-time domain. Sci Rep 2024; 14:14377. [PMID: 38909077 PMCID: PMC11193768 DOI: 10.1038/s41598-024-64182-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2024] [Accepted: 06/05/2024] [Indexed: 06/24/2024] Open
Abstract
We present a formally exact and simulation-free approach for the normalization of X-ray Thomson scattering (XRTS) spectra based on the f-sum rule of the imaginary-time correlation function (ITCF). Our method works for any degree of collectivity, over a broad range of temperatures, and is applicable even in nonequilibrium situations. In addition to giving us model-free access to electronic correlations, this new approach opens up the intriguing possibility to extract a plethora of physical properties from the ITCF based on XRTS experiments.
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Affiliation(s)
- T Dornheim
- Center for Advanced Systems Understanding (CASUS), 02826, Görlitz, Germany.
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328, Dresden, Germany.
| | - T Döppner
- Lawrence Livermore National Laboratory (LLNL), California, 94550, Livermore, USA
| | - A D Baczewski
- Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, 87185, USA
| | - P Tolias
- Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm, 100 44, Sweden
| | - M P Böhme
- Center for Advanced Systems Understanding (CASUS), 02826, Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328, Dresden, Germany
- Technische Universität Dresden, 01062, Dresden, Germany
| | - Zh A Moldabekov
- Center for Advanced Systems Understanding (CASUS), 02826, Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328, Dresden, Germany
| | - Th Gawne
- Center for Advanced Systems Understanding (CASUS), 02826, Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328, Dresden, Germany
| | - D Ranjan
- Institut für Physik, Universität Rostock, 18057, Rostock, Germany
| | - D A Chapman
- First Light Fusion, Yarnton, Oxfordshire, UK
| | - M J MacDonald
- Lawrence Livermore National Laboratory (LLNL), California, 94550, Livermore, USA
| | | | - D Kraus
- Institut für Physik, Universität Rostock, 18057, Rostock, Germany
| | - J Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328, Dresden, Germany
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2
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Moldabekov Z, Gawne TD, Schwalbe S, Preston TR, Vorberger J, Dornheim T. Ultrafast Heating-Induced Suppression of d-Band Dominance in the Electronic Excitation Spectrum of Cuprum. ACS OMEGA 2024; 9:25239-25250. [PMID: 38882083 PMCID: PMC11170750 DOI: 10.1021/acsomega.4c02920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Revised: 05/08/2024] [Accepted: 05/20/2024] [Indexed: 06/18/2024]
Abstract
The combination of isochoric heating of solids by free-electron lasers (FELs) and in situ diagnostics by X-ray Thomson scattering (XRTS) allows for measurements of material properties at warm dense matter (WDM) conditions relevant for astrophysics, inertial confinement fusion, and materials science. In the case of metals, the FEL beam pumps energy directly into electrons with the lattice structure of ions being nearly unaffected. This leads to a unique transient state that gives rise to a set of interesting physical effects, which can serve as a reliable testing platform for WDM theories. In this work, we present extensive linear-response time-dependent density functional theory (TDDFT) results for the electronic dynamic structure factor of isochorically heated copper with a face-centered cubic lattice. At ambient conditions, the plasmon is heavily damped due to the presence of d-band excitations, and its position is independent of the wavenumber. In contrast, the plasmon feature starts to dominate the excitation spectrum and has a Bohm-Gross-type plasmon dispersion for temperatures T ≥ 4 eV, where the quasi-free electrons in the interstitial region are in the WDM regime. In addition, we analyze the thermal changes in the d-band excitations and outline the possibility to use future XRTS measurements of isochorically heated copper as a controlled testbed for WDM theories.
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Affiliation(s)
- Zhandos Moldabekov
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Thomas D Gawne
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Sebastian Schwalbe
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | | | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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3
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Filinov AV, Bonitz M. Equation of state of partially ionized hydrogen and deuterium plasma revisited. Phys Rev E 2023; 108:055212. [PMID: 38115427 DOI: 10.1103/physreve.108.055212] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 10/31/2023] [Indexed: 12/21/2023]
Abstract
We present improved first-principle fermionic path integral Monte Carlo (PIMC) simulation results for a dense partially ionized hydrogen (deuterium) plasma, for temperatures in the range 15000K≤T≤400000K and densities 7×10^{-7}g/cm^{3}≤ρ_{H}≤0.085g/cm^{3} (1.4×10^{-6}g/cm^{3}≤ρ_{D}≤0.17g/cm^{3}), corresponding to 100≥r_{s}≥2, where r_{s}=r[over ¯]/a_{B} is the ratio of the mean interparticle distance to the Bohr radius. These simulations are based on the fermionic propagator PIMC (FP-PIMC) approach in the grand canonical ensemble [Filinov et al., Contrib. Plasma Phys. 61, e202100112 (2021)0863-104210.1002/ctpp.202100112] and fully account for correlation and quantum degeneracy and spin effects. For the application to hydrogen and deuterium, we develop a combination of the fourth-order factorization and the pair product ansatz for the density matrix. Moreover, we avoid the fixed node approximation that may lead to uncontrolled errors in restricted PIMC (RPIMC). Our results allow us to critically reevaluate the accuracy of the RPIMC simulations for hydrogen by Hu et al. [Phys. Rev. B 84, 224109 (2011)1098-012110.1103/PhysRevB.84.224109] and of various chemical models. The deviations are generally found to be small, but for the lowest temperature, T=15640 K they reach several percent. We present detailed tables with our first principles results for the pressure and energy isotherms. We expect our updated results will serve as a valuable benchmark for comparison with other methods.
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Affiliation(s)
- A V Filinov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
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4
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Nichols KA, Hu SX, White AJ, Goncharov VN, Mihaylov DI, Collins LA, Shaffer NR, Karasiev VV. Time-dependent density-functional-theory calculations of the nonlocal electron stopping range for inertial confinement fusion applications. Phys Rev E 2023; 108:035206. [PMID: 37849196 DOI: 10.1103/physreve.108.035206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Accepted: 08/18/2023] [Indexed: 10/19/2023]
Abstract
Nonlocal electron transport is important for understanding laser-target coupling for laser-direct-drive (LDD) inertial confinement fusion (ICF) simulations. Current models for the nonlocal electron mean free path in radiation-hydrodynamic codes are based on plasma-physics models developed decades ago; improvements are needed to accurately predict the electron conduction in LDD simulations of ICF target implosions. We utilized time-dependent density functional theory (TD-DFT) to calculate the electron stopping power (SP) in the so-called conduction-zone plasmas of polystyrene in a wide range of densities and temperatures relevant to LDD. Compared with the modified Lee-More model, the TD-DFT calculations indicated a lower SP and a higher stopping range for nonlocal electrons. We fit these electron SP calculations to obtain a global analytical model for the electron stopping range as a function of plasma conditions and the nonlocal electron kinetic energy. This model was implemented in the one-dimensional radiation-hydrodynamic code lilac to perform simulations of LDD ICF implosions, which are further compared with simulations by the standard modified Lee-More model. Results from these integrated simulations are discussed in terms of the implications of this TD-DFT-based mean-free-path model to ICF simulations.
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Affiliation(s)
- K A Nichols
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14623-1299, USA
| | - S X Hu
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14623-1299, USA
- Department of Mechanical Engineering, University of Rochester, Rochester, New York 14623-1299, USA
| | - A J White
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - V N Goncharov
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
- Department of Mechanical Engineering, University of Rochester, Rochester, New York 14623-1299, USA
| | - D I Mihaylov
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
| | - L A Collins
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - N R Shaffer
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
| | - V V Karasiev
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
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5
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Svensson P, Campbell T, Graziani F, Moldabekov Z, Lyu N, Batista VS, Richardson S, Vinko SM, Gregori G. Development of a new quantum trajectory molecular dynamics framework. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220325. [PMID: 37393934 PMCID: PMC10315217 DOI: 10.1098/rsta.2022.0325] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 01/19/2023] [Indexed: 07/04/2023]
Abstract
An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Pontus Svensson
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Thomas Campbell
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Frank Graziani
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Zhandos Moldabekov
- Center of Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
- Yale Quantum Institute, Yale University, New Haven, CT 06511, USA
| | | | - Sam M Vinko
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK
| | - Gianluca Gregori
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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6
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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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7
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Dornheim T, Vorberger J, Moldabekov ZA, Böhme M. Analysing the dynamic structure of warm dense matter in the imaginary-time domain: theoretical models and simulations. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220217. [PMID: 37393936 DOI: 10.1098/rsta.2022.0217] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Accepted: 01/10/2023] [Indexed: 07/04/2023]
Abstract
Rigorous diagnostics of experiments with warm dense matter are notoriously difficult. A key method is X-ray Thomson scattering (XRTS), but the interpretation of XRTS measurements is usually based on theoretical models that entail various approximations. Recently, Dornheim et al. [Nat. Commun. 13, 7911 (2022)] introduced a new framework for temperature diagnostics of XRTS experiments that is based on imaginary-time correlation functions. On the one hand, switching from the frequency to the imaginary-time domain gives one direct access to a number of physical properties, which facilitates the extraction of the temperature of arbitrarily complex materials without relying on any models or approximations. On the other hand, the bulk of theoretical work in dynamic quantum many-body theory is devoted to the frequency domain, and, to the best of our knowledge, the manifestation of physics properties within the imaginary-time density-density correlation function (ITCF) remains poorly understood. In the present work, we aim to fill this gap by introducing a simple, semi-analytical model for the imaginary-time dependence of two-body correlations within the framework of imaginary-time path integrals. As a practical example, we compare our new model to extensive ab initio path integral Monte Carlo results for the ITCF of a uniform electron gas, and find excellent agreement over a broad range of wavenumbers, densities and temperatures. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Maximilian Böhme
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
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8
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Babbush R, Huggins WJ, Berry DW, Ung SF, Zhao A, Reichman DR, Neven H, Baczewski AD, Lee J. Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods. Nat Commun 2023; 14:4058. [PMID: 37429883 DOI: 10.1038/s41467-023-39024-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 05/26/2023] [Indexed: 07/12/2023] Open
Abstract
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.
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Affiliation(s)
| | | | - Dominic W Berry
- Department of Physics and Astronomy, Macquarie University, Sydney, NSW, Australia
| | - Shu Fay Ung
- Department of Chemistry, Columbia University, New York, NY, USA
| | - Andrew Zhao
- Google Quantum AI, Venice, CA, USA
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA
| | | | | | - Andrew D Baczewski
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, NM, USA
| | - Joonho Lee
- Google Quantum AI, Venice, CA, USA.
- Department of Chemistry, Columbia University, New York, NY, USA.
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, USA.
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9
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Schörner M, Bethkenhagen M, Döppner T, Kraus D, Fletcher LB, Glenzer SH, Redmer R. X-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula. Phys Rev E 2023; 107:065207. [PMID: 37464593 DOI: 10.1103/physreve.107.065207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 05/10/2023] [Indexed: 07/20/2023]
Abstract
We study ab initio approaches for calculating x-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula that expresses the inelastic contribution in terms of the dielectric function. We study the electronic dynamic structure factor computed from the Mermin dielectric function using an ab initio electron-ion collision frequency in comparison to computations using a linear-response time-dependent density functional theory (LR-TDDFT) framework for hydrogen and beryllium and investigate the dispersion of free-free and bound-free contributions to the scattering signal. A separate treatment of these contributions, where only the free-free part follows the Mermin dispersion, shows good agreement with LR-TDDFT results for ambient-density beryllium, but breaks down for highly compressed matter where the bound states become pressure ionized. LR-TDDFT is used to reanalyze x-ray Thomson scattering experiments on beryllium demonstrating strong deviations from the plasma conditions inferred with traditional analytic models at small scattering angles.
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Affiliation(s)
| | - Mandy Bethkenhagen
- École Normale Supérieure de Lyon, Laboratoire de Géologie de Lyon, CNRS UMR 5276, 69364 Lyon, Cedex 07, France
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Tilo Döppner
- Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Dominik Kraus
- University of Rostock, Institute of Physics, 18051 Rostock, Germany
- Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
| | - Luke B Fletcher
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | | | - Ronald Redmer
- University of Rostock, Institute of Physics, 18051 Rostock, Germany
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10
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Döppner T, Bethkenhagen M, Kraus D, Neumayer P, Chapman DA, Bachmann B, Baggott RA, Böhme MP, Divol L, Falcone RW, Fletcher LB, Landen OL, MacDonald MJ, Saunders AM, Schörner M, Sterne PA, Vorberger J, Witte BBL, Yi A, Redmer R, Glenzer SH, Gericke DO. Observing the onset of pressure-driven K-shell delocalization. Nature 2023:10.1038/s41586-023-05996-8. [PMID: 37225995 DOI: 10.1038/s41586-023-05996-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 03/22/2023] [Indexed: 05/26/2023]
Abstract
The gravitational pressure in many astrophysical objects exceeds one gigabar (one billion atmospheres)1-3, creating extreme conditions where the distance between nuclei approaches the size of the K shell. This close proximity modifies these tightly bound states and, above a certain pressure, drives them into a delocalized state4. Both processes substantially affect the equation of state and radiation transport and, therefore, the structure and evolution of these objects. Still, our understanding of this transition is far from satisfactory and experimental data are sparse. Here we report on experiments that create and diagnose matter at pressures exceeding three gigabars at the National Ignition Facility5 where 184 laser beams imploded a beryllium shell. Bright X-ray flashes enable precision radiography and X-ray Thomson scattering that reveal both the macroscopic conditions and the microscopic states. The data show clear signs of quantum-degenerate electrons in states reaching 30 times compression, and a temperature of around two million kelvins. At the most extreme conditions, we observe strongly reduced elastic scattering, which mainly originates from K-shell electrons. We attribute this reduction to the onset of delocalization of the remaining K-shell electron. With this interpretation, the ion charge inferred from the scattering data agrees well with ab initio simulations, but it is significantly higher than widely used analytical models predict6.
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Affiliation(s)
- T Döppner
- Lawrence Livermore National Laboratory, Livermore, CA, USA.
| | - M Bethkenhagen
- Institute of Physics, University of Rostock, Rostock, Germany
- École Normale Supérieure de Lyon, LGLTPE, CNRS UMR 5276, Lyon, France
| | - D Kraus
- Institute of Physics, University of Rostock, Rostock, Germany
- Department of Physics, University of California Berkeley, Berkeley, CA, USA
- Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany
| | - P Neumayer
- GSI Helmholtz-Zentrum für Schwerionenforschung, Darmstadt, Germany
| | | | - B Bachmann
- Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - R A Baggott
- The John Adams Institute for Accelerator Science, Imperial College London, London, UK
| | - M P Böhme
- Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany
- Center for Advanced Systems Understanding (CASUS), Görlitz, Germany
- Technische Universität Dresden, Dresden, Germany
| | - L Divol
- Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - R W Falcone
- Department of Physics, University of California Berkeley, Berkeley, CA, USA
| | - L B Fletcher
- SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - O L Landen
- Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - M J MacDonald
- Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - A M Saunders
- Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - M Schörner
- Institute of Physics, University of Rostock, Rostock, Germany
| | - P A Sterne
- Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - J Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany
| | - B B L Witte
- Institute of Physics, University of Rostock, Rostock, Germany
- SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - A Yi
- Los Alamos National Laboratory, Los Alamos, NM, USA
| | - R Redmer
- Institute of Physics, University of Rostock, Rostock, Germany
| | - S H Glenzer
- SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - D O Gericke
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry, UK
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11
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Moldabekov ZA, Lokamani M, Vorberger J, Cangi A, Dornheim T. Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons. J Chem Phys 2023; 158:094105. [PMID: 36889956 DOI: 10.1063/5.0135729] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within the Kohn-Sham density functional theory for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of the warm dense matter. Generated by laser-induced compression and heating in the laboratory, the warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing with the exact quantum Monte Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used, compared with the previously reported results for the PBE, PBEsol, local-density approximation, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy.
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Affiliation(s)
- Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Mani Lokamani
- Information Services and Computing, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Insitute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Attila Cangi
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
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12
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Böhme M, Moldabekov ZA, Vorberger J, Dornheim T. Static Electronic Density Response of Warm Dense Hydrogen: Ab Initio Path Integral Monte Carlo Simulations. PHYSICAL REVIEW LETTERS 2022; 129:066402. [PMID: 36018668 DOI: 10.1103/physrevlett.129.066402] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Revised: 05/12/2022] [Accepted: 06/23/2022] [Indexed: 06/15/2023]
Abstract
The properties of hydrogen under extreme conditions are important for many applications, including inertial confinement fusion and astrophysical models. A key quantity is given by the electronic density response to an external perturbation, which is probed in x-ray Thomson scattering experiments-the state of the art diagnostics from which system parameters like the free electron density n_{e}, the electronic temperature T_{e}, and the charge state Z can be inferred. In this work, we present highly accurate path integral Monte Carlo results for the static electronic density response of hydrogen. We obtain the static exchange-correlation (XC) kernel K_{XC}, which is of central relevance for many applications, such as time-dependent density functional theory. This gives us a first unbiased look into the electronic density response of hydrogen in the warm-dense matter regime, thereby opening up a gamut of avenues for future research.
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Affiliation(s)
- Maximilian Böhme
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
| | - Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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13
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Thermal excitation signals in the inhomogeneous warm dense electron gas. Sci Rep 2022; 12:1093. [PMID: 35058531 PMCID: PMC8776784 DOI: 10.1038/s41598-022-05034-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 12/30/2021] [Indexed: 12/16/2022] Open
Abstract
We investigate the emergence of electronic excitations from the inhomogeneous electronic structure at warm dense matter parameters based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They include satellite signals around the standard plasmon feature, transformation of plasmons to optical modes, and double-plasmon modes. These modes exhibit a pronounced dependence on the temperature. This makes them potentially invaluable for the diagnostics of plasma parameters in the warm dense matter regime. We demonstrate that these modes can be probed with present experimental techniques.
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14
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Rightley S, Baalrud SD. Kinetic model for electron-ion transport in warm dense matter. Phys Rev E 2021; 103:063206. [PMID: 34271617 DOI: 10.1103/physreve.103.063206] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Accepted: 05/03/2021] [Indexed: 12/23/2022]
Abstract
We present a model for electron-ion transport in warm dense matter that incorporates Coulomb coupling effects into the quantum Boltzmann equation of Uehling and Uhlenbeck through the use of a statistical potential of mean force. Although the model presented here can be derived rigorously in the classical limit [S. D. Baalrud and J. Daligault, Phys. Plasmas 26, 082106 (2019)PHPAEN1070-664X10.1063/1.5095655], its quantum generalization is complicated by the uncertainty principle. Here we apply an existing model for the potential of mean force based on the quantum Ornstein-Zernike equation coupled with an average-atom model [C. E. Starrett, High Energy Density Phys. 25, 8 (2017)1574-181810.1016/j.hedp.2017.09.003]. This potential contains correlations due to both Coulomb coupling and exchange, and the collision kernel of the kinetic theory enforces Pauli blocking while allowing for electron diffraction and large-angle collisions. We use the Uehling-Uhlenbeck equation to predict the momentum and temperature relaxation times and electrical conductivity of solid density aluminum plasma based on electron-ion collisions. We present results for density and temperature conditions that span the transition from classical weakly-coupled plasma to degenerate moderately-coupled plasma. Our findings agree well with recent quantum molecular dynamics simulations.
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Affiliation(s)
- Shane Rightley
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
| | - Scott D Baalrud
- Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA
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15
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Zhang H, Zhang S, Kang D, Dai J, Bonitz M. Finite-temperature density-functional-theory investigation on the nonequilibrium transient warm-dense-matter state created by laser excitation. Phys Rev E 2021; 103:013210. [PMID: 33601505 DOI: 10.1103/physreve.103.013210] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Accepted: 12/24/2020] [Indexed: 11/07/2022]
Abstract
We present a finite-temperature density-functional-theory investigation of the nonequilibrium transient electronic structure of warm dense Li, Al, Cu, and Au created by laser excitation. Photons excite electrons either from the inner shell orbitals or from the valence bands according to the photon energy, and give rise to isochoric heating of the sample. Localized states related to the 3d orbital are observed for Cu when the hole lies in the inner shell 3s orbital. The electrical conductivity for these materials at nonequilibrium states is calculated using the Kubo-Greenwood formula. The change of the electrical conductivity, compared to the equilibrium state, is different for the case of holes in inner shell orbitals or the valence band. This is attributed to the competition of two factors: the shift of the orbital energies due to reduced screening of core electrons, and the increase of chemical potential due to the excitation of electrons. The finite-temperature effect of both the electrons and the ions on the electrical conductivity is discussed in detail. This work is helpful to better understand the physics of laser excitation experiments of warm dense matter.
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Affiliation(s)
- Hengyu Zhang
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Shen Zhang
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, China.,Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - Dongdong Kang
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, China
| | - Jiayu Dai
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, China
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
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16
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Jin R, Abdullah MM, Jurek Z, Santra R, Son SK. Transient ionization potential depression in nonthermal dense plasmas at high x-ray intensity. Phys Rev E 2021; 103:023203. [PMID: 33735970 DOI: 10.1103/physreve.103.023203] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 01/22/2021] [Indexed: 11/07/2022]
Abstract
The advent of x-ray free-electron lasers (XFELs), which provide intense ultrashort x-ray pulses, has brought a new way of creating and analyzing hot and warm dense plasmas in the laboratory. Because of the ultrashort pulse duration, the XFEL-produced plasma will be out of equilibrium at the beginning, and even the electronic subsystem may not reach thermal equilibrium while interacting with a femtosecond timescale pulse. In the dense plasma, the ionization potential depression (IPD) induced by the plasma environment plays a crucial role for understanding and modeling microscopic dynamical processes. However, all theoretical approaches for IPD have been based on local thermal equilibrium (LTE), and it has been controversial to use LTE IPD models for the nonthermal situation. In this work, we propose a non-LTE (NLTE) approach to calculate the IPD effect by combining a quantum-mechanical electronic-structure calculation and a classical molecular dynamics simulation. This hybrid approach enables us to investigate the time evolution of ionization potentials and IPDs during and after the interaction with XFEL pulses, without the limitation of the LTE assumption. In our NLTE approach, the transient IPD values are presented as distributions evolving with time, which cannot be captured by conventional LTE-based models. The time-integrated ionization potential values are in good agreement with benchmark experimental data on solid-density aluminum plasma and other theoretical predictions based on LTE. The present work is promising to provide critical insights into nonequilibrium dynamics of dense plasma formation and thermalization induced by XFEL pulses.
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Affiliation(s)
- Rui Jin
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany.,Department of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
| | | | - Zoltan Jurek
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany.,The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Robin Santra
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany.,The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany.,Department of Physics, Universität Hamburg, Jungiusstrasse 9, 20355 Hamburg, Germany
| | - Sang-Kil Son
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany.,The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
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17
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Dornheim T, Cangi A, Ramakrishna K, Böhme M, Tanaka S, Vorberger J. Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory. PHYSICAL REVIEW LETTERS 2020; 125:235001. [PMID: 33337174 DOI: 10.1103/physrevlett.125.235001] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 10/12/2020] [Accepted: 11/03/2020] [Indexed: 06/12/2023]
Abstract
We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v. The ESA combines the recent neural-net representation by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum Monte Carlo data of the on-top pair distribution function g(0). It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
| | - Attila Cangi
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
| | - Kushal Ramakrishna
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
| | - Maximilian Böhme
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
| | - Shigenori Tanaka
- Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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18
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Dornheim T, Vorberger J. Finite-size effects in the reconstruction of dynamic properties from ab initio path integral Monte Carlo simulations. Phys Rev E 2020; 102:063301. [PMID: 33466040 DOI: 10.1103/physreve.102.063301] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 11/15/2020] [Indexed: 06/12/2023]
Abstract
We systematically investigate finite-size effects in the dynamic structure factor S(q,ω) of the uniform electron gas obtained via the analytic continuation of ab initio path integral Monte Carlo data for the imaginary-time density-density correlation function F(q,τ). Using the recent scheme by Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.255001], we find that the reconstructed spectra are not afflicted with any finite-size effects for as few as N=14 electrons both at warm dense matter (WDM) conditions and at the margins of the strongly correlated electron liquid regime. Our results further corroborate the high quality of our current description of the dynamic density response of correlated electrons, which is of high importance for many applications in WDM theory and beyond.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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19
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Starrett CE, Shaffer N. Multiple scattering theory for dense plasmas. Phys Rev E 2020; 102:043211. [PMID: 33212669 DOI: 10.1103/physreve.102.043211] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 10/04/2020] [Indexed: 06/11/2023]
Abstract
Dense plasmas occur in stars, giant planets, and in inertial fusion experiments. Accurate modeling of the electronic structure of these plasmas allows for prediction of material properties that can in turn be used to simulate these astrophysical objects and terrestrial experiments. But modeling them remains a challenge. Here we explore the Korringa-Kohn-Rostoker Green's function (KKR-GF) method for this purpose. We find that it is able to predict equation of state in good agreement with other state-of-the-art methods, where they are accurate and viable. In addition, it is shown that the computational cost does not significantly change with temperature, in contrast with other approaches. Moreover, the method does not use pseudopotentials-core states are calculated self consistently. We conclude that KKR-GF is a very promising method for dense plasma simulation.
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Affiliation(s)
- C E Starrett
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - N Shaffer
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
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20
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Dornheim T, Vorberger J, Bonitz M. Nonlinear Electronic Density Response in Warm Dense Matter. PHYSICAL REVIEW LETTERS 2020; 125:085001. [PMID: 32909774 DOI: 10.1103/physrevlett.125.085001] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 07/20/2020] [Indexed: 06/11/2023]
Abstract
Warm dense matter (WDM)-an extreme state with high temperatures and densities that occurs, e.g., in astrophysical objects-constitutes one of the most active fields in plasma physics and materials science. These conditions can be realized in the lab by shock compression or laser excitation, and the most accurate experimental diagnostics is achieved with lasers and free electron lasers which is theoretically modeled using linear response theory. Here, we present first ab initio path integral Monte Carlo results for the nonlinear density response of correlated electrons in WDM and show that for many situations of experimental relevance nonlinear effects cannot be neglected.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-028262 Görlitz, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, D-01328 Dresden, Germany
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
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21
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Shaffer NR, Starrett CE. Model of electron transport in dense plasmas spanning temperature regimes. Phys Rev E 2020; 101:053204. [PMID: 32575252 DOI: 10.1103/physreve.101.053204] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Accepted: 04/28/2020] [Indexed: 11/07/2022]
Abstract
We present a new model of electron transport in warm and hot dense plasmas which combines the quantum Landau-Fokker-Planck equation with the concept of mean-force scattering. We obtain electrical and thermal conductivities across several orders of magnitude in temperature, from warm dense matter conditions to hot, nondegenerate plasma conditions, including the challenging crossover regime between the two. The small-angle approximation characteristic of Fokker-Planck collision theories is mitigated to good effect by the construction of accurate effective Coulomb logarithms based on mean-force scattering, which allows the theory to remain accurate even at low temperatures, as compared with high-fidelity quantum simulation results. Electron-electron collisions are treated on equal footing as electron-ion collisions. Their accurate treatment is found to be essential for hydrogen, and is expected to be important to other low-Z elements. We find that electron-electron scattering remains influential to the value of the thermal conductivity down to temperatures somewhat below the Fermi energy. The accuracy of the theory seems to falter only for the behavior of the thermal conductivity at very low temperatures due to a subtle interplay between the Pauli exclusion principle and the small-angle approximation as they pertain to electron-electron scattering. Even there, the model is in fair agreement with ab initio simulations.
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22
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Ramakrishna K, Vorberger J. Ab initio dielectric response function of diamond and other relevant high pressure phases of carbon. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:095401. [PMID: 31703214 DOI: 10.1088/1361-648x/ab558e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The electronic structure and dielectric properties of the diamond, body centered cubic diamond (bc8), and hexagonal diamond (lonsdaleite) phases of carbon are computed using density functional theory and many-body perturbation theory with the emphasis on the excitonic picture of the solid phases relevant in the regimes of high-pressure physics and warm dense matter. We also discuss the capabilities of reproducing the inelastic x-ray scattering spectra in comparison with the existing models in light of recent x-ray scattering experiments on carbon and carbon bearing materials in the Megabar range.
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Affiliation(s)
- Kushal Ramakrishna
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany. Technische Universität Dresden, 01062 Dresden, Germany
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23
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Shaffer NR, Starrett CE. Correlations between conduction electrons in dense plasmas. Phys Rev E 2020; 101:013208. [PMID: 32069618 DOI: 10.1103/physreve.101.013208] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Indexed: 11/07/2022]
Abstract
Most treatments of electron-electron correlations in dense plasmas either ignore them entirely (random phase approximation) or neglect the role of ions (jellium approximation). In this work, we go beyond both these approximations to derive a formula for the electron-electron static structure factor which properly accounts for the contributions of both ionic structure and quantum-mechanical dynamic response in the electrons. The result can be viewed as a natural extension of the quantum Ornstein-Zernike theory of ionic and electronic correlations, and it is suitable for dense plasmas in which the ions are classical and the conduction electrons are quantum-mechanical. The corresponding electron-electron pair distribution functions are compared with the results of path integral Monte Carlo simulations, showing good agreement whenever no strong electron resonance states are present. We construct approximate potentials of mean force which describe the effective screened interaction between electrons. Significant deviations from Debye-Hückel screening are present at temperatures and densities relevant to high-energy density experiments involving warm and hot dense plasmas. The presence of correlations between conduction electrons is likely to influence the electron-electron contribution to the electrical and thermal conductivity. It is expected that excitation processes involving the conduction electrons (e.g., free-free absorption) will also be affected.
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Affiliation(s)
- Nathaniel R Shaffer
- Los Alamos National Laboratory, P. O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - Charles E Starrett
- Los Alamos National Laboratory, P. O. Box 1663, Los Alamos, New Mexico 87545, USA
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24
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Dornheim T, Vorberger J, Groth S, Hoffmann N, Moldabekov ZA, Bonitz M. The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation. J Chem Phys 2019; 151:194104. [DOI: 10.1063/1.5123013] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- T. Dornheim
- Center for Advanced Systems Understanding (CASUS), Görlitz, Germany
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - J. Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, D-01328 Dresden, Germany
| | - S. Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - N. Hoffmann
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, D-01328 Dresden, Germany
| | - Zh. A. Moldabekov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
- Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi Str. 71, 050040 Almaty, Kazakhstan
| | - M. Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
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25
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Bruner A, Cavaletto SM, Govind N, Mukamel S. Resonant X-ray Sum-Frequency-Generation Spectroscopy of K-Edges in Acetyl Fluoride. J Chem Theory Comput 2019; 15:6832-6839. [DOI: 10.1021/acs.jctc.9b00642] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Adam Bruner
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697, United States
| | - Stefano M. Cavaletto
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697, United States
| | - Niranjan Govind
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697, United States
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26
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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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27
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Hollebon P, Ciricosta O, Desjarlais MP, Cacho C, Spindloe C, Springate E, Turcu ICE, Wark JS, Vinko SM. Ab initio simulations and measurements of the free-free opacity in aluminum. Phys Rev E 2019; 100:043207. [PMID: 31770899 DOI: 10.1103/physreve.100.043207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2018] [Indexed: 06/10/2023]
Abstract
The free-free opacity in dense systems is a property that both tests our fundamental understanding of correlated many-body systems, and is needed to understand the radiative properties of high energy-density plasmas. Despite its importance, predictive calculations of the free-free opacity remain challenging even in the condensed matter phase for simple metals. Here we show how the free-free opacity can be modelled at finite-temperatures via time-dependent density functional theory, and illustrate the importance of including local field corrections, core polarization, and self-energy corrections. Our calculations for ground-state Al are shown to agree well with experimental opacity measurements performed on the Artemis laser facility across a wide range of extreme ultraviolet wavelengths. We extend our calculations across the melt to the warm-dense matter regime, finding good agreement with advanced plasma models based on inverse bremsstrahlung at temperatures above 10 eV.
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Affiliation(s)
- P Hollebon
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - O Ciricosta
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - M P Desjarlais
- Pulsed Power Sciences Center, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - C Cacho
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - C Spindloe
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - E Springate
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - I C E Turcu
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - J S Wark
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - S M Vinko
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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28
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Nenov A, Segatta F, Bruner A, Mukamel S, Garavelli M. X-ray linear and non-linear spectroscopy of the ESCA molecule. J Chem Phys 2019; 151:114110. [DOI: 10.1063/1.5116699] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Artur Nenov
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
| | - Francesco Segatta
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
| | - Adam Bruner
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697,
USA
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697,
USA
| | - Marco Garavelli
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
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29
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Dornheim T, Groth S, Vorberger J, Bonitz M. Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter. PHYSICAL REVIEW LETTERS 2018; 121:255001. [PMID: 30608805 DOI: 10.1103/physrevlett.121.255001] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2018] [Indexed: 06/09/2023]
Abstract
The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q,ω) constitutes a key quantity as it is directly measured in x-ray Thomson scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q,ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q,ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q,ω) over substantial parts of the warm dense matter regime.
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Affiliation(s)
- T Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - S Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - J Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
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30
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Ding YH, White AJ, Hu SX, Certik O, Collins LA. Ab Initio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory. PHYSICAL REVIEW LETTERS 2018; 121:145001. [PMID: 30339443 DOI: 10.1103/physrevlett.121.145001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2018] [Indexed: 06/08/2023]
Abstract
Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the α-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for ab initio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For α-particle stopping in warm and solid-density DT plasmas, the ab initio TD-OF-DFT simulations show a lower stopping power up to ∼25% in comparison with three stopping-power models often used in the high-energy-density physics community.
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Affiliation(s)
- Y H Ding
- Laboratory for Laser Energetics, University of Rochester, 250 E. River Road, Rochester, New York 14623, USA
| | - A J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - S X Hu
- Laboratory for Laser Energetics, University of Rochester, 250 E. River Road, Rochester, New York 14623, USA
| | - O Certik
- Computational and Computer Science 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
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31
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Mo C, Fu Z, Kang W, Zhang P, He XT. First-Principles Estimation of Electronic Temperature from X-Ray Thomson Scattering Spectrum of Isochorically Heated Warm Dense Matter. PHYSICAL REVIEW LETTERS 2018; 120:205002. [PMID: 29864337 DOI: 10.1103/physrevlett.120.205002] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2017] [Revised: 03/24/2018] [Indexed: 06/08/2023]
Abstract
Through the perturbation formula of time-dependent density functional theory broadly employed in the calculation of solids, we provide a first-principles calculation of x-ray Thomson scattering spectrum of isochorically heated aluminum foil, as considered in the experiments of Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001], where ions were constrained near their lattice positions. From the calculated spectra, we find that the electronic temperature cannot exceed 2 eV, much smaller than the previous estimation of 6 eV via the detailed balance relation. Our results may well be an indication of unique electronic properties of warm dense matter, which can be further illustrated by future experiments. The lower electronic temperature predicted partially relieves the concern on the heating of x-ray free electron laser to the sample when used in structure measurement.
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Affiliation(s)
- Chongjie Mo
- HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China
- School of Physics, Peking University, Beijing 100871, China
| | - Zhenguo Fu
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - Wei Kang
- HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China
- College of Engineering, Peking University, Beijing 100871, China
- Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ping Zhang
- HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
- Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
| | - X T He
- HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
- Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
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32
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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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33
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Medvedev N, Ziaja B. Multistep transition of diamond to warm dense matter state revealed by femtosecond X-ray diffraction. Sci Rep 2018; 8:5284. [PMID: 29588526 PMCID: PMC5869726 DOI: 10.1038/s41598-018-23632-8] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2017] [Accepted: 03/08/2018] [Indexed: 11/09/2022] Open
Abstract
Diamond bulk irradiated with a free-electron laser pulse of 6100 eV photon energy, 5 fs duration, at the ~19-25 eV/atom absorbed doses, is studied theoretically on its way to warm dense matter state. Simulations with our hybrid code XTANT show disordering on sub-100 fs timescale, with the diffraction peak (220) vanishing faster than the peak (111). The warm dense matter formation proceeds as a nonthermal damage of diamond with the band gap collapse triggering atomic disordering. Short-living graphite-like state is identified during a few femtoseconds between the disappearance of (220) peak and the disappearance of (111) peak. The results obtained are compared with the data from the recent experiment at SACLA, showing qualitative agreement. Challenges remaining for the accurate modeling of the transition of solids to warm dense matter state and proposals for supplementary measurements are discussed in detail.
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Affiliation(s)
- Nikita Medvedev
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, Prague 8, 18221, Czech Republic. .,Institute of Plasma Physics, Czech Academy of Sciences, Za Slovankou 3, Prague 8, 18200, Czech Republic.
| | - Beata Ziaja
- Center for Free-Electron Laser Science, DESY, Hamburg, 22607, Germany. .,Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, 31-342, Poland.
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34
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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.
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Affiliation(s)
- Dongdong Kang
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
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35
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Vorberger J, Chapman DA. Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering. Phys Rev E 2018; 97:013203. [PMID: 29448372 DOI: 10.1103/physreve.97.013203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Indexed: 06/08/2023]
Abstract
We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.
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Affiliation(s)
- J Vorberger
- Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf e.V., 01328 Dresden, Germany
| | - D A Chapman
- AWE plc, Aldermaston, Reading RG7 4PR, United Kingdom
- Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry CV4 7AL, United Kingdom
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36
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Cho D, Rouxel JR, Kowalewski M, Lee JY, Mukamel S. Attosecond X-ray Diffraction Triggered by Core or Valence Ionization of a Dipeptide. J Chem Theory Comput 2017; 14:329-338. [DOI: 10.1021/acs.jctc.7b00920] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Affiliation(s)
- Daeheum Cho
- Department
of Chemistry, University of California, Irvine, California 92697-2025, United States
- School
of Advanced Materials Science and Engineering, SKKU Advanced Institute
of Nanotechnology (SAINT), Sungkyunkwan University, Suwon 16419, Republic of Korea
| | - Jérémy R. Rouxel
- Department
of Chemistry, University of California, Irvine, California 92697-2025, United States
| | - Markus Kowalewski
- Department
of Chemistry, University of California, Irvine, California 92697-2025, United States
| | - Jin Yong Lee
- Department
of Chemistry, Sungkyunkwan University, Suwon 16419, Republic of Korea
| | - Shaul Mukamel
- Department
of Chemistry, University of California, Irvine, California 92697-2025, United States
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37
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Groth S, Dornheim T, Sjostrom T, Malone FD, Foulkes WMC, Bonitz M. Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions. PHYSICAL REVIEW LETTERS 2017; 119:135001. [PMID: 29341671 DOI: 10.1103/physrevlett.119.135001] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2017] [Indexed: 06/07/2023]
Abstract
In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 117, 156403 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.156403], we presented the first quantum Monte Carlo (QMC) results for the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below θ=k_{B}T/E_{F}=0.5 and (ii) QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first completely ab initio exchange-correlation free energy functional; the accuracy achieved is an unprecedented ∼0.3%. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.
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Affiliation(s)
- Simon Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Tobias Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Travis Sjostrom
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Fionn D Malone
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
- Physics Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, USA
| | - W M C Foulkes
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
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38
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Bruner A, Hernandez S, Mauger F, Abanador PM, LaMaster DJ, Gaarde MB, Schafer KJ, Lopata K. Attosecond Charge Migration with TDDFT: Accurate Dynamics from a Well-Defined Initial State. J Phys Chem Lett 2017; 8:3991-3996. [PMID: 28792225 DOI: 10.1021/acs.jpclett.7b01652] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We investigate the ability of time-dependent density functional theory (TDDFT) to capture attosecond valence electron dynamics resulting from sudden X-ray ionization of a core electron. In this special case the initial state can be constructed unambiguously, allowing for a simple test of the accuracy of the dynamics. The response following nitrogen K-edge ionization in nitrosobenzene shows excellent agreement with fourth-order algebraic diagrammatic construction (ADC(4)) results, suggesting that a properly chosen initial state allows TDDFT to adequately capture attosecond charge migration. Visualizing hole motion using an electron localization picture (ELF), we provide an intuitive chemical interpretation of the charge migration as a superposition of Lewis dot resonance structures.
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Affiliation(s)
- Adam Bruner
- Department of Chemistry, Louisiana State University , Baton Rouge, Louisiana 70803, United States
| | - Samuel Hernandez
- Department of Chemistry, Louisiana State University , Baton Rouge, Louisiana 70803, United States
| | - François Mauger
- Department of Physics and Astronomy, Louisiana State University , Baton Rouge, Louisiana 70803, United States
| | - Paul M Abanador
- Department of Physics and Astronomy, Louisiana State University , Baton Rouge, Louisiana 70803, United States
| | - Daniel J LaMaster
- Department of Chemistry, Louisiana State University , Baton Rouge, Louisiana 70803, United States
| | - Mette B Gaarde
- Department of Physics and Astronomy, Louisiana State University , Baton Rouge, Louisiana 70803, United States
| | - Kenneth J Schafer
- Department of Physics and Astronomy, Louisiana State University , Baton Rouge, Louisiana 70803, United States
| | - Kenneth Lopata
- Department of Chemistry, Louisiana State University , Baton Rouge, Louisiana 70803, United States
- Center for Computation & Technology, Louisiana State University , Baton Rouge, Louisiana 70803, United States
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39
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Daligault J. Crossover from Classical to Fermi Liquid Behavior in Dense Plasmas. PHYSICAL REVIEW LETTERS 2017; 119:045002. [PMID: 29341759 DOI: 10.1103/physrevlett.119.045002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2017] [Indexed: 06/07/2023]
Abstract
We explore the crossover from classical plasma to quantum Fermi liquid behavior of electrons in dense plasmas. To this end, we analyze the evolution with density and temperature of the momentum lifetime of a test electron introduced in a dense electron gas. This allows us (1) to determine the boundaries of the crossover region in the temperature-density plane and to shed light on the evolution of scattering properties across it, (2) to quantify the role of the fermionic nature of electrons on electronic collisions across the crossover region, and (3) to explain how the concept of the Coulomb logarithm emerges at a high enough temperature but disappears at a low enough temperature.
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Affiliation(s)
- Jérôme Daligault
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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40
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Liu H, Zhang Y, Kang W, Zhang P, Duan H, He XT. Molecular dynamics simulation of strong shock waves propagating in dense deuterium, taking into consideration effects of excited electrons. Phys Rev E 2017; 95:023201. [PMID: 28297841 DOI: 10.1103/physreve.95.023201] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2016] [Indexed: 06/06/2023]
Abstract
We present a molecular dynamics simulation of shock waves propagating in dense deuterium with the electron force field method [J. T. Su and W. A. Goddard, Phys. Rev. Lett. 99, 185003 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.185003], which explicitly takes the excitation of electrons into consideration. Nonequilibrium features associated with the excitation of electrons are systematically investigated. We show that chemical bonds in D_{2} molecules lead to a more complicated shock wave structure near the shock front, compared with the results of classical molecular dynamics simulation. Charge separation can bring about accumulation of net charges on large scales, instead of the formation of a localized dipole layer, which might cause extra energy for the shock wave to propagate. In addition, the simulations also display that molecular dissociation at the shock front is the major factor that accounts for the "bump" structure in the principal Hugoniot. These results could help to build a more realistic picture of shock wave propagation in fuel materials commonly used in the inertial confinement fusion.
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Affiliation(s)
- Hao Liu
- HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
| | - Yin Zhang
- Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
| | - Wei Kang
- HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
- Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ping Zhang
- HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - Huiling Duan
- HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
- Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
| | - X T He
- HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
- Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
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41
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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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42
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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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Dharuman G, Verboncoeur J, Christlieb A, Murillo MS. Atomic bound state and scattering properties of effective momentum-dependent potentials. Phys Rev E 2016; 94:043205. [PMID: 27841554 DOI: 10.1103/physreve.94.043205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2016] [Indexed: 06/06/2023]
Abstract
Effective classical dynamics provide a potentially powerful avenue for modeling large-scale dynamical quantum systems. We have examined the accuracy of a Hamiltonian-based approach that employs effective momentum-dependent potentials (MDPs) within a molecular-dynamics framework through studies of atomic ground states, excited states, ionization energies, and scattering properties of continuum states. Working exclusively with the Kirschbaum-Wilets (KW) formulation with empirical MDPs [C. L. Kirschbaum and L. Wilets, Phys. Rev. A 21, 834 (1980)0556-279110.1103/PhysRevA.21.834], optimization leads to very accurate ground-state energies for several elements (e.g., N, F, Ne, Al, S, Ar, and Ca) relative to Hartree-Fock values. The KW MDP parameters obtained are found to be correlated, thereby revealing some degree of transferability in the empirically determined parameters. We have studied excited-state orbits of electron-ion pair to analyze the consequences of the MDP on the classical Coulomb catastrophe. From the optimized ground-state energies, we find that the experimental first- and second-ionization energies are fairly well predicted. Finally, electron-ion scattering was examined by comparing the predicted momentum transfer cross section to a semiclassical phase-shift calculation; optimizing the MDP parameters for the scattering process yielded rather poor results, suggesting a limitation of the use of the KW MDPs for plasmas.
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Affiliation(s)
- Gautham Dharuman
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - John Verboncoeur
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Andrew Christlieb
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
| | - Michael S Murillo
- New Mexico Consortium, Los Alamos, New Mexico 87544, USA
- Computational Physics and Methods Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
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Pradhan E, Magyar RJ, Akimov AV. Scaling relationships for nonadiabatic energy relaxation times in warm dense matter: toward understanding the equation of state. Phys Chem Chem Phys 2016; 18:32466-32476. [DOI: 10.1039/c6cp06827h] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dependence of nonadiabatic ion-electron energy transfer rates in warm dense aluminum on the mass density and temperature with decoherence changing this relationship qualitatively.
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Affiliation(s)
| | - Rudolph J. Magyar
- Center for Computing Research
- Sandia National Laboratories
- Albuquerque
- USA
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