1
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Dornheim T, Schwalbe S, Moldabekov ZA, Vorberger J, Tolias P. Ab Initio Path Integral Monte Carlo Simulations of the Uniform Electron Gas on Large Length Scales. J Phys Chem Lett 2024; 15:1305-1313. [PMID: 38285536 PMCID: PMC10860150 DOI: 10.1021/acs.jpclett.3c03193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 01/17/2024] [Accepted: 01/22/2024] [Indexed: 01/31/2024]
Abstract
The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, materials science, and related disciplines. At finite temperatures, the gold standard is given by ab initio path integral Monte Carlo (PIMC) simulations, which do not require any empirical input but exhibit an exponential increase in the required computation time for Fermionic systems with an increase in system size N. Very recently, computing Fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles has been suggested. In our work, we use this technique to perform very large (N ≤ 1000) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of the investigated properties, i.e., the static structure factor, the static density response function, and the local field correction, over the entire range of length scales.
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Affiliation(s)
- Tobias Dornheim
- Center
for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Sebastian Schwalbe
- Center
for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Zhandos A. Moldabekov
- Center
for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Jan Vorberger
- Institute
of Radiation Physics, Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Panagiotis Tolias
- Space
and Plasma Physics, Royal Institute of Technology
(KTH), Stockholm SE-100 44, Sweden
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2
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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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3
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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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4
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Moldabekov Z, Böhme M, Vorberger J, Blaschke D, Dornheim T. Ab Initio Static Exchange-Correlation Kernel across Jacob's Ladder without Functional Derivatives. J Chem Theory Comput 2023; 19:1286-1299. [PMID: 36724889 PMCID: PMC9979610 DOI: 10.1021/acs.jctc.2c01180] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
The electronic exchange─correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an external perturbation. In this work, we present a formally exact methodology for the computation of the system specific static XC kernel exclusively within the framework of density functional theory (DFT) and without employing functional derivatives─no external input apart from the usual XC-functional is required. We compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model under both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC functionals, and it has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects. The observed excellent agreement to the QMC reference data demonstrates that presented framework is capable to capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers.
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Affiliation(s)
- Zhandos Moldabekov
- Center
for Advanced Systems Understanding (CASUS), D-02826Görlitz, Germany,Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328Dresden, Germany,E-mail:
| | - Maximilian Böhme
- Center
for Advanced Systems Understanding (CASUS), D-02826Görlitz, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328Dresden, Germany
| | - David Blaschke
- Institute
of Theoretical Physics, University of Wroclaw, 50-204Wroclaw, Poland
| | - Tobias Dornheim
- Center
for Advanced Systems Understanding (CASUS), D-02826Görlitz, Germany,Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328Dresden, Germany,E-mail:
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5
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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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6
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Cerantola V, Rosa AD, Konôpková Z, Torchio R, Brambrink E, Rack A, Zastrau U, Pascarelli S. New frontiers in extreme conditions science at synchrotrons and free electron lasers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:274003. [PMID: 33930892 DOI: 10.1088/1361-648x/abfd50] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 04/30/2021] [Indexed: 06/12/2023]
Abstract
Synchrotrons and free electron lasers are unique facilities to probe the atomic structure and electronic properties of matter at extreme thermodynamical conditions. In this context, 'matter at extreme pressures and temperatures' was one of the science drivers for the construction of low emittance 4th generation synchrotron sources such as the Extremely Brilliant Source of the European Synchrotron Radiation Facility and hard x-ray free electron lasers, such as the European x-ray free electron laser. These new user facilities combine static high pressure and dynamic shock compression experiments to outstanding high brilliance and submicron beams. This combination not only increases the data-quality but also enlarges tremendously the accessible pressure, temperature and density space. At the same time, the large spectrum of available complementary x-ray diagnostics for static and shock compression studies opens unprecedented insights into the state of matter at extremes. The article aims at highlighting a new horizon of scientific opportunities based on the synergy between extremely brilliant synchrotrons and hard x-ray free electron lasers.
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Affiliation(s)
- Valerio Cerantola
- European X-ray Free-Electron Laser, Holzkoppel 4, 22869 Schenefeld, Germany
| | | | - Zuzana Konôpková
- European X-ray Free-Electron Laser, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Raffaella Torchio
- ESRF-The European Synchrotron, 71 Avenue des Martyrs, Grenoble 38000, France
| | - Erik Brambrink
- European X-ray Free-Electron Laser, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Alexander Rack
- ESRF-The European Synchrotron, 71 Avenue des Martyrs, Grenoble 38000, France
| | - Ulf Zastrau
- European X-ray Free-Electron Laser, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Sakura Pascarelli
- European X-ray Free-Electron Laser, Holzkoppel 4, 22869 Schenefeld, Germany
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7
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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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8
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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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9
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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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10
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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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11
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Choi Y, Dharuman G, Murillo MS. High-frequency response of classical strongly coupled plasmas. Phys Rev E 2019; 100:013206. [PMID: 31499843 DOI: 10.1103/physreve.100.013206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Indexed: 06/10/2023]
Abstract
The dynamic structure factor (DSF) of the Yukawa system is here obtained with highly converged molecular dynamics (MD) over the entire liquid phase. The data provide a rigorous test of theoretical models of ion-acoustic wave-dispersion relations, the intermediate scattering function, and the high-frequency response. We compare our MD results with seven diverse models, finding good agreement among those that enforce the three basic sum rules for dispersion properties, although one of the models has previously unreported spurious peaks. The MD simulations reveal that at intermediate frequencies ω, the high-frequency response of the DSF follows a power law, going approximately as ω^{-p}, where p>0, and p shows nontrivial dependencies on the wave vector q and the plasma parameters κ and Γ. In contrast, among the seven comparison models, the predicted high-frequency response is found to be independent of {q,κ,Γ}. This high-frequency power suggests a useful fitting form. In addition, these results expose limitations of several models and, moreover, suggest that some approaches are difficult or impossible to extend because of the lack of finite moments. We also find the double-plasmon resonance peak in our MD simulations that none of the theoretical models predicts.
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Affiliation(s)
- Yongjun Choi
- Institute for Cyber-Enabled Research, Michigan State University, East Lansing, Michigan 48824, USA
| | - Gautham Dharuman
- Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Michael S Murillo
- Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
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12
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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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13
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Moldabekov ZA, Groth S, Dornheim T, Kählert H, Bonitz M, Ramazanov TS. Structural characteristics of strongly coupled ions in a dense quantum plasma. Phys Rev E 2018; 98:023207. [PMID: 30253556 DOI: 10.1103/physreve.98.023207] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2018] [Indexed: 06/08/2023]
Abstract
The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjölander (STLS) approximation. Different cross-checks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the structural properties, such as the pair distribution and the static structure factor, of strongly coupled ions. The results are highly sensitive to the features of the screened pair interaction potential. This effect is particularly visible in the static structure factor. The applicability range of the screened potential computed from STLS is identified in terms of density and temperature of the electrons. It is demonstrated that at r_{s}>1, where r_{s} is the ratio of the mean interelectronic distance to the Bohr radius, electronic correlations beyond RPA have a nonnegligible effect on the structural properties. Additionally, the applicability of the hypernetted chain approximation for the calculation of the structural properties using the screened pair interaction potential is analyzed employing the effective coupling parameter approach.
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Affiliation(s)
- Zh A Moldabekov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
- Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, 71 Al-Farabi str., 050040 Almaty, Kazakhstan
| | - S Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - T Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - H Kählert
- 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
| | - T S Ramazanov
- Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, 71 Al-Farabi str., 050040 Almaty, Kazakhstan
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14
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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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15
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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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16
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Groth S, Dornheim T, Bonitz M. Configuration path integral Monte Carlo approach to the static density response of the warm dense electron gas. J Chem Phys 2017; 147:164108. [DOI: 10.1063/1.4999907] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
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17
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Rozmus W, Brantov A, Fortmann-Grote C, Bychenkov VY, Glenzer S. Electrostatic fluctuations in collisional plasmas. Phys Rev E 2017; 96:043207. [PMID: 29347579 DOI: 10.1103/physreve.96.043207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Indexed: 06/07/2023]
Abstract
We present a theory of electrostatic fluctuations in two-component plasmas where electrons and ions are described by Maxwellian distribution functions at unequal temperatures. Based on the exact solution of the Landau kinetic equation, that includes electron-electron, electron-ion, and ion-ion collision integrals, the dynamic form factor, S(k[over ⃗],ω), is derived for weakly coupled plasmas. The collective plasma responses at ion-acoustic, Langmuir, and entropy mode resonances are described for arbitrary wave numbers and frequencies in the entire range of plasma collisionality. The collisionless limit of S(k[over ⃗],ω) and the strong-collision result based on the fluctuation-dissipation theorem and classical transport at T_{e}=T_{i} are recovered and discussed. Results of several Thomson scattering experiments in the broad range of plasma parameters are described and discussed by means of our theory for S(k[over ⃗],ω).
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Affiliation(s)
- W Rozmus
- Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1
| | - A Brantov
- P.N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow 117924, Russia
| | | | - V Yu Bychenkov
- P.N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow 117924, Russia
| | - S Glenzer
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
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18
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Dornheim T, Groth S, Vorberger J, Bonitz M. Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas. Phys Rev E 2017; 96:023203. [PMID: 28950530 DOI: 10.1103/physreve.96.023203] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Indexed: 06/07/2023]
Abstract
The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here we employ the recently developed ab initio permutation blocking path integral Monte Carlo (PB-PIMC) technique [T. Dornheim et al., New J. Phys. 17, 073017 (2015)10.1088/1367-2630/17/7/073017] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows us to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new ab initio data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.
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Affiliation(s)
- Tobias Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Simon Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
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19
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Fu ZG, Wang Z, Li ML, Li DF, Kang W, Zhang P. Dynamic properties of the energy loss of multi-MeV charged particles traveling in two-component warm dense plasmas. Phys Rev E 2016; 94:063203. [PMID: 28085472 DOI: 10.1103/physreve.94.063203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2016] [Indexed: 06/06/2023]
Abstract
The energy loss of multi-MeV charged particles moving in two-component warm dense plasmas (WDPs) is studied theoretically beyond the random-phase approximation. The short-range correlations between particles are taken into account via dynamic local field corrections (DLFC) in a Mermin dielectric function for two-component plasmas. The mean ionization states are obtained by employing the detailed configuration accounting model. The Yukawa-type effective potential is used to derive the DLFC. Numerically, the DLFC are obtained via self-consistent iterative operations. We find that the DLFC are significant around the maximum of the stopping power. Furthermore, by using the two-component extended Mermin dielectric function model including the DLFC, the energy loss of a proton with an initial energy of ∼15 MeV passing through a WDP of beryllium with an electronic density around the solid value n_{e}≈3×10^{23}cm^{-3} and with temperature around ∼40 eV is estimated numerically. The numerical result is reasonably consistent with the experimental observations [A. B. Zylsta et al., Phys. Rev. Lett. 111, 215002 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.215002]. Our results show that the partial ionization and the dynamic properties should be of importance for the stopping of charged particles moving in the WDP.
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Affiliation(s)
- Zhen-Guo Fu
- Center for Fusion Energy Science and Technology, CAEP, P.O. Box 8009, Beijing 100088, China
- Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
| | - Zhigang Wang
- Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
| | - Meng-Lei Li
- Center for Fusion Energy Science and Technology, CAEP, P.O. Box 8009, Beijing 100088, China
- Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
| | - Da-Fang Li
- Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
| | - Wei Kang
- HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China
| | - Ping Zhang
- Center for Fusion Energy Science and Technology, CAEP, P.O. Box 8009, Beijing 100088, China
- Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
- HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China
- Center for Compression Science, CAEP, Mianyang 621900, China
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20
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Johnson WR, Nilsen J. Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter. Phys Rev E 2016; 93:033205. [PMID: 27078473 DOI: 10.1103/physreve.93.033205] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2016] [Indexed: 11/07/2022]
Abstract
The influence of finite relaxation times on Thomson scattering from warm dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree well with values inferred from the Ziman formula for the static conductivity and also with rates inferred from a fit to the frequency-dependent conductivity. Transport cross sections determined by the phase-shift analysis in the average-atom potential are compared with those evaluated in the commonly used Born approximation. The Born approximation converges to the exact cross sections at high energies; however, differences that occur at low energies lead to corresponding differences in relaxation rates. The relative importance of including relaxation time when modeling x-ray Thomson scattering spectra is examined by comparing calculations of the free-electron dynamic structure function for Thomson scattering using Lindhard and Mermin dielectric functions. Applications are given to warm dense Be plasmas, with temperatures ranging from 2 to 32 eV and densities ranging from 2 to 64 g/cc.
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Affiliation(s)
- W R Johnson
- Department of Physics, 225 Nieuwland Science Hall, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - J Nilsen
- Lawrence Livermore National Laboratory,PO Box 808, Livermore, California 94551, USA
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21
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Sperling P, Gamboa EJ, Lee HJ, Chung HK, Galtier E, Omarbakiyeva Y, Reinholz H, Röpke G, Zastrau U, Hastings J, Fletcher LB, Glenzer SH. Free-electron X-ray laser measurements of collisional-damped plasmons in isochorically heated warm dense matter. PHYSICAL REVIEW LETTERS 2015; 115:115001. [PMID: 26406836 DOI: 10.1103/physrevlett.115.115001] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2015] [Indexed: 06/05/2023]
Abstract
We present the first highly resolved measurements of the plasmon spectrum in an ultrafast heated solid. Multi-keV x-ray photons from the Linac Coherent Light Source have been focused to one micrometer diameter focal spots producing solid density aluminum plasmas with a known electron density of n_{e}=1.8×10^{23} cm^{-3}. Detailed balance is observed through the intensity ratio of up- and down-shifted plasmons in x-ray forward scattering spectra measuring the electron temperature. The plasmon damping is treated by electron-ion collision models beyond the Born approximation to determine the electrical conductivity of warm dense aluminum.
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Affiliation(s)
- P Sperling
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - E J Gamboa
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
| | - H J Lee
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
| | - H K Chung
- Nuclear Data Section, Division of Physical and Chemical Sciences, International Atomic Energy Agency, A-1400 Vienna, Austria
| | - E Galtier
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
| | - Y Omarbakiyeva
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
- International IT University, 050040 Almaty, Kazakhstan
| | - H Reinholz
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
- University of Western Australia, WA 6009 Crawley, Australia
| | - G Röpke
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - U Zastrau
- European XFEL, Albert-Einstein-Ring 19, 22761 Hamburg, Germany
| | - J Hastings
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
| | - L B Fletcher
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
| | - S H Glenzer
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 72 Menlo Park, California 94025, USA
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22
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Plagemann KU, Rüter HR, Bornath T, Shihab M, Desjarlais MP, Fortmann C, Glenzer SH, Redmer R. Ab initio calculation of the ion feature in x-ray Thomson scattering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:013103. [PMID: 26274290 DOI: 10.1103/physreve.92.013103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Indexed: 06/04/2023]
Abstract
The spectrum of x-ray Thomson scattering is proportional to the dynamic structure factor. An important contribution is the ion feature which describes elastic scattering of x rays off electrons. We apply an ab initio method for the calculation of the form factor of bound electrons, the slope of the screening cloud of free electrons, and the ion-ion structure factor in warm dense beryllium. With the presented method we can calculate the ion feature from first principles. These results will facilitate a better understanding of x-ray scattering in warm dense matter and an accurate measurement of ion temperatures which would allow determining nonequilibrium conditions, e.g., along shock propagation.
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Affiliation(s)
| | - Hannes R Rüter
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Thomas Bornath
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Mohammed Shihab
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
- Physics Department, Faculty of Science, Tanta University, 31527 Tanta, Egypt
| | | | - Carsten Fortmann
- Quantumwise A/S, Lersø Parkallé 107, DK-2100 Copenhagen, Denmark
| | - Siegfried H Glenzer
- High Energy Density Science, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Ronald Redmer
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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23
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Vorberger J, Gericke DO. Ab initio approach to model x-ray diffraction in warm dense matter. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:033112. [PMID: 25871229 DOI: 10.1103/physreve.91.033112] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2014] [Indexed: 06/04/2023]
Abstract
It is demonstrated how the static electron-electron structure factor in warm dense matter can be obtained from density functional theory in combination with quantum Monte Carlo data. In contrast to theories assuming well-separated bound and free states, this ab initio approach yields also valid results for systems close to the Mott transition (pressure ionization), where bound states are strongly modified and merge with the continuum. The approach is applied to x-ray Thomson scattering and compared to predictions of the Chihara formula whereby we use the ion-ion and electron-ion structure from the same simulations. The results show significant deviations of the screening cloud from the often applied Debye-like form.
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Affiliation(s)
- J Vorberger
- Max-Planck-Institut für die Physik Komplexer Systeme, 01187 Dresden, Germany
| | - D O Gericke
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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24
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Arkhipov YV, Ashikbayeva AB, Askaruly A, Davletov AE, Tkachenko IM. Dielectric function of dense plasmas, their stopping power, and sum rules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:053102. [PMID: 25493892 DOI: 10.1103/physreve.90.053102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2014] [Indexed: 06/04/2023]
Abstract
Mathematical, particularly, asymptotic properties of the random-phase approximation, Mermin approximation, and extended Mermin-type approximation of the coupled plasma dielectric function are analyzed within the method of moments. These models are generalized for two-component plasmas. Some drawbacks and advantages of the above models are pointed out. The two-component plasma stopping power is shown to be enhanced with respect to that of the electron fluid.
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Affiliation(s)
- Yu V Arkhipov
- Department of Physics and Technology, IETP, al-Farabi Kazakh National University, al-Farabi 71, 050040 Almaty, Kazakhstan
| | - A B Ashikbayeva
- Department of Physics and Technology, IETP, al-Farabi Kazakh National University, al-Farabi 71, 050040 Almaty, Kazakhstan
| | - A Askaruly
- Department of Physics and Technology, IETP, al-Farabi Kazakh National University, al-Farabi 71, 050040 Almaty, Kazakhstan
| | - A E Davletov
- Department of Physics and Technology, IETP, al-Farabi Kazakh National University, al-Farabi 71, 050040 Almaty, Kazakhstan
| | - I M Tkachenko
- Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
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25
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Xu K. Current-voltage characteristics and increase in the quantum efficiency of three-terminal gate and avalanche-based silicon LEDs. APPLIED OPTICS 2013; 52:6669-6675. [PMID: 24085165 DOI: 10.1364/ao.52.006669] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2013] [Accepted: 08/15/2013] [Indexed: 06/02/2023]
Abstract
In this paper, the emission of visible light by a monolithically integrated silicon p-n junction under reverse-bias is discussed. The modulation of light intensity is achieved using an insulated-gate terminal on the surface of the p-n junction. By varying the gate voltage, the breakdown voltage of the p-n junction will be adjustable so that the reverse current I(sub) flowing through the p-n junction at a fixed reverse-bias voltage is changed. It is observed that the light, which is emitted from the defects located at the p-n junction, depends closely on the reverse current I(sub). In regard to the phenomenon of electroluminescence, the relationship between the optical emission power and the reverse current I(sub) is linear. On the other hand, it is observed that both the quantum efficiency and the power conversion efficiency are able to have obvious enhancement, although the reverse-bias of the p-n junction is reduced and the corresponding reverse-current is much lower. Moreover, the successful fabrication on monolithic silicon light source on the bulk silicon by means of standard silicon complementary metal-oxide-semiconductor process technology is presented.
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26
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Chapman DA, Vorberger J, Gericke DO. Reduced coupled-mode approach to electron-ion energy relaxation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:013102. [PMID: 23944563 DOI: 10.1103/physreve.88.013102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2013] [Indexed: 06/02/2023]
Abstract
We present a reduced model for the energy transfer via coupled collective modes in two-temperature plasmas based on quantum statistical theory. The model is compared with exact numerical evaluations of the coupled-mode (CM) energy transfer rate and with alternative reduced approaches over a range of conditions in the warm dense matter (WDM) and inertial confinement fusion (ICF) regimes. Our approach shows excellent agreement with an exact treatment of the CM rate and supports the importance of the coupled-mode effect for the temperature and energy relaxation in WDM and ICF plasmas. We find that electronic damping of collective ion density fluctuations is crucial for correctly describing the mode spectrum and, thus, the energy exchange. The reduced CM approach is studied over a wide parameter space, enabling us to establish its limits of applicability.
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Affiliation(s)
- D A Chapman
- Plasma Physics Department, AWE plc, Aldermaston, Reading RG7 4PR, United Kingdom
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27
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Falk K, Regan SP, Vorberger J, Crowley BJB, Glenzer SH, Hu SX, Murphy CD, Radha PB, Jephcoat AP, Wark JS, Gericke DO, Gregori G. Comparison between x-ray scattering and velocity-interferometry measurements from shocked liquid deuterium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:043112. [PMID: 23679534 DOI: 10.1103/physreve.87.043112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2012] [Revised: 02/02/2013] [Indexed: 06/02/2023]
Abstract
The equation of state of light elements is essential to understand the structure of Jovian planets and inertial confinement fusion research. The Omega laser was used to drive a planar shock wave in the cryogenically cooled deuterium, creating warm dense matter conditions. X-ray scattering was used to determine the spectrum near the boundary of the collective and noncollective scattering regimes using a narrow band x-ray source in backscattering geometry. Our scattering spectra are thus sensitive to the individual electron motion as well as the collective plasma behavior and provide a measurement of the electron density, temperature, and ionization state. Our data are consistent with velocity-interferometry measurements previously taken on the same shocked deuterium conditions and presented by K. Falk et al. [High Energy Density Phys. 8, 76 (2012)]. This work presents a comparison of the two diagnostic systems and offers a detailed discussion of challenges encountered.
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Affiliation(s)
- K Falk
- Department of Physics, Clarendon Laboratory, University of Oxford, Oxford, OX1 3PU, United Kingdom
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28
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Vorberger J, Donko Z, Tkachenko IM, Gericke DO. Dynamic ion structure factor of warm dense matter. PHYSICAL REVIEW LETTERS 2012; 109:225001. [PMID: 23368129 DOI: 10.1103/physrevlett.109.225001] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2012] [Indexed: 06/01/2023]
Abstract
The dynamics of the ion structure in warm dense matter is determined by molecular dynamics simulations using an effective ion-ion potential. This potential is obtained from ab initio simulations and has a strong short-range repulsion added to a screened Coulomb potential. Models based on static or dynamic local field corrections are found to be insufficient to describe the data. An extended Mermin approach, a hydrodynamic model, and the method of moments with local constraints are capable of reproducing the numerical results but have rather limited predictive powers as they all need some numerical data as input. The method of moments is found to be the most promising.
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Affiliation(s)
- J Vorberger
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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29
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Bobrov VB. Features of the dielectric permittivity of the Coulomb system and the true dielectric state. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:026401. [PMID: 23005863 DOI: 10.1103/physreve.86.026401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2012] [Indexed: 06/01/2023]
Abstract
Based on the linear response theory and the diagram technique of the perturbation theory, the correlation between the homogeneous and isotropic Coulomb system permittivity features caused by the nonzero static conductivity and the effects of external electrostatic field screening is determined. The results obtained can be used to study the metal-dielectric transition at zero temperature beyond the scope of the adiabatic approximation for nuclei. It is shown that at the critical point the matter consisting of electrons and nuclei of the same type is in the "true" dielectric state characterized by the zero static conductivity and the absence of screening of the weak electrostatic field.
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Affiliation(s)
- V B Bobrov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow 125412, Russia.
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30
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Chapman DA, Gericke DO. Analysis of Thomson scattering from nonequilibrium plasmas. PHYSICAL REVIEW LETTERS 2011; 107:165004. [PMID: 22107396 DOI: 10.1103/physrevlett.107.165004] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2011] [Indexed: 05/31/2023]
Abstract
We develop the theory for light scattering as a diagnostic method for plasmas in nonequilibrium states. We show how well-known nonequilibrium features, like beam acoustic modes, arise in the spectra. The analysis of an experiment with strongly driven electrons demonstrates the abilities of the new approach; we find qualitatively different scattering spectra for different times and excellent agreement with the experimental data after time integration. Finally, an analysis of data from dense beryllium suggests that an energetic electron component exists in this experiment as well.
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Affiliation(s)
- D A Chapman
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry, United Kingdom
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31
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Thiele R, Sperling P, Chen M, Bornath T, Fäustlin RR, Fortmann C, Glenzer SH, Kraeft WD, Pukhov A, Toleikis S, Tschentscher T, Redmer R. Thomson scattering on inhomogeneous targets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056404. [PMID: 21230599 DOI: 10.1103/physreve.82.056404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2010] [Indexed: 05/30/2023]
Abstract
The introduction of brilliant free-electron lasers enables new pump-probe experiments to characterize warm dense matter states. For instance, a short-pulse optical laser irradiates a liquid hydrogen jet that is subsequently probed with brilliant soft x-ray radiation. The strongly inhomogeneous plasma prepared by the optical laser is characterized with particle-in-cell simulations. The interaction of the soft x-ray probe radiation for different time delays between pump and probe with the inhomogeneous plasma is also taken into account via radiative hydrodynamic simulations. We calculate the respective scattering spectrum based on the Born-Mermin approximation for the dynamic structure factor considering the full density and temperature-dependent Thomson scattering cross section throughout the target. We can identify plasmon modes that are generated in different target regions and monitor their temporal evolution. Therefore, such pump-probe experiments are promising tools not only to measure the important plasma parameters density and temperature but also to gain valuable information about their time-dependent profile through the target. The method described here can be applied to various pump-probe scenarios by combining optical lasers and soft x ray, as well as x-ray sources.
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Affiliation(s)
- R Thiele
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany.
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32
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Neumayer P, Fortmann C, Döppner T, Davis P, Falcone RW, Kritcher AL, Landen OL, Lee HJ, Lee RW, Niemann C, Le Pape S, Glenzer SH. Plasmons in strongly coupled shock-compressed matter. PHYSICAL REVIEW LETTERS 2010; 105:075003. [PMID: 20868053 DOI: 10.1103/physrevlett.105.075003] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2010] [Indexed: 05/29/2023]
Abstract
We present the first measurements of the plasmon dispersion and damping in laser shock-compressed solid matter. Petawatt laser produced K-α radiation scatters on boron targets compressed by a 10 ns-long 400 J laser pulse. In the vicinity of the Fermi momentum, the scattering spectra show dispersionless, collisionally damped plasmons, indicating a strongly coupled electron liquid. These observations agree with calculations that include the Born-Mermin approximation to account for electron-ion collisional damping and local field corrections reflecting electron-electron correlations.
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Affiliation(s)
- P Neumayer
- Lawrence Livermore National Laboratory, Livermore, California 94551, USA
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Gericke DO, Vorberger J, Wünsch K, Gregori G. Screening of ionic cores in partially ionized plasmas within linear response. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:065401. [PMID: 20866471 DOI: 10.1103/physreve.81.065401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2010] [Indexed: 05/29/2023]
Abstract
We employ a pseudopotential approach to investigate the screening of ionic cores in partially ionized plasmas. Here, the effect of the tightly bound electrons is condensed into an effective potential between the (free) valence electrons and the ionic cores. Even for weak electron-ion coupling, the corresponding screening clouds show strong modifications from the Debye result for elements heavier than helium. Modifications of the theoretically predicted x-ray scattering signal and implications on measurements are discussed.
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Affiliation(s)
- D O Gericke
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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