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French M, Röpke G, Schörner M, Bethkenhagen M, Desjarlais MP, Redmer R. Electronic transport coefficients from density functional theory across the plasma plane. Phys Rev E 2022; 105:065204. [PMID: 35854489 DOI: 10.1103/physreve.105.065204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Accepted: 05/18/2022] [Indexed: 06/15/2023]
Abstract
We investigate the thermopower and Lorenz number of hydrogen with Kohn-Sham density functional theory (DFT) across the plasma plane toward the near-classical limit, i.e., weakly degenerate and weakly coupled states. Our results are in concordance with certain limiting values for the Lorentz plasma, a model system which only considers electron-ion scattering. Thereby, we clearly show that the widely used method of calculating transport properties via the Kubo-Greenwood (KG) formalism does not capture electron-electron scattering processes. Our discussion also addresses the inadequateness of assuming a Drude-like frequency behavior for the conductivity of nondegenerate plasmas by revisiting the relaxation time approximation within kinetic theory.
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Affiliation(s)
- Martin French
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
| | - Gerd Röpke
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
| | - Maximilian Schörner
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
| | - Mandy Bethkenhagen
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
- École Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Géologie de Lyon, CNRS UMR 5276, 69364 Lyon Cedex 07, France
| | | | - Ronald Redmer
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
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2
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Röpke G, Schörner M, Redmer R, Bethkenhagen M. Virial expansion of the electrical conductivity of hydrogen plasmas. Phys Rev E 2021; 104:045204. [PMID: 34781483 DOI: 10.1103/physreve.104.045204] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Accepted: 09/22/2021] [Indexed: 11/07/2022]
Abstract
The low-density limit of the electrical conductivity σ(n,T) of hydrogen as the simplest ionic plasma is presented as a function of the temperature T and mass density n in the form of a virial expansion of the resistivity. Quantum statistical methods yield exact values for the lowest virial coefficients which serve as a benchmark for analytical approaches to the electrical conductivity as well as for numerical results obtained from density functional theory-based molecular dynamics simulations (DFT-MD) or path-integral Monte Carlo simulations. While these simulations are well suited to calculate σ(n,T) in a wide range of density and temperature, in particular, for the warm dense matter region, they become computationally expensive in the low-density limit, and virial expansions can be utilized to balance this drawback. We present new results of DFT-MD simulations in that regime and discuss the account of electron-electron collisions by comparison with the virial expansion.
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Affiliation(s)
- G Röpke
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - M Schörner
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - R Redmer
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - M Bethkenhagen
- École Normale Supérieure de Lyon, Laboratoire de Géologie de Lyon, LGLTPE UMR 5276, Centre Blaise Pascal, 46 allée d'Italie, Lyon 69364, France
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3
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Kumar S, Poser AJ, Schöttler M, Kleinschmidt U, Dietrich W, Wicht J, French M, Redmer R. Ionization and transport in partially ionized multicomponent plasmas: Application to atmospheres of hot Jupiters. Phys Rev E 2021; 103:063203. [PMID: 34271624 DOI: 10.1103/physreve.103.063203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 05/17/2021] [Indexed: 06/13/2023]
Abstract
We study ionization and transport processes in partially ionized multicomponent plasmas. The plasma composition is calculated via a system of coupled mass-action laws. The electronic transport properties are determined by the electron-ion and electron-neutral transport cross sections. The influence of electron-electron scattering is considered via a correction factor to the electron-ion contribution. Based on these data, the electrical and thermal conductivities as well as the Lorenz number are calculated. For the thermal conductivity, we consider also the contributions of the translational motion of neutral particles and of the dissociation, ionization, and recombination reactions. We apply our approach to a partially ionized plasma composed of hydrogen, helium, and a small fraction of metals (Li, Na, Ca, Fe, K, Rb, and Cs) as typical for atmospheres of hot Jupiters. We present results for the plasma composition and the transport properties as a function of density and temperature and then along typical P-T profiles for the outer part of the hot Jupiter HD 209458b. The electrical conductivity profile allows revising the Ohmic heating power related to the fierce winds in the planet's atmosphere. We show that the higher temperatures suggested by recent interior models could boost the conductivity and thus the Ohmic heating power to values large enough to explain the observed inflation of HD 209458b.
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Affiliation(s)
- Sandeep Kumar
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - Anna Julia Poser
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - Manuel Schöttler
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - Uwe Kleinschmidt
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - Wieland Dietrich
- Max-Planck-Institut für Sonnensystemforschung, 37077 Göttingen, Germany
| | - Johannes Wicht
- Max-Planck-Institut für Sonnensystemforschung, 37077 Göttingen, Germany
| | - Martin French
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - Ronald Redmer
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
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4
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Ultrafast multi-cycle terahertz measurements of the electrical conductivity in strongly excited solids. Nat Commun 2021; 12:1638. [PMID: 33712576 PMCID: PMC7977037 DOI: 10.1038/s41467-021-21756-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 02/10/2021] [Indexed: 11/10/2022] Open
Abstract
Key insights in materials at extreme temperatures and pressures can be gained by accurate measurements that determine the electrical conductivity. Free-electron laser pulses can ionize and excite matter out of equilibrium on femtosecond time scales, modifying the electronic and ionic structures and enhancing electronic scattering properties. The transient evolution of the conductivity manifests the energy coupling from high temperature electrons to low temperature ions. Here we combine accelerator-based, high-brightness multi-cycle terahertz radiation with a single-shot electro-optic sampling technique to probe the evolution of DC electrical conductivity using terahertz transmission measurements on sub-picosecond time scales with a multi-undulator free electron laser. Our results allow the direct determination of the electron-electron and electron-ion scattering frequencies that are the major contributors of the electrical resistivity. The electrical conductivity is critical to understand warm dense matter, but the accurate measurement is extremely challenging. Here the authors use multi-cycle THz pulses to measure the conductivity of gold foils strongly heated by free-electron laser, determining the individual contributions of electron-electron and electron-ion scattering.
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5
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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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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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7
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Zaporozhets Y, Mintsev V, Fortov V, Reinholz H, Röpke G, Rosmej S, Omarbakiyeva YA. Polarized angular-dependent reflectivity and density-dependent profiles of shock-compressed xenon plasmas. Phys Rev E 2019; 99:043202. [PMID: 31108619 DOI: 10.1103/physreve.99.043202] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/26/2018] [Indexed: 11/07/2022]
Abstract
New data for the reflectivity of shock-compressed xenon plasmas at pressures of 10-12 GPa at large incident angles are presented. In addition, measurements have been performed at different densities. These data allow to analyze the free-electron density profile across the shock wave front. Assuming a Fermi-like density profile, the width of the front layer is inferred. The reflectivity coefficients for the s- and p-polarized waves are calculated. The influence of atoms, which was taken into account on the level of the collision frequency, proves to be essential for the understanding of the reflection process. Subsequently, a unique density profile is sufficient to obtain good agreement with the experimental data at different incident angles and at all investigated optical laser frequencies. Reflectivity measurements for different densities allow to determine the dependence of shock-front density profiles on the plasma parameters. As a result, it was found that the width of the front layer increases with decreasing density.
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Affiliation(s)
- Y Zaporozhets
- Institute of Problems of Chemical Physics, Chernogolovka, Moscow Reg., 142432 Russia
| | - V Mintsev
- Institute of Problems of Chemical Physics, Chernogolovka, Moscow Reg., 142432 Russia
| | - V Fortov
- Institute of Problems of Chemical Physics, Chernogolovka, Moscow Reg., 142432 Russia
| | - H Reinholz
- University of Western Australia, School of Physics, 35 Stirling Highway, Crawley, Western Australia 6009, Australia and University of Rostock, Institute of Physics, Universitätsplatz 1, D-18051 Rostock, Germany
| | - G Röpke
- University of Rostock, Institute of Physics, Universitätsplatz 1, D-18051 Rostock, Germany
| | - S Rosmej
- Carl von Ossietzky University of Oldenburg, Institute of Physics, D-26111 Oldenburg, Germany
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8
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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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9
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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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10
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Rosmej S, Reinholz H, Röpke G. Contribution of electron-atom collisions to the plasma conductivity of noble gases. Phys Rev E 2017; 95:063208. [PMID: 28709212 DOI: 10.1103/physreve.95.063208] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2017] [Indexed: 11/07/2022]
Abstract
We present an approach which allows the consistent treatment of bound states in the context of dc conductivity in dense partially ionized noble gas plasmas. Besides electron-ion and electron-electron collisions, further collision mechanisms owing to neutral constituents are taken into account. Especially at low temperatures of 10^{4}to10^{5} K, electron-atom collisions give a substantial contribution to the relevant correlation functions. We suggest an optical potential for the description of the electron-atom scattering which is applicable for all noble gases. The electron-atom momentum-transfer cross section is in agreement with experimental scattering data. In addition, the influence of the medium is analyzed, the optical potential is advanced including screening effects. The position of the Ramsauer minimum is influenced by the plasma. Alternative approaches for the electron-atom potential are discussed. Good agreement of calculated conductivity with experimental data for noble gas plasmas is obtained.
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Affiliation(s)
- S Rosmej
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany
| | - 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
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11
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Desjarlais MP, Scullard CR, Benedict LX, Whitley HD, Redmer R. Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering. Phys Rev E 2017; 95:033203. [PMID: 28415190 DOI: 10.1103/physreve.95.033203] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 06/07/2023]
Abstract
We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.
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Affiliation(s)
| | | | - Lorin X Benedict
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Heather D Whitley
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Ronald Redmer
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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12
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Veysman M, Röpke G, Winkel M, Reinholz H. Optical conductivity of warm dense matter within a wide frequency range using quantum statistical and kinetic approaches. Phys Rev E 2016; 94:013203. [PMID: 27575226 DOI: 10.1103/physreve.94.013203] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2016] [Indexed: 06/06/2023]
Abstract
Fundamental properties of warm dense matter are described by the dielectric function, which gives access to the frequency-dependent electrical conductivity; absorption, emission, and scattering of radiation; charged particles stopping; and further macroscopic properties. Different approaches to the dielectric function and the related dynamical collision frequency are compared in a wide frequency range. The high-frequency limit describing inverse bremsstrahlung and the low-frequency limit of the dc conductivity are considered. Sum rules and Kramers-Kronig relation are checked for the generalized linear response theory and the standard approach following kinetic theory. The results are discussed in application to aluminum, xenon, and argon plasmas.
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Affiliation(s)
- M Veysman
- Joint Institute for High Temperatures (JIHT) RAS, Izhorskaya 13/19, Moscow 125412, Russia
| | - G Röpke
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
- National Research Nuclear University (MEPhI), 115409 Moscow, Russia
| | - M Winkel
- Institute for Advanced Simulation, Juelich Supercomputing Centre, Forschungszentrum, Juelich GmbH, 52425 Juelich, Germany
- ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany
| | - H Reinholz
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
- The University of Western Australia, School of Physics, Crawley, Western Australia 6009, Australia
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13
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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: 19] [Impact Index Per Article: 2.1] [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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