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Gao CZ, Zhang CB, Cai Y, Wu Y, Fan ZF, Wang P, Wang JG. Assessment of the electron-proton energy relaxation rates extracted from molecular dynamics simulations in weakly-coupled hydrogen plasmas. Phys Rev E 2023; 107:015203. [PMID: 36797881 DOI: 10.1103/physreve.107.015203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 12/23/2022] [Indexed: 06/18/2023]
Abstract
Electron-proton energy relaxation rates are assessed using molecular dynamics (MD) simulations in weakly-coupled hydrogen plasmas. To this end, we use various approaches to extract the energy relaxation rate from MD-simulated temperatures, and we find that existing extracting approaches may yield results with a sizable discrepancy larger than the variance between analytical models, which is further verified by well-known case studies. Present results show that two of the extracting approaches can produce identical results, which is attributed to a proper treatment of relaxation evolution. To discriminate the use of various methods, an empirical criterion with respect to initial plasma temperatures is proposed, which can self-consistently explain the cases considered. In addition, for a transient electron-proton plasma, we show that it is possible to extrapolate the Coulomb logarithm from that derived by initial plasma parameters in a single MD calculation, which is reasonably consistent with previous MD data. Our results are helpful to obtain accurate MD-based energy relaxation rates.
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Affiliation(s)
- Cong-Zhang Gao
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China
| | - Cun-Bo Zhang
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China
| | - Ying Cai
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China
| | - Yong Wu
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China
| | - Zheng-Feng Fan
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China
| | - Pei Wang
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China
| | - Jian-Guo Wang
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China
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2
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Adrian PJ, Florido R, Grabowski PE, Mancini R, Bachmann B, Benedict LX, Johnson MG, Kabadi N, Lahmann B, Li CK, Petrasso RD, Rinderknecht HG, Regan SP, Séguin FH, Singleton RL, Sio H, Sutcliffe GD, Whitley HD, Frenje JA. Measurements of ion-electron energy-transfer cross section in high-energy-density plasmas. Phys Rev E 2022; 106:L053201. [PMID: 36559377 DOI: 10.1103/physreve.106.l053201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 09/02/2022] [Indexed: 06/17/2023]
Abstract
We report on measurements of the ion-electron energy-transfer cross section utilizing low-velocity ion stopping in high-energy-density plasmas at the OMEGA laser facility. These measurements utilize a technique that leverages the close relationship between low-velocity ion stopping and ion-electron equilibration. Shock-driven implosions of capsules filled with D^{3}He gas doped with a trace amount of argon are used to generate densities and temperatures in ranges from 1×10^{23} to 2×10^{24} cm^{-3} and from 1.4 to 2.5 keV, respectively. The energy loss of 1-MeV DD tritons and 3.7-MeV D^{3}He alphas that have velocities lower than the average velocity of the thermal electrons is measured. The energy loss of these ions is used to determine the ion-electron energy-transfer cross section, which is found to be in excellent agreement with quantum-mechanical calculations in the first Born approximation. This result provides an experimental constraint on ion-electron energy transfer in high-energy-density plasmas, which impacts the modeling of alpha heating in inertial confinement fusion implosions, magnetic-field advection in stellar atmospheres, and energy balance in supernova shocks.
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Affiliation(s)
- P J Adrian
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - R Florido
- iUNAT, Departamento de Física, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
| | - P E Grabowski
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - R Mancini
- Department of Physics, University of Nevada, Reno, Reno, Nevada 89557, USA
| | - B Bachmann
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - L X Benedict
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - M Gatu Johnson
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - N Kabadi
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - B Lahmann
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - C K Li
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - R D Petrasso
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - H G Rinderknecht
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - S P Regan
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - F H Séguin
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - R L Singleton
- SavantX Research Center, Santa Fe, New Mexico 87501, USA
- School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - H Sio
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - G D Sutcliffe
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - H D Whitley
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - J A Frenje
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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3
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Ma Q, Dai J, Kang D, Murillo MS, Hou Y, Zhao Z, Yuan J. Extremely Low Electron-ion Temperature Relaxation Rates in Warm Dense Hydrogen: Interplay between Quantum Electrons and Coupled Ions. PHYSICAL REVIEW LETTERS 2019; 122:015001. [PMID: 31012692 DOI: 10.1103/physrevlett.122.015001] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Revised: 10/24/2018] [Indexed: 06/09/2023]
Abstract
Theoretical and computational modeling of nonequilibrium processes in warm dense matter represents a significant challenge. The electron-ion relaxation process in warm dense hydrogen is investigated here by nonequilibrium molecular dynamics using the constrained electron force field (CEFF) method. CEFF evolves wave packets that incorporate dynamic quantum diffraction that obviates the Coulomb catastrophe. Predictions from this model reveal temperature relaxation times as much as three times longer than prior molecular dynamics results based on quantum statistical potentials. Through analyses of energy distributions and mean free paths, this result can be traced to delocalization. Finally, an improved GMS [Gericke, Murillo, and Schlanges, Phys. Rev. E 78, 025401 (2008)PRESCM1539-375510.1103/PhysRevE.78.025401] model is proposed, in which the Coulomb logarithms are in good agreement with CEFF results.
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Affiliation(s)
- Qian Ma
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Jiayu Dai
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Dongdong Kang
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - M S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Yong Hou
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Zengxiu Zhao
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Jianmin Yuan
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
- Graduate School of China Academy of Engineering Physics, Beijing 100193, P. R. China
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4
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Benedict LX, Surh MP, Stanton LG, Scullard CR, Correa AA, Castor JI, Graziani FR, Collins LA, Čertík O, Kress JD, Murillo MS. Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime. Phys Rev E 2017; 95:043202. [PMID: 28505713 DOI: 10.1103/physreve.95.043202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2016] [Indexed: 06/07/2023]
Abstract
We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K<T_{e}<10^{9}K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealing to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.
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Affiliation(s)
- Lorin X Benedict
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Michael P Surh
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Liam G Stanton
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | | | - Alfredo A Correa
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - John I Castor
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Frank R Graziani
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Lee A Collins
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ondřej Čertík
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Michael S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
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5
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Faussurier G, Blancard C. Temperature relaxation in dense plasma mixtures. Phys Rev E 2016; 94:033210. [PMID: 27739738 DOI: 10.1103/physreve.94.033210] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2016] [Indexed: 11/07/2022]
Abstract
We present a model to calculate temperature-relaxation rates in dense plasma mixtures. The electron-ion relaxation rates are calculated using an average-atom model and the ion-ion relaxation rates by the Landau-Spitzer approach. This method allows the study of the temperature relaxation in many-temperature electron-ion and ion-ion systems such as those encountered in inertial confinement fusion simulations. It is of interest for general nonequilibrium thermodynamics dealing with energy flows between various systems and should find broad use in present high energy density experiments.
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6
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Abstract
We present a model to calculate temperature-relaxation rates in dense plasmas. The electron-ion interaction potential and the thermodynamic data of interest are provided by an average-atom model. This approach allows the study of the temperature relaxation in a two-temperature electron-ion system.
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7
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Benedict LX, Surh MP, Castor JI, Khairallah SA, Whitley HD, Richards DF, Glosli JN, Murillo MS, Scullard CR, Grabowski PE, Michta D, Graziani FR. Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:046406. [PMID: 23214699 DOI: 10.1103/physreve.86.046406] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2012] [Indexed: 06/01/2023]
Abstract
We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical two-body potentials and a generalized Lenard-Balescu (GLB) theory capable of treating multicomponent weakly coupled plasmas. The GLB is used in two modes: (1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction and (2) with the classical (ℏ→0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough. In addition, we show that classical calculations with statistical potentials derived from the exact quantum two-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.
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Affiliation(s)
- Lorin X Benedict
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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8
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Xu B, Hu SX. Effects of electron-ion temperature equilibration on inertial confinement fusion implosions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:016408. [PMID: 21867323 DOI: 10.1103/physreve.84.016408] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2011] [Indexed: 05/31/2023]
Abstract
The electron-ion temperature relaxation essentially affects both the laser absorption in coronal plasmas and the hot-spot formation in inertial confinement fusion (ICF). It has recently been reexamined for plasma conditions closely relevant to ICF implosions using either classical molecular-dynamics simulations or analytical methods. To explore the electron-ion temperature equilibration effects on ICF implosion performance, we have examined two Coulomb logarithm models by implementing them into our hydrocodes, and we have carried out hydrosimulations for ICF implosions. Compared to the Lee-More model that is currently used in our standard hydrocodes, the two models predict substantial differences in laser absorption, coronal temperatures, and neutron yields for ICF implosions at the OMEGA Laser Facility [Boehly et al. Opt. Commun. 133, 495 (1997)]. Such effects on the triple-picket direct-drive design at the National Ignition Facility (NIF) have also been explored. Based on the validity of the two models, we have proposed a combined model of the electron-ion temperature-relaxation rate for the overall ICF plasma conditions. The hydrosimulations using the combined model for OMEGA implosions have shown ∼6% more laser absorption, ∼6%-15% higher coronal temperatures, and ∼10% more neutron yield, when compared to the Lee-More model prediction. It is also noticed that the gain for the NIF direct-drive design can be varied by ∼10% among the different electron-ion temperature-relaxation models.
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Affiliation(s)
- Barry Xu
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299, USA
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9
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Hu SX, Militzer B, Goncharov VN, Skupsky S. Strong coupling and degeneracy effects in inertial confinement fusion implosions. PHYSICAL REVIEW LETTERS 2010; 104:235003. [PMID: 20867248 DOI: 10.1103/physrevlett.104.235003] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2009] [Indexed: 05/29/2023]
Abstract
Accurate knowledge about the equation of state (EOS) of deuterium is critical to inertial confinement fusion (ICF). Low-adiabat ICF implosions routinely access strongly coupled and degenerate plasma conditions. Using the path integral Monte Carlo method, we have derived a first-principles EOS (FPEOS) table of deuterium. It is the first ab initio EOS table which completely covers typical ICF implosion trajectory in the density and temperature ranges of ρ=0.002-1596 g/cm3 and T=1.35 eV-5.5 keV. Discrepancies in internal energy and pressure have been found in strongly coupled and degenerate regimes with respect to SESAME EOS. Hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table have indicated significant differences in peak density, areal density (ρR), and neutron yield relative to SESAME simulations.
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Affiliation(s)
- S X Hu
- Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York 14623, USA.
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Rygg JR, Frenje JA, Li CK, Séguin FH, Petrasso RD, Meyerhofer DD, Stoeckl C. Electron-ion thermal equilibration after spherical shock collapse. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:026403. [PMID: 19792264 DOI: 10.1103/physreve.80.026403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2009] [Indexed: 05/28/2023]
Abstract
A comprehensive set of dual nuclear product observations provides a snapshot of imploding inertial confinement fusion capsules at the time of shock collapse, shortly before the final stages of compression. The collapse of strong convergent shocks at the center of spherical capsules filled with D(2) and (3)He gases induces D-D and D-(3)He nuclear production. Temporal and spectral diagnostics of products from both reactions are used to measure shock timing, temperature, and capsule areal density. The density and temperature inferred from these measurements are used to estimate the electron-ion thermal coupling and demonstrate a lower electron-ion relaxation rate for capsules with lower initial gas density.
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Affiliation(s)
- J R Rygg
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Benedict LX, Glosli JN, Richards DF, Streitz FH, Hau-Riege SP, London RA, Graziani FR, Murillo MS, Benage JF. Molecular dynamics simulations of electron-ion temperature equilibration in an SF6 plasma. PHYSICAL REVIEW LETTERS 2009; 102:205004. [PMID: 19519037 DOI: 10.1103/physrevlett.102.205004] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2008] [Indexed: 05/27/2023]
Abstract
We use classical molecular dynamics to investigate electron-ion temperature equilibration in a two-temperature SF6 plasma. We choose a density of 1.0 x 10;{19}SF_{6} molecules per cm;{3} and initial temperatures of T_{e} = 100 eV and T_{S} = T_{F} = 15 eV, in accordance with experiments currently underway at Los Alamos National Laboratory. Our computed relaxation time lies between two oft-used variants of the Landau-Spitzer relaxation formula which invoke static screening. Discrepancies are also found when comparing to the predictions made by more recent theoretical approaches. These differences should be large enough to be measured in the upcoming experiments.
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Affiliation(s)
- Lorin X Benedict
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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Daligault J, Dimonte G. Correlation effects on the temperature-relaxation rates in dense plasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:056403. [PMID: 19518572 DOI: 10.1103/physreve.79.056403] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2008] [Revised: 03/19/2009] [Indexed: 05/27/2023]
Abstract
We present a model for the rate of temperature relaxation between electrons and ions in plasmas. The model includes self-consistently the effects of particle screening, electron degeneracy, and correlations between electrons and ions. We successfully validate the model over a wide range of plasma coupling against molecular-dynamics simulations of classical plasmas of like-charged electrons and ions. We present calculations of the relaxation rates in dense hydrogen and show that, while electron-ion correlation effects are indispensable in classical, like-charged plasmas at any density and temperature, quantum diffraction effects prevail over electron-ion correlation effects in dense hydrogen plasmas.
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Affiliation(s)
- Jérôme Daligault
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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