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Nagayama T, Schaeuble MA, Fein JR, Loisel GP, Wu M, Mayes DC, Hansen SB, Knapp PF, Webb TJ, Schwarz J, Vesey RA. A generalized approach to x-ray data modeling for high-energy-density plasma experiments. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:2887772. [PMID: 37129462 DOI: 10.1063/5.0128811] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 03/27/2023] [Indexed: 05/03/2023]
Abstract
Accurate understanding of x-ray diagnostics is crucial for both interpreting high-energy-density experiments and testing simulations through quantitative comparisons. X-ray diagnostic models are complex. Past treatments of individual x-ray diagnostics on a case-by-case basis have hindered universal diagnostic understanding. Here, we derive a general formula for modeling the absolute response of non-focusing x-ray diagnostics, such as x-ray imagers, one-dimensional space-resolved spectrometers, and x-ray power diagnostics. The present model is useful for both data modeling and data processing. It naturally accounts for the x-ray crystal broadening. The new model verifies that standard approaches for a crystal response can be good approximations, but they can underestimate the total reflectivity and overestimate spectral resolving power by more than a factor of 2 in some cases near reflectivity edge features. We also find that a frequently used, simplified-crystal-response approximation for processing spectral data can introduce an absolute error of more than an order of magnitude and the relative spectral radiance error of a factor of 3. The present model is derived with straightforward geometric arguments. It is more general and is recommended for developing a unified picture and providing consistent treatment over multiple x-ray diagnostics. Such consistency is crucial for reliable multi-objective data analyses.
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Affiliation(s)
- T Nagayama
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - M A Schaeuble
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - J R Fein
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - G P Loisel
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - M Wu
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - D C Mayes
- University of Texas at Austin, Austin, Texas 78712, USA
| | - S B Hansen
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - P F Knapp
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - T J Webb
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - J Schwarz
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - R A Vesey
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
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2
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Krief M. Number of populated electronic configurations in a hot dense plasma. Phys Rev E 2021; 103:033206. [PMID: 33862695 DOI: 10.1103/physreve.103.033206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Accepted: 03/11/2021] [Indexed: 11/07/2022]
Abstract
In hot dense plasmas of intermediate or high-Z elements in the state of local thermodynamic equilibrium, the number of electronic configurations contributing to key macroscopic quantities such as the spectral opacity and equation of state can be enormous. In this work we present systematic methods for the analysis of the number of relativistic electronic configurations in a plasma. While the combinatoric number of configurations can be huge even for mid-Z elements, the number of configurations which have non-negligible population is much lower and depends strongly and nontrivially on temperature and density. We discuss two useful methods for the estimation of the number of populated configurations: (i) using an exact calculation of the total combinatoric number of configurations within superconfigurations in a converged super-transition-array (STA) calculation, and (ii) by using an estimate for the multidimensional width of the probability distribution for electronic population over bound shells, which is binomial if electron exchange and correlation effects are neglected. These methods are analyzed, and the mechanism which leads to the huge number of populated configurations is discussed in detail. Comprehensive average-atom finite-temperature density functional theory (DFT) calculations are performed in a wide range of temperature and density for several low-, mid-, and high-Z plasmas. The effects of temperature and density on the number of populated configurations are discussed and explained.
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Affiliation(s)
- Menahem Krief
- Racah Institute of Physics, The Hebrew University, 9190401 Jerusalem, Israel
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3
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Nagayama T, Bailey JE, Loisel GP, Dunham GS, Rochau GA, Blancard C, Colgan J, Cossé P, Faussurier G, Fontes CJ, Gilleron F, Hansen SB, Iglesias CA, Golovkin IE, Kilcrease DP, MacFarlane JJ, Mancini RC, More RM, Orban C, Pain JC, Sherrill ME, Wilson BG. Systematic Study of L-Shell Opacity at Stellar Interior Temperatures. PHYSICAL REVIEW LETTERS 2019; 122:235001. [PMID: 31298873 DOI: 10.1103/physrevlett.122.235001] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2019] [Indexed: 06/10/2023]
Abstract
The first systematic study of opacity dependence on atomic number at stellar interior temperatures is used to evaluate discrepancies between measured and modeled iron opacity [J. E. Bailey et al., Nature (London) 517, 56 (2015)NATUAS0028-083610.1038/nature14048]. High-temperature (>180 eV) chromium and nickel opacities are measured with ±6%-10% uncertainty, using the same methods employed in the previous iron experiments. The 10%-20% experiment reproducibility demonstrates experiment reliability. The overall model-data disagreements are smaller than for iron. However, the systematic study reveals shortcomings in models for density effects, excited states, and open L-shell configurations. The 30%-45% underestimate in the modeled quasicontinuum opacity at short wavelengths was observed only from iron and only at temperature above 180 eV. Thus, either opacity theories are missing physics that has nonmonotonic dependence on the number of bound electrons or there is an experimental flaw unique to the iron measurement at temperatures above 180 eV.
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Affiliation(s)
- T Nagayama
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J E Bailey
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G P Loisel
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G S Dunham
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G A Rochau
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | | | - J Colgan
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ph Cossé
- CEA, DAM, DIF, F-91297 Arpajon, France
| | | | - C J Fontes
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | - S B Hansen
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - C A Iglesias
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - I E Golovkin
- Prism Computational Sciences, Madison, Wisconsin 53711, USA
| | - D P Kilcrease
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J J MacFarlane
- Prism Computational Sciences, Madison, Wisconsin 53711, USA
| | - R C Mancini
- University of Nevada, Reno, Nevada 89557, USA
| | - R M More
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - C Orban
- Ohio State University, Columbus, Ohio 43210, USA
| | - J-C Pain
- CEA, DAM, DIF, F-91297 Arpajon, France
| | - M E Sherrill
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - B G Wilson
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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4
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Loisel GP, Bailey JE, Liedahl DA, Fontes CJ, Kallman TR, Nagayama T, Hansen SB, Rochau GA, Mancini RC, Lee RW. Benchmark Experiment for Photoionized Plasma Emission from Accretion-Powered X-Ray Sources. PHYSICAL REVIEW LETTERS 2017; 119:075001. [PMID: 28949679 DOI: 10.1103/physrevlett.119.075001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2017] [Indexed: 06/07/2023]
Abstract
The interpretation of x-ray spectra emerging from x-ray binaries and active galactic nuclei accreted plasmas relies on complex physical models for radiation generation and transport in photoionized plasmas. These models have not been sufficiently experimentally validated. We have developed a highly reproducible benchmark experiment to study spectrum formation from a photoionized silicon plasma in a regime comparable to astrophysical plasmas. Ionization predictions are higher than inferred from measured absorption spectra. Self-emission measured at adjustable column densities tests radiation transport effects, demonstrating that the resonant Auger destruction assumption used to interpret black hole accretion spectra is inaccurate.
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Affiliation(s)
- G P Loisel
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J E Bailey
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - D A Liedahl
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - C J Fontes
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - T R Kallman
- Goddard Space Flight Center NASA, Greenbelt, Maryland 20771, USA
| | - T Nagayama
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - S B Hansen
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G A Rochau
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - R C Mancini
- University of Nevada, Reno, Nevada 89557, USA
| | - R W Lee
- University of California, Berkeley, California 94720, USA
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5
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Nagayama T, Bailey JE, Loisel GP, Rochau GA, MacFarlane JJ, Golovkin IE. Numerical investigations of potential systematic uncertainties in iron opacity measurements at solar interior temperatures. Phys Rev E 2017; 95:063206. [PMID: 28709238 DOI: 10.1103/physreve.95.063206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2017] [Indexed: 06/07/2023]
Abstract
Iron opacity calculations presently disagree with measurements at an electron temperature of ∼180-195 eV and an electron density of (2-4)×10^{22}cm^{-3}, conditions similar to those at the base of the solar convection zone. The measurements use x rays to volumetrically heat a thin iron sample that is tamped with low-Z materials. The opacity is inferred from spectrally resolved x-ray transmission measurements. Plasma self-emission, tamper attenuation, and temporal and spatial gradients can all potentially cause systematic errors in the measured opacity spectra. In this article we quantitatively evaluate these potential errors with numerical investigations. The analysis exploits computer simulations that were previously found to reproduce the experimentally measured plasma conditions. The simulations, combined with a spectral synthesis model, enable evaluations of individual and combined potential errors in order to estimate their potential effects on the opacity measurement. The results show that the errors considered here do not account for the previously observed model-data discrepancies.
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Affiliation(s)
- T Nagayama
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J E Bailey
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G P Loisel
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G A Rochau
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J J MacFarlane
- Prism Computational Sciences, Madison, Wisconsin 53711, USA
| | - I E Golovkin
- Prism Computational Sciences, Madison, Wisconsin 53711, USA
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6
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Loisel GP, Wu M, Stolte W, Kruschwitz C, Lake P, Dunham GS, Bailey JE, Rochau GA. Measurement and models of bent KAP(001) crystal integrated reflectivity and resolution (invited). THE REVIEW OF SCIENTIFIC INSTRUMENTS 2016; 87:11D502. [PMID: 27910652 DOI: 10.1063/1.4960149] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The Advanced Light Source beamline-9.3.1 x-rays are used to calibrate the rocking curve of bent potassium acid phthalate (KAP) crystals in the 2.3-4.5 keV photon-energy range. Crystals are bent on a cylindrically convex substrate with a radius of curvature ranging from 2 to 9 in. and also including the flat case to observe the effect of bending on the KAP spectrometric properties. As the bending radius increases, the crystal reflectivity converges to the mosaic crystal response. The X-ray Oriented Programs (xop) multi-lamellar model of bent crystals is used to model the rocking curve of these crystals and the calibration data confirm that a single model is adequate to reproduce simultaneously all measured integrated reflectivities and rocking-curve FWHM for multiple radii of curvature in both 1st and 2nd order of diffraction.
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Affiliation(s)
- G P Loisel
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - M Wu
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - W Stolte
- National Security Technologies, LLC, Livermore, California 94551, USA
| | - C Kruschwitz
- National Security Technologies, LLC, Los Alamos, New Mexico 87544, USA
| | - P Lake
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G S Dunham
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J E Bailey
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G A Rochau
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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