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Title: Opacity of shock-heated boron plasmas

Abstract

Standard measures of opacity, the imaginary part of the atomic scattering factor f 2 and the x-ray mass attenuation coefficient μ/ρ, are assessed in shock-heated boron, boron carbide and boron nitride plasmas. The Hugoniot equation, relating the temperature T behind a shock wave to the compression ratio ρ/ρ 0 across the shock front, is used in connection with the plasma equation of state to determine the pressure p, effective plasma charge Z* and the K-shell occupation in terms of ρ/ρ 0. Solutions of the Hugoniot equation (determined within the framework of the generalized Thomas–Fermi theory) show that the K-shell occupation in low-Z ions decreases rapidly from 2 to 0.1 as the temperature increases from 20 eV to 500 eV; a temperature range in which the shock compression ratio is near 4. The average-atom model (a quantum mechanical version of the generalized Thomas–Fermi theory) is used to determine K-shell and continuum wave functions and the photoionization cross section for x-rays in the energy range ω = 1 eV to 10 keV, where the opacity is dominated by the atomic photoionization process. For an uncompressed boron plasma at T= 10 eV, where the K-shell is filled, the average-atom cross section, the atomicmore » scattering factor and the mass attenuation coefficient are all shown to agree closely with previous (cold matter) tabulations [1, 2, 3]. For shock-compressed plasmas, the dependence of μ/ρ on temperature can be approximated by scaling previously tabulated cold-matter values by the relative K-shell occupation; yet, there is a relatively small residual dependence arising from the photoionization cross section. Attenuation coefficients μ for a 9 keV x-ray are given as functions of T along the Hugoniot for B, C, B 4C and BN plasmas.« less

Authors:
 [1];  [2]
  1. Univ. of Notre Dame, IN (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1557064
Report Number(s):
LLNL-JRNL-758940
Journal ID: ISSN 1574-1818; 947182
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
High Energy Density Physics
Additional Journal Information:
Journal Volume: 31; Journal Issue: C; Journal ID: ISSN 1574-1818
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 74 ATOMIC AND MOLECULAR PHYSICS; 52.50.Lp: Plasma production and heating by shock waves and compression; 56.65.Rr: Particle in cell method; 52.70.-m: Plasma diagnostic techniques; 52.25.Os: Emission; absorption; scattering of electromagnetic radiation

Citation Formats

Johnson, W. R., and Nilsen, J. Opacity of shock-heated boron plasmas. United States: N. p., 2019. Web. doi:10.1016/j.hedp.2019.01.008.
Johnson, W. R., & Nilsen, J. Opacity of shock-heated boron plasmas. United States. doi:10.1016/j.hedp.2019.01.008.
Johnson, W. R., and Nilsen, J. Fri . "Opacity of shock-heated boron plasmas". United States. doi:10.1016/j.hedp.2019.01.008.
@article{osti_1557064,
title = {Opacity of shock-heated boron plasmas},
author = {Johnson, W. R. and Nilsen, J.},
abstractNote = {Standard measures of opacity, the imaginary part of the atomic scattering factor f2 and the x-ray mass attenuation coefficient μ/ρ, are assessed in shock-heated boron, boron carbide and boron nitride plasmas. The Hugoniot equation, relating the temperature T behind a shock wave to the compression ratio ρ/ρ0 across the shock front, is used in connection with the plasma equation of state to determine the pressure p, effective plasma charge Z* and the K-shell occupation in terms of ρ/ρ0. Solutions of the Hugoniot equation (determined within the framework of the generalized Thomas–Fermi theory) show that the K-shell occupation in low-Z ions decreases rapidly from 2 to 0.1 as the temperature increases from 20 eV to 500 eV; a temperature range in which the shock compression ratio is near 4. The average-atom model (a quantum mechanical version of the generalized Thomas–Fermi theory) is used to determine K-shell and continuum wave functions and the photoionization cross section for x-rays in the energy range ω = 1 eV to 10 keV, where the opacity is dominated by the atomic photoionization process. For an uncompressed boron plasma at T= 10 eV, where the K-shell is filled, the average-atom cross section, the atomic scattering factor and the mass attenuation coefficient are all shown to agree closely with previous (cold matter) tabulations [1, 2, 3]. For shock-compressed plasmas, the dependence of μ/ρ on temperature can be approximated by scaling previously tabulated cold-matter values by the relative K-shell occupation; yet, there is a relatively small residual dependence arising from the photoionization cross section. Attenuation coefficients μ for a 9 keV x-ray are given as functions of T along the Hugoniot for B, C, B4C and BN plasmas.},
doi = {10.1016/j.hedp.2019.01.008},
journal = {High Energy Density Physics},
number = C,
volume = 31,
place = {United States},
year = {2019},
month = {3}
}

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This content will become publicly available on March 15, 2020
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