Opacity of shock-heated boron plasmas

Abstract

Standard measures of opacity, the imaginary part of the atomic scattering factor f2 and the x-ray mass attenuation coefficient μ/ρ, are evaluated 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) reveal 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; however, 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.