Opacity of Shock-Heated Boron Plasmas
Standard measures of opacity, the imaginary part of the atomic scattering factor $f_2$ and the x-ray mass attenuation coefficient $\mu/\rho$, 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 $\rho/\rho_0$ across the shock front, is used in connection with the plasma equation of state to determine the pressure $p$, effective plasma charge $Z^\ast$ and the K-shell occupation in terms of $\rho/\rho_0$. 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 20eV to 500eV; 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 $\omega=1$eV to 10keV, 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. For shock-compressed plasmas, the dependence of the $\mu/\rho$ 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 $\mu$ for a 9 keV x-ray are given as functions of $T$ along the Hugoniot for B, C, B$_4$C and BN plasmas.