Radiative and atomic properties of C and CH plasmas in the warm-dense-matter regime

A theoretical model based on the method of super transition arrays (STA) is used to compute the emissivities, opacities, and average ionization states of carbon (C) and polystyrene (CH) plasmas in the warm-dense matter regime in which the coupling constant varies between 0.02 to 2.0. The accuracy of results of STA calculations is assessed by benchmarking against the available experimental data and results obtained using other theoretical methods, assuming that a state of local thermodynamic equilibrium exists in the plasma. In the case of a carbon plasma, the STA method yields spectral features that are in reasonably good agreement with Dirac-Fock and Hartree-Fock-Slater theories; in the case of CH, we find that STA-derived opacities are very similar to those derived using quantum-molecular-dynamics density-functional theory and Hartree-Fock method down to plasma temperature of about 20 eV. Our calculations also compare favorably with available experimental measurements of Gamboa et al. [High Energy Density Phys. 11, 75 (2014)] of the plasma temperature and average ionization state behind a blast wave in a pure carbon foam. Although the STA-computed average-ionization charge state in the rarefaction region appears to be lower than the experimental data, it is within the experimental uncertainty and the discrepancy is nevertheless consistent with results reported using an atomic kinetic model. In addition, we further predict the temperature dependence of average ionization states of CH plasma in the same temperature range as for the carbon plasma.

Figure 1

Schematic representation of a mixture in a volume $V$. Red (light gray) and blue (dark gray) represent two different components in the mixture.

Figure 2

The carbon average ionization $\overline{\mathrm{Z}}$ as a function of temperature at 0.2 ${\mathrm{g}/\mathrm{cm}}^3$ are compared to SCAALP [47], Purgatorio [48], FLYCHK [49], Thomas-Fermi (TF) model, and experimental data [46].

Figure 3

The carbon average ionization $\overline{Z}$ as a function of plasma temperature. The solid circles and squares are the measured $\overline{Z}$ data from the shocked foam [52]. The data are divided into the shocked layer and rarefaction groups. The solid and dashed lines are the STA and FLYCHK results, respectively, evaluated at 2/5, 1, and 3.5 times the initial or uncompressed carbon foam density of 0.34 ${\mathrm{g}/\mathrm{cm}}^3$.

Figure 4

Emission spectrum of carbon plasma at a temperature of 50 eV and density of 4.3 $\times {10}^{-3} {\mathrm{g}/\mathrm{cm}}^3$. The locations of 1s ionization thresholds of C III, C IV, and C V are indicated by arrows.

Figure 5

(a) A comparison of the radiative opacity (Planckian) of carbon at a density of 2.24 ${\mathrm{g}/\mathrm{cm}}^3$ and a temperature of 100 eV; (b) the breakdown of different contributions from the bound-bound, bound-free, and free-free transitions of the total opacity.

Figure 6

The density dependence of the radiative opacity (Planckian) for carbon at a plasma temperature of (a) 50 eV and (b) 100 eV.

Figure 7

STA results for CH. The diamond is the experimental datum of CH foils from Fig. 8 in Ref. [44].

Figure 8

The Rosseland opacity of CH as a function of photon energy for a plasma density of (i) 4.0 ${\mathrm{g}/\mathrm{cm}}^3$ and (ii) 50.0 ${\mathrm{g}/\mathrm{cm}}^3$ and temperature (a) 11.0 eV, (b) 43.0 eV, and (c) 86.0 eV.

Figure 9

The Rosseland mean opacity of CH as a function of plasma temperature for four different densities: (a) 0.5 ${\mathrm{g}/\mathrm{cm}}^3$, (b) 4.0 ${\mathrm{g}/\mathrm{cm}}^3$, (c) 10.0 ${\mathrm{g}/\mathrm{cm}}^3$, and (d) 50.0 ${\mathrm{g}/\mathrm{cm}}^3$.