Nonideal effect of free electrons on ionization equilibrium and radiative property in dense plasmas

The thermodynamic as well as optical properties of strongly coupled plasmas depend crucially on the average degree of ionization and the ionic state composition, which, however, cannot be determined by using the normal Saha equation usually used for the ideal plasmas. Hence, an adequate treatment of the ionization balance and the charge state distribution of strongly coupled plasmas is still a challenge for theory due to the interactions between the electrons and ions and among the electrons themselves. Based on a local density temperature-dependent ion-sphere model, the Saha equation approach is extended to the regime of strongly coupled plasmas by taking into account the free-electron-ion interaction, the free-free-electron interaction, the nonuniform free-electron space distribution, and the free-electron quantum partial degeneracy. All the quantities, including the bound orbitals with ionization potential depression, free-electron distribution, and bound and free-electron partition function contributions, are calculated self-consistently in the theoretical formalism. This study shows that the ionization equilibrium is evidently modified by considering the above nonideal characteristics of the free electrons. Our theoretical formalism is validated by the explanation of a recent experimental measurement of the opacity of dense hydrocarbon.

Figure 1

Relative partition functions ($b_i$ in Eq. (4)) of the free electrons for different charge states in Fe plasmas at a temperature of 200 eV and mass densities of 1.0 g ${\mathrm{cm}}^{-3}$, 4.0 g ${\mathrm{cm}}^{-3}$, 7.874 g ${\mathrm{cm}}^{-3}$, and 15.748 g ${\mathrm{cm}}^{-3}$, respectively. For each plasma condition, the partition functions are relative to that of the uniform electron gas $[Z_e=2{\left(\frac{2\pi m_{e}kT}{h^2}\right)}^{3/2}]$.

Figure 2

Relative partition functions ($b_i$ in Eq. (4)) of the free electrons for different charge states in Fe plasmas at a mass density of 7.874 g ${\mathrm{cm}}^{-3}$ and temperatures of 100 eV, 200 eV, 300 eV, 600 eV, and 1000 eV, respectively. For each plasma condition, the partition functions are relative to those of the uniform electron gas $[Z_e=2{\left(\frac{2\pi m_{e}kT}{h^2}\right)}^{3/2}]$.

Figure 3

Comparison of charge state distribution of Fe plasmas with (solid lines) and without (dashed lines) considering the effect of NIC of free electrons at mass densities of (a) 1.0 g ${\mathrm{cm}}^{-3}$, (b) 7.874 g ${\mathrm{cm}}^{-3}$, and (c) 15.748 g ${\mathrm{cm}}^{-3}$ and at temperatures of 100 eV (solid and dashed black lines), 200 eV (solid and dashed red lines), 300 eV (solid and dashed green lines), 600 eV (solid and dashed blue lines), and 1000 eV (solid and dashed brown lines).

Figure 4

Comparison of average degree of ionization of Fe plasmas with (solid black and colored lines) and without (dashed black and colored lines) considering the effect of NIC of free electrons as a function of plasma temperature at mass densities of 1.0 g ${\mathrm{cm}}^{-3}$ (green lines), 7.874 g ${\mathrm{cm}}^{-3}$ (red lines), and 15.748 g ${\mathrm{cm}}^{-3}$ (black lines).

Figure 5

Opacity of dense ${\mathrm{C}}_9{\mathrm{H}}_{10}$ at a photon energy of 9 keV with and without considering the NIC effect. The plasma conditions are determined at the shock front along the shock Hugoniot (central red line) measured by Kritcher et al. [1]. Another two red lines correspond to uncertainty contours in the measurement. We also give the theoretical results of the normalized opacity with and without 1 at % F (black line). Comparisons are made with the experimental measurement and theoretical results through detailed configuration accounting (DCA) [1].