Effect of configuration widths on the spectra of local thermodynamic equilibrium plasmas

Number of populated electronic configurations in a hot dense plasma

In hot dense plasmas of intermediate or high-Z elements in the state of local thermodynamic equilibrium, the number of electronic configurations contributing to key macroscopic quantities such as the spectral opacity and equation of state can be enormous. In this work we present systematic methods for the analysis of the number of relativistic electronic configurations in a plasma. While the combinatoric number of configurations can be huge even for mid-Z elements, the number of configurations which have non-negligible population is much lower and depends strongly and nontrivially on temperature and density. We discuss two useful methods for the estimation of the number of populated configurations: (i) using an exact calculation of the total combinatoric number of configurations within superconfigurations in a converged super-transition-array (STA) calculation, and (ii) by using an estimate for the multidimensional width of the probability distribution for electronic population over bound shells, which is binomial if electron exchange and correlation effects are neglected. These methods are analyzed, and the mechanism which leads to the huge number of populated configurations is discussed in detail. Comprehensive average-atom finite-temperature density functional theory (DFT) calculations are performed in a wide range of temperature and density for several low-, mid-, and high-Z plasmas. The effects of temperature and density on the number of populated configurations are discussed and explained.

Summation of the spectra of all partially resolved transition arrays in a supertransition array

It is shown that the contributions of all partially resolved transition arrays (PRTAs) to the spectrum of a supertransition array (STA) may be summed by an efficient analytical method. The method is similar to the configurationally resolved super transition array method [G. Hazak and Y. Kurzweil, High Energy Density Phys. 8, 290 (2012)1574-181810.1016/j.hedp.2012.05.001] and avoids the Gaussianity assumption of the partially resolved super transition arrays method [B. G. Wilson, C. A. Iglesias, and M. H. Chen High Energy Density Phys. 14, 67 (2015)1574-181810.1016/j.hedp.2015.02.007], thus yielding an STA spectrum which is resolved down to the PRTA level.

Further stable methods for the calculation of partition functions in the superconfiguration approach

The extension to recursion over holes of the Gilleron and Pain method for calculating partition functions of a canonical ensemble of noninteracting bound electrons is presented as well as a generalization for the efficient computation of collisional line broadening.

Theoretical investigation of the increase in the Rosseland mean opacity for hot dense mixtures

Based on a detailed configuration accounting model with the term structures treated by the unresolved transition array model, a large scale calculation has been performed for the opacities of medium- and high-Z materials and mixtures. Agreement between our calculated results and previous theoretical simulations is obtained. By filling in the low-opacity regions of one material with the high-opacity regions of other materials, the Rosseland mean opacity of their combination will be increased. This should be of great interest to hohlraum design in indirect-drive inertial confinement fusion. Based on our studies, many mixtures, such as Au+Nd, or Ho+Sn, can result in a similar (or higher) increase in the Rosseland mean as the previously proposed Au+Gd mixture.

Generalization of super-transition-array methods to hot dense plasmas by using optimum independent particle reference systems

The computation of superconfiguration partition functions relies upon independent electron statistics, with electron-electron contributions included as an average first-order correction factor. The decomposition into a first-order correction and reference independent electron system has degrees of freedom not exploited by current methods. We present a derivation for the conventional choice of decomposition and propose a different method for obtaining an optimal decomposition for each superconfiguration. This constitutes an alternative procedure to recomputing self-consistent fields for the refinement of superconfiguration partition functions. Numerical results are presented and discussed.

Theoretical study of opacity for a mixture of gold and gadolinium at a high temperature

Using the detailed configuration accounting with the term structures treated by the unresolved transition array model, we have presented a method to calculate the spectral-resolved opacity for high temperature and density plasmas. Due to the fully relativistic treatment, incorporated with the quantum defect theory to handle the huge number of transition arrays from configurations with high principal quantum number, we can calculate the opacity of any medium- and high-Z plasmas conveniently. In the present work, the frequency-dependent opacity and the Rosseland mean opacity are calculated for a mixture of gold and gadolinium at a high temperature, 250 eV, and three densities, 0.1 g/cm(3), 1.0 g/cm(3), and 10.0 g/cm(3). Agreement between our theoretical results and experimental measurements and other theoretical simulations is obtained.