A Configurationally-Resolved-Super-Transition-Arrays method for calculation of the spectral absorption coefficient in hot plasmas

Abstract

a b s t r a c tA new method, 'Configurationally-Resolved-Super-Transition-Arrays', for calculation of the spectral absorption coefficient in hot plasmas is presented. In the new method, the spectrum of each SuperTransition-Array is evaluated as the Fourier transform of a single Complex Pseudo Partition Function, which represents the exact analytical sum of the contributions of all constituting unresolved transition arrays sharing the same set of one-electron solutions. Thus, in the new method, the spectrum of each Super-Transition-Array is resolved down to the level of the (unresolved) transition arrays. It is shown that the corresponding spectrum, evaluated by the traditional Super-Transition-Arrays (STA) method [14], is just the coarse-grained Gaussian approximation of the Configurationally-Resolved-Super-TransitionArray. A new computer program is presented, capable of evaluating the absorption coefficient by both the new configurationally resolved and the traditional Gaussian Super-Transition-Arrays methods. A numerical example of gold at temperature 1 keV and density 0.5 gr/cm 3 , is presented, demonstrating the simplicity, efficiency and accuracy of the new method.

Key to understanding supersonic radiative Marshak waves using simple models and advanced simulations

“…Although the experimental setups that were examined employed different foams, densities and compounds, doping, dimensions, etc., the simple semi-analytic model reproduces the experimental data very well, with differences of less than 10%. The model is based on the Using the exact opacity, CRSTA tables [36,37] and SESAME tables [38], or QEOS [39] EOS tables, we have fitted for every material its numerical parameters in the relevant experimental regime (by mean of temperatures and densities), for using by the different simple semi-analytic models. The parameters for the foams are above the double-line, and for the coats are beneath the double-line.…”

“…In the current work, we are interested in foam parameters (rather then solid gold as in [27]), so g, α and λ were extracted by fitting Eq. 3a to the opacity spectrum calculated using CRSTA [36,37]. f , β and µ were extracted by fitting Eq.…”

“…We note that this expression is for supersonic heat-wave (without hydrodynamic motion), since the Be is optically thin, and in ≈ 200eV it is mostly supersonic. As in the foams, the parameters for the opacity was fitted to CRSTA tables [36,37], and for the EOS, SESAME table [38]. The different parameters for the different materials (Gold, Be) are presented in the Appendix.…”

Computation of Atomic Astrophysical Opacities

“…In these methods, the transition array between two configurations is usually reduced to a single Gaussian but can be replaced by a sum of partially resolved transition arrays represented by Gaussians [79,80] that are then sampled statistically to simulate detailed line accounting [81]. For heavy ions where UTAs still fall short, a higher-level extension referred to as the super-transition-array (STA) method involves the grouping of many configurations into a single superconfiguration, whereby the UTA summation to a single STA can be performed analytically [82][83][84]. Recent STA calculations of the RMO in the solar convection zone boundary agree very well with both OP and OPAL, and predict a meager heavy-element (Z > 28) contribution [26].…”

Accounting for highly excited states in detailed opacity calculations

“…Some other approaches were proposed to overcome the limits of statistical methods. For instance, in order to improve the accuracy of the STA approach, Hazak and Kurzweil [29] developed an interesting method, named CRSTA (Configurationally Resolved Super Transition Arrays); however, its degree of refinement is limited to the configurations, the terms structure being included statistically through UTA widths and shifts [30].…”