Orbital relaxation effects on temperature diagnostics of mid-Z plasmas

The orbital relaxation effect was studied in the calculations and diagnostics of the L-shell absorption spectra (2p→3d,4d,5d) of iron and bromine plasmas. A detailed level accounting model was developed to calculate the huge number of L-shell absorption lines of the two typical mid-Z plasmas. The orbital sets were generated by the optimizations according to the initial and final states, respectively. It was found that the L-shell line positions agree with the experimental iron and bromine spectra better when the orbital relaxations were included in calculations. Since experimental mid-Z spectra have few detailed line structures, calculations without considering orbital relaxations may misinterpret the spectra and consequently lead to underestimations of the plasma temperatures.     

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利用SHML模型计算了密度为ρ=1g·cm-3、温度为150eV、200eV、250eV、300eV、400eV的Sn等离子体的随光子能量变化的辐射不透明度及Rosseland平均不透明度.分析了不透明度随光子能量变化曲线的吸收峰值(不透明度峰值)与能级跃迁的对应关系.还将Sn的Rosseland平均不透明度与DCA/UTA及STA模型计算结果作了比较,吻合较好.     

Opacity calculations for high-Z plasma in non-local thermodynamic equilibrium

Opacity of high-Z element plasma in non-local thermodynamic equilibrium (NLTE) is calculated. In the calculation, a collisional radiative model in detailed-configuration-accounting (DCA) is applied to population calculations for NLTE plasmas. Configuration-averaged rate coefficients that needed in the rate equations are obtained based on the first order perturbation theory. The Hatree-Fock-Slater self-consistent-field method is used to calculate the electron wave functions. The spin-orbit splitting is included in the spectrum calculations. The unresolved transition array method is used in the opacity calculations. The calculated frequency-dependent opacity of high-Z plasma Lu is presented. The comparison shows that the present spectrum agrees with another theoretical result well except that the present one shifts a little to the lower energy due to its lower mean ionization stage. The effects of highly doubly excited states on ionization balance and on the opacity are investigated. The mean ionization stage increases more than three stages when doubly excited states 5l6l′ and 5l5l′ are not included in the population calculations and the absorption spectrum also shifts to the higher energy.     

The effect of unresolved transition arrays on plasma opacity calculations

Unresolved transition arrays (UTAs) are a method of approximating complex atomic physics in plasma opacity calculations, and as such are very important in modern plasma dynamic simulations. In this paper we use full atomic physics calculations to test various UTA models, paying particular attention to the lineshape and its effect on the mean opacity. We find that a Gaussian lineshape is sufficient provided that the line width is correctly determined. This width can be calculated using existing formulae, or approximated by neglecting correlations between term line energies and strengths or the selection rules on term - term transitions. We have quantified transition array narrowing due to correlations for a set of iron transitions and shown that a simple model for these incurs fairly large random errors. The neglect of the selection rules is also seen to result in random errors of up to an order of magnitude. These results may prove very useful in the future development of opacity codes, in particular those intended to run in line with hydrodynamic simulations.     

稠密Ar等离子体不透明度的计算

用屏蔽氢离子模型计算了冲击压缩产生的温度T～1.8 eV,密度ρ～0.0044 g/cm3稠密氩等离子体随光子能量变化的辐射不透明度,并与实验作了比较,探讨了冲击压缩产生的稠密等离子体中自由-自由吸收、束缚-自由吸收和束缚-束缚吸收对不透明度的贡献.计算结果表明,对冲击压缩产生的稠密等离子体,自由-自由吸收对不透明度的贡献非常大,特别当光子能量较低时(hv～2.0 eV )自由-自由吸收为不透明的主要部分,因此较好地计算自由-自由吸收项对冲击压缩产生的稠密等离子体不透明度的研究是非常重要的.     

Saha’s ionization equation for highZ elements

Saha’s ionization equation has been solved for highZ elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bohr’s formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha’s equation solutions has been checked by comparing theP _T andE _T computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV.     

Opacity and radiative power losses calculations

In this contribution we present results on opacity and radiative power losses in laser-produced plasmas. We focus our attention on the inner shell transition array 1s–2p in an aluminum plasma. At high densities, electron, Doppler and ion Stark broadening play a role in line merging. This is why the PPP line-shape code developed at Université de Provence was adapted to calculate opacity and radiative power losses in Al and Ge ions. Atomic physics data required in PPP calculations is provided by an MCDF code. Comparison with experiments is discussed.     

Anomalous photo-ionization of 4d shell in medium-Z ionized atoms

Photoionization (PI) cross sections (PICS) are necessary for the simulation of astrophysical and ICF plasmas. In order to be used in plasma modeling, the PICS are usually fit to simple analytical formulas. We observed an unusual spectral shape of the PICS of the 4d shell of ionized Xe and other elements, computed with different codes: a local minimum occurs around twice the threshold energy. We explain this phenomenon as interference between the bound 4d wavefunction and the free electron wavefunction, which is similar to the Cooper minima for neutral atoms. Consequently, the usual fitting formulas, which consist of a combination of inverse powers of the frequency beyond threshold, may yield rates for PI and radiative recombination (RR) that are incorrect by orders of magnitude. A new fitting algorithm is proposed and is included in the latest version of HULLAC.v9.5.     

The relativistic virial theorem in plasma EOS calculations

A method is presented for accurate calculation of equation of state (EOS) for warm dense matter. The method extends an approach presented recently, based on the adjustment of the correlation energy to impose consistency between two pressure representations: the volume derivative of the free energy and the relativistic virial theorem. In this work we show that the free energy of any neutral system obeys a fundamental differential equation, which bypasses the correlation specifics and serves as a basis to enhance EOS approximations. Specifically, we start with LDA calculations and improve the results significantly using this equation with a boundary condition at the zero pressure point. The method retains the emphasis on thermal excitations, but connects to the appropriate results at low temperatures. It effectively compensates for simplifications, including the use of a spherical model to account for global solid structure effects. EOS and opacities are calculated on the same footing for low to high Z elements and in large domains of density and temperature without recourse to parametric fitting procedures. Excellent agreement is obtained with experiments. Finally the method is applied successfully to calculate EOS and opacities for mixtures. Results for C–H mixture are compared with other calculations.     

Measuring thickness of translucent plastic by scanner

Thickness measurement is important in various engineering fields. The several methods have been used to measure the thickness. This work explains a novel method for measuring the thickness of translucent plastic materials using scanner. The plastic samples were scanned against a white and a black background and the RGB parameters of obtained images were used to measure the opacity. Then, the thickness was calculated using relationship between thickness and opacity of samples. The best thickness prediction was obtained using a 3rd polynomial regression with the XYZ parameter.