Measurements of extreme uv opacities in hot dense Al, Fe, and Ho

Adaptive Algorithm for the Generation of Superconfigurations in Hot-Plasma Opacity Calculations

In hot plasmas, such as the ones encountered in astrophysics or laser-fusion studies, the number of ionic excited states may become huge, and the relevant electron configurations cannot always be handled individually. The Super Transition Array approach enables one to calculate the massic photo-absorption cross-section (or radiative opacity) in a statistical manner consisting of grouping configurations close in energy into superconfigurations. One of the main issues of the method, beyond its spectral resolution, is the determination of the most relevant configurations that contribute to opacity. In this work, we discuss different aspects of the generation of superconfigurations in a hot plasma and propose a new adaptive algorithm.

Super Transition Arrays: A Tool for Studying Spectral Properties of Hot Plasmas

For the theoretical study of X and extreme-UV spectra of ions in plasmas, quantum mechanics brings more detailed results than statistical physics. However, it is impossible to handle individually the billions of levels that must be taken into account in order to properly describe hot plasmas. Such levels can be gathered into electronic configurations or superconfigurations (groups of configurations) and the corresponding calculations rely on appropriate statistical methods, for local or non-local thermodynamic equilibrium plasmas. In this article we present the basic principles of the Super-Transition-Array approach as well as its practical implementation. During the last decades, calculations performed with the SCO code (Superconfiguration Code for Opacity) have been compared to opacity measurements. The code includes static screening of ions by plasma and is well suited for studying plasma density effects (for example pressure ionization) on opacity and equation of state. The recently developed SCO-RCG code (Superconfiguration Code for Opacity combined with Robert Cowan’s “G” subroutine) combines statistical methods from SCO and fine-structure (detailed-level-accounting) calculations using subroutine RCG from Cowan’s code. SCO-RCG enables us to obtain very detailed spectra and to significantly improve the interpretation of experimental spectra. The Super-Transition-Array formalism is still the cornerstone of several opacity codes, and new ideas are emerging, such as the Configurationally Resolved-Super-Transition-Array approach or the extension of the Partially Resolved-Transition-Array concept to the superconfiguration method.

Systematic Study of L-Shell Opacity at Stellar Interior Temperatures

The first systematic study of opacity dependence on atomic number at stellar interior temperatures is used to evaluate discrepancies between measured and modeled iron opacity [J. E. Bailey et al., Nature (London) 517, 56 (2015)NATUAS0028-083610.1038/nature14048]. High-temperature (>180  eV) chromium and nickel opacities are measured with ±6%-10% uncertainty, using the same methods employed in the previous iron experiments. The 10%-20% experiment reproducibility demonstrates experiment reliability. The overall model-data disagreements are smaller than for iron. However, the systematic study reveals shortcomings in models for density effects, excited states, and open L-shell configurations. The 30%-45% underestimate in the modeled quasicontinuum opacity at short wavelengths was observed only from iron and only at temperature above 180 eV. Thus, either opacity theories are missing physics that has nonmonotonic dependence on the number of bound electrons or there is an experimental flaw unique to the iron measurement at temperatures above 180 eV.

Detailed Opacity Calculations for Astrophysical Applications

Nowadays, several opacity codes are able to provide data for stellar structure models, but the computed opacities may show significant differences. In this work, we present state-of-the-art precise spectral opacity calculations, illustrated by stellar applications. The essential role of laboratory experiments to check the quality of the computed data is underlined. We review some X-ray and XUV laser and Z-pinch photo-absorption measurements as well as X-ray emission spectroscopy experiments involving hot dense plasmas produced by ultra-high-intensity laser irradiation. The measured spectra are systematically compared with the fine-structure opacity code SCO-RCG. The focus is on iron, due to its crucial role in understanding asteroseismic observations of β Cephei-type and Slowly Pulsating B stars, as well as of the Sun. For instance, in β Cephei-type stars, the iron-group opacity peak excites acoustic modes through the “kappa-mechanism”. Particular attention is paid to the higher-than-predicted iron opacity measured at the Sandia Z-machine at solar interior conditions. We discuss some theoretical aspects such as density effects, photo-ionization, autoionization or the “filling-the-gap” effect of highly excited states.

Extreme ultraviolet spectrometer for the Shenguang III laser facility

An extreme ultraviolet spectrometer has been developed for high-energy density physics experiments at the Shenguang-III (SG-III) laser facility. Alternative use of two different varied-line-spacing gratings covers a wavelength range of 10-260 Å. A newly developed x-ray framing camera with single wide strip line is designed to record time-gated spectra with ~70 ps temporal resolution and 20 lp/mm spatial resolution. The width of the strip line is up to 20 mm, enhancing the capability of the spatial resolving measurements. All components of the x-ray framing camera are roomed in an aluminum air box. The whole spectrometer is mounted on a diagnostic instrument manipulator at the SG-III laser facility for the first time. A new alignment method for the spectrometer based on the superimposition of two laser focal spots is developed. The approaches of the alignment including offline and online two steps are described. A carbon spectrum and an aluminum spectrum have been successfully recorded by the spectrometer using 2400 l/mm and 1200 l/mm gratings, respectively. The experimental spectral lines show that the spectral resolution of the spectrometer is about 0.2 Å and 1 Å for the 2400 l/mm and 1200 l/mm gratings, respectively. A theoretical calculation was carried out to estimate the maximum resolving power of the spectrometer.

Opacity of iron, nickel, and copper plasmas in the x-ray wavelength range: theoretical interpretation of 2p-3d absorption spectra

This paper deals with theoretical studies on the 2p-3d absorption in iron, nickel, and copper plasmas related to LULI2000 (Laboratoire pour l'Utilisation des Lasers Intenses, 2000J facility) measurements in which target temperatures were of the order of 20 eV and plasma densities were in the range 0.004-0.01 g/cm(3). The radiatively heated targets were close to local thermodynamic equilibrium (LTE). The structure of 2p-3d transitions has been studied with the help of the statistical superconfiguration opacity code SCO and with the fine-structure atomic physics codes HULLAC and FAC. A new mixed version of the sco code allowing one to treat part of the configurations by detailed calculation based on the Cowan's code RCG has been also used in these comparisons. Special attention was paid to comparisons between theory and experiment concerning the term features which cannot be reproduced by SCO. The differences in the spin-orbit splitting and the statistical (thermal) broadening of the 2p-3d transitions have been investigated as a function of the atomic number Z. It appears that at the conditions of the experiment the role of the term and configuration broadening was different in the three analyzed elements, this broadening being sensitive to the atomic number. Some effects of the temperature gradients and possible non-LTE effects have been studied with the help of the radiative-collisional code SCRIC. The sensitivity of the 2p-3d structures with respect to temperature and density in medium-Z plasmas may be helpful for diagnostics of LTE plasmas especially in future experiments on the Δn=0 absorption in medium-Z plasmas for astrophysical applications.

Resonant and near-threshold photoionization cross sections of Fe14+

Photoionization (PI) of Fe14+ in the range from 450 to 1100 eV was measured at the BESSY II storage ring using an electron beam ion trap achieving high target-ion area densities of 10(10)  cm(-2). Photoabsorption by this ion is observed in astrophysical spectra and plasmas, but until now cross sections and resonance energies could only be provided by calculations. We reach a resolving power E/ΔE of at least 6500, outstanding in the present energy range, which enables benchmarking and improving the most advanced theories for PI of ions in high charge states.

Diagnostic development in precise opacity measurement of radiatively heated Al plasma on Shenguang II laser facility

Simultaneous measurements of the self-emission spectrum, the backlighting source spectrum, and the transmission spectrum in one shot, which reduce the experimental uncertainties from shot-to-shot fluctuation, are essential for precise opacity experiments. In order to achieve precise absorption spectrum of Al plasmas, a special half sample sandwich target was designed and short backlighter was used to provide time- and space-resolving diagnostics on the Shenguang II high power laser facility. In the measurement, a cylindrical cavity with CH foam baffles was used to provide a clean x-ray radiation environment for sample heating. The x-ray source spectrum, the transmission spectrum, and the self-emission spectrum of the soft x-ray heated Al sample were recorded in one shot with a penta-erythritol tetrakis (hydroxymethy) methane C(CH(2)OH)(4) (PET) crystal spectrometer by using the point-projection method. Experimental results have been compared with the calculation results of a detailed level accounting opacity code.

Radiative heating of plastic-tamped aluminum foil by x rays from a foam-buffered hohlraum

The time dependence of the x-ray absorption of aluminum samples heated with intense radiation sources from a foam-buffered gold hohlraum has been studied in this work. Hydrodynamic simulations were used to illustrate the plasma conditions in the plastic-tamped aluminum foils contained in this type of hohlraum. Experiments were conducted to measure the K -shell x-ray absorption spectra of the aluminum sample. With densities taken from the hydrodynamic simulations, electron temperatures were then inferred by fitting the measured absorption spectra with detailed-term-accounting calculations. The inferred temperatures have a maximum of about 93eV and were found to agree within 25% with the simulated results at times after 1ns , indicating that the use of foam shields, together with a compact cavity, has created a clean and high-temperature radiation source preferable to opacity measurements.

Spectrally resolved and Rosseland and Planck mean opacities of iron plasmas at temperatures above 100 eV: a systematic study

The radiative opacity of iron plasmas at high temperatures is very important in astrophysics. The spectrally resolved radiative opacity and Rosseland and Planck means were investigated by using the detailed-level-accounting (DLA) model for iron plasmas at high temperatures and a variety of density. The accuracy of atomic data such as energy levels and transition probabilities is checked by comparison with data from the National Institute of Standards and Technology. The transmission of iron plasma at a temperature of 156 eV and an electron density of 6.9 x 10(21) cm(-3) is studied in detail and compared with results of a recent experiment [Bailey et al., Phys. Rev. Lett. 99, 265002 (2007)] and other theoretical results. General good agreement is found between our DLA transmission and the experimental and other theoretical results. By using our developed DLA model, we can deduce valuable information on the physical condition of the plasma created in the experiment. The information includes the fractional distribution of different ion stages and whether the plasma is in local thermodynamic equilibrium or not. Illustrative results are given for three isothermal sequences of 100, 150, and 200 eV with different mass densities and for three isodensity sequences of 0.1, 0.05, and 0.01 g/cm3 with different temperatures. The Rosseland and Planck mean opacities are compared with other theoretical results obtained by the Los Alamos light element detailed configuration opacity code.

Detailed diagnostics for a hot bromine plasma by the open M-shell opacity

The experimental transmission spectrum of a hot bromine plasma [J. E. Bailey, J. Quant. Spectrosc. Radiat. Transf. 81, 31 (2003)] has been simulated by using a detailed level accounting model (DLA). With assumption of the local thermodynamic equilibrium, the major absorption lines of the experimental spectrum are well reproduced by the present DLA calculation, and the details of the absorption line shapes are used to determine the temperature of the plasma. In contrast to the results of two former statistical models, where the temperature was determined via a global fitting to the experimental data, the present DLA diagnoses the plasma temperature by the line ratios of different charge states in the 2p-->3d transition groups resulting in a temperature of 37 eV . It is shown that a change of 1 eV in temperature could cause perceptible changes in the simulated spectrum. It is also shown that the 2 p1/2 -->3 d3/2 absorptions have been overestimated by the statistical models.

Influence of detailed line treatment on the opacity of iron plasmas in the 2p-3d energy region

The transmission spectrum has been calculated using a detailed-level-accounting model for iron plasmas in local thermodynamic equilibrium in the 2p-3d excitation energy region. The calculation is motivated by the large difference between the theories obtained by statistical methods such as unresolved transition array and superconfiguration transition array and the experiment reported in the literature. Detailed studies have been carried out on the effects of the width of individual lines and configuration interaction. The results show that the saturation of individual lines is evident in the transmission. These effects should be considered carefully to obtain an accurate opacity or transmission. In view of the uncertainties in the experiment, rather good agreement is found between our theoretical result and the experiment when these effects are taken into account in the calculation.

Radiative opacities and configuration interaction effects of hot iron plasma using a detailed term accounting model

We have calculated the radiative opacities of iron plasma in local thermodynamic equilibrium using a detailed term accounting model. The extensive atomic data are obtained by multiconfiguration Hartree-Fock (MCHF) method, with Breit-Pauli relativistic corrections. Extensive configuration interaction (CI) has been included based on LS coupling to obtain energy levels and the bound-bound transition cross sections. A detailed configuration accounting model is applied to evaluate the bound-free absorption cross sections. We simulate two experimental transmission spectra [G. Winhart et al., Phys. Rev. E 53, R1332 (1996); P. T. Springer et al., J. Quant. Spectrosc. Radiat. Transf. 58, 927 (1997)] to verify our calculation model, one is at a temperature of 22 eV and a density of 10(-2) g/cm(3) and the other is at a temperature of 20 eV and a lower density of 10(-4) g/cm(3). It is shown that the strong CI can effectively change the oscillator strengths in contrast to the single configuration HF method. For both of the two simulated transmission spectra good agreement is obtained between the present MCHF results and the experimental data. Spectrally resolved opacities and Planck and Rosseland mean opacities are also calculated. For the isothermal sequence of T=20 eV, when the density decreases from 10(-2) to 10(-5) g/cm(3), the linewidth also decreases so that the iron transition arrays show more discrete line structures and the linewidth becomes very important to the Rosseland mean opacity.

Detailed-term-accounting approximation calculations of the radiative opacity of aluminum plasmas: a systematic study

The spectrally resolved radiative opacity and the Rosseland and Planck mean opacities are calculated by using the detailed-term-accounting approximation for aluminum plasmas with varieties of density and temperature. The results are presented along a 40 eV isothermal sequence, a 0.01 g/cm(3) isodense sequence, and a sequence with average ionization degree Z* approximately 7.13. Particular attention is given to the influence of the detailed treatment of spectral lines on the Rosseland mean opacity under different thermodynamic conditions. The results show that at densities of 0.004 g/cm(3) and higher, the opacities are not very sensitive to the spectral linewidth within a reasonable range. As examples, the Rosseland mean opacity, which is most sensitive to the detailed linewidth, at 40 eV and 0.004 g/cm(3) changes no more than 15%, when we change the electron impact spectral linewidth artificially by reducing it by 50% or increasing it twice, and at 40 eV and 0.1 g/cm(3) it changes less than 5%. For comparison, we also carried out calculations by using an average atom model. For the Rosseland mean opacities, the two models show quite large differences, in particular at low densities, while for the Planck mean opacities the results of the two models are much closer.

Detailed-term-accounting-approximation calculations of the radiative opacity of laser-produced Al plasmas

An extensive configuration interaction (CI) scheme and the R-matrix method are combined to calculate the radiative opacity for laser-produced aluminum plasma in local thermodynamic equilibrium using the detailed-term-accounting (DTA) approximation. The CI scheme is used to obtain the absorption oscillator strengths of the electric dipole allowed transitions for evaluating the bound-bound absorption cross sections, and the R-matrix method is used to obtain the bound-free absorption (photoionization) cross sections. For an aluminum plasma at a temperature of 20 eV and the density of 0.01 g/cm(3), the Rosseland and Planck mean opacities are calculated to be 4184 and 24891 cm(2)/g, respectively, by integrating the spectrally resolved opacities with Rosseland and Planck weighting functions. The two mean opacities are also obtained by using the average atom model, and they are 22520 and 30402 cm(2)/g, respectively. The optical transmission from the photon energy of 70-250 eV, which was experimentally measured by Winhart et al. [G. Winhart et al. Phys. Rev. E 53, R1332 (1996)], is also calculated. Generally good agreement is found between our DTA and experimental transmission. Our theoretical result reproduces all structures shown in the experiment, whereas some of the structures near the higher energy edge did not show up in some other opacity models. These structures are attributed to the detailed treatment of the photoionization process.