Nearly a century ago it was recognized that radiation absorption by stellar matter controls the internal temperature profiles within stars. Laboratory opacity measurements, however, have never been performed at stellar interior conditions, introducing uncertainties in stellar models. A particular problem arose when refined photosphere spectral analysis led to reductions of 30-50 per cent in the inferred amounts of carbon, nitrogen and oxygen in the Sun. Standard solar models using the revised element abundances disagree with helioseismic observations that determine the internal solar structure using acoustic oscillations. This could be resolved if the true mean opacity for the solar interior matter were roughly 15 per cent higher than predicted, because increased opacity compensates for the decreased element abundances. Iron accounts for a quarter of the total opacity at the solar radiation/convection zone boundary. Here we report measurements of wavelength-resolved iron opacity at electron temperatures of 1.9-2.3 million kelvin and electron densities of (0.7-4.0) × 10(22) per cubic centimetre, conditions very similar to those in the solar region that affects the discrepancy the most: the radiation/convection zone boundary. The measured wavelength-dependent opacity is 30-400 per cent higher than predicted. This represents roughly half the change in the mean opacity needed to resolve the solar discrepancy, even though iron is only one of many elements that contribute to opacity.

Theoretical opacities are required for calculating energy transport in plasmas. In particular, understanding stellar interiors, inertial fusion, and Z pinches depends on the opacities of mid-atomic-number elements over a wide range of temperatures. The 150–300 eV temperature range is particularly interesting. The opacity models are complex and experimental validation is crucial. For example, solar models presently disagree with helioseismology and one possible explanation is inadequate theoretical opacities. Testing these opacities requires well-characterized plasmas at temperatures high enough to produce the ion charge states that exist in the sun. Typical opacity experiments heat a sample using x rays and measure the spectrally resolved transmission with a backlight. The difficulty grows as the temperature increases because the heating x-ray source must supply more energy and the backlight must be bright enough to overwhelm the plasma self-emission. These problems can be overcome with the new generation of high energy density (HED) facilities. For example, recent experiments at Sandia’s Z facility [M. K. Matzen et al., Phys. Plasmas 12, 055503 (2005)] measured the transmission of a mixed Mg and Fe plasma heated to 156±6 eV. This capability will also advance opacity science for other HED plasmas. This tutorial reviews experimental methods for testing opacity models, including experiment design, transmission measurement methods, accuracy evaluation, and plasma diagnostics. The solar interior serves as a focal problem and Z facility experiments illustrate the techniques.

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The Gibbs-Bogolyubov inequality is used to establish a mapping between the Yukawa system and both the hard-sphere and the one-component reference systems. The transport coefficients of self-diffusion, shear viscosity, and thermal conductivity are computed for the Yukawa fluid using known properties of the reference systems. Comparisons are made with simulation results. For sufficiently strong screening, the hard-sphere reference system yields a lower upper bound of the Yukawa Helmholtz free energy and a better estimate of the Yukawa transport coefficients.

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The aim of this paper is to provide experimental data on various expanded elements in the warm dense matter regime. The experiments were done on the experimental facility “enceinte à plasma isochore” and are evaluated through a thorough comparison with ab initio calculations, average-atom codes, and chemical models. This comparison allows for the evaluation of the experimental temperatures that are not accessible to the measurements and permits the building of useful data tables gathering energy, pressure, conductivity, and temperatures. We summarize experiments performed on aluminum (0.1 and 0.3 g/cm3), nickel (0.2 g/cm3), titanium (0.1 g/cm3), copper (0.3 and 0.5 g/cm3), silver (0.43 g/cm3), gold (0.5 g/cm3), boron (0.094 g/cm3), and silicon (0.21 g/cm3) for temperatures ranging from 0.5 eV to 3-4 eV.

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This paper presents an improved analytical expression for the x-ray dynamic structure factor from a dense plasma which includes the effects of weakly bound electrons. This result can be applied to describe scattering from low to moderate Z plasmas, and it covers the entire range of plasma conditions that can be found in inertial confinement fusion experiments, from ideal to degenerate up to moderately coupled systems. The theory is used to interpret x-ray scattering experiments from solid density carbon plasmas and to extract accurate measurements of electron temperature, electron density, and charge state. The experimental results are applied to validate various equation-of-state models for carbon plasmas.