F. Gilleron

Opacity Studies of Iron in the 15-30eV Temperature Range

Absorption of the 2p-3d transitions of iron has been measured using point projection spectroscopy. Thin C tamped Fe foils were heated around 20 eV by X-rays generated in gold spherical hohlraums irradiated by the high-power laser ASTERIX IV. Absorption of Fe V to Fe X has been observed in the spectral vicinity of 730 eV (17 A). The Ag backlighter source and absorbed spectra were recorded on the same shot by a TlAP crystal spectrograph. The experimental spectra have been reproduced by the two superconfiguration local thermodynamic equilibrium codes SCO and STA. Detailed statistical calculations of the different ionic structures have also been performed with the Spin Orbit Split Arrays method, allowing the determination of ion populations. The electron temperature and average ionization obtained by fitting the experiment with the different calculations were compared with radiative hydrodynamic simulations.

A consistent approach for mixed detailed and statistical calculation of opacities in hot plasmas

Abstract Absorption and emission spectra of plasmas with multicharged-ions contain transition arrays with a huge number of coalescent electric-dipole (E1) lines, which are well suited for treatment by the unresolved transition array and derivative methods. But, some transition arrays show detailed features whose description requires diagonalization of the Hamiltonian matrix. We developed a hybrid opacity code, called SCORCG, which combines statistical approaches with fine-structure calculations consistently. Data required for the computation of detailed transition arrays (atomic configurations and atomic radial integrals) are calculated by the superconfiguration code SCO (Super-Configuration Opacity), which provides an accurate description of the plasma screening effects on the wave-functions. Level energies as well as position and strength of spectral lines are computed by an adapted RCG routine of R. D. Cowan. The resulting code provides opacities for hot plasmas and can handle mid-Z elements. The code is also a powerful tool for the interpretation of recent laser and Z-pinch experimental spectra, as well as for validation of statistical methods.

Non-LTE opacity calculations with n − l splitting for radiative hydrodynamic codes

Abstract We present a new method for calculating opacities in a non-LTE plasma, based on modeling of the one-electron atomic potential in the framework of the “average atom” approach. In this model, the collisional-radiative equations of an average ion are solved and the resulting screened charges are used to reconstruct the one-electron atomic potential. Average atom wave functions, oscillator strengths and Slater integrals are calculated by quantum mechanics in the reconstructed potential. Dipolar matrix elements have improved values compared to hydrogenic formulas, especially for orbitals close to the ion core. Configuration accounting is done using the independent electron approximation and perturbation theory. Our method, compared to previous LTE average atom calculations gives realistic values of plasma opacities, especially in the soft x-ray range where the Δn = 0 transitions play an important role. A comparison of radiative hydrodynamics simulations performed with opacities calculated in the n and n − l representation shows significant differences.

Radiative properties of stellar plasmas and open challenges

The lifetime of solar-like stars, the envelope structure of more massive stars, and stellar acoustic frequencies largely depend on the radiative properties of the stellar plasma. Up to now, these complex quantities have been estimated only theoretically. The development of the powerful tools of helio- and astero- seismology has made it possible to gain insights on the interiors of stars. Consequently, increased emphasis is now placed on knowledge of the monochromatic opacity coefficients. Here we review how these radiative properties play a role, and where they are most important. We then concentrate specifically on the envelopes of β Cephei variable stars. We discuss the dispersion of eight different theoretical estimates of the monochromatic opacity spectrum and the challenges we need to face to check these calculations experimentally.

Radiative heating of B, Al and Ni thin foils at 15–25 eV temperatures

Several thin foils have been heated by X-ray radiation emitted by a small gold cavity irradiated with the LULI facility Nd glass laser. The foils were heated to moderate temperatures (10–25 eV) in conditions near local thermodynamic equilibrium. Measurements of the absorption of Kα transitions of aluminum, of the K-shell transitions of boron, and of the n=2–3 and 4 transitions of nickel are reported. A 5000 l/mm transmission grating spectrograph recorded the boron data, and a flat thallium hydrogen phthalate (TlAP) crystal was used for aluminum and nickel absorption measurements. The nickel and aluminum spectra indicate a higher temperature (22–25 eV) than the boron case (14 eV), explained by a difference in the absorption spectra of these elements. In the Ni case the measured 2p-3d spin–orbit–split absorption structures compared well with theoretical spectra obtained with the SCO superconfiguration code using the spin orbit split transition arrays formalism (SOSA). The heating of the foils as calculated with radiative hydrodynamic simulations is very similar to the experimental data.

Accounting for highly excited states in detailed opacity calculations

Abstract In multiply-charged ion plasmas, a significant number of electrons may occupy high-energy orbitals. These “Rydberg” electrons, when they act as spectators, are responsible for a number of satellites of X-ray absorption or emission lines, yielding a broadening of the red wing of the resonance lines. The contribution of such satellite lines may be important, because of the high degeneracy of the relevant excited configurations which give these large Boltzmann weights. However, it is in general difficult to take these configurations into account since they are likely to give rise to a large number of lines. We propose to model the perturbation induced by the spectators in a way similar to the Partially-Resolved-Transition-Array approach recently published by C. Iglesias. It consists in a partial detailed-line-accounting calculation in which the effect of the Rydberg spectators is included through a shift and width, expressed in terms of the canonical partition functions, which are key-ingredients of the Super-Transition-Arrays model. The resulting method can a priori be used in any detailed-configuration/line-accounting opacity code.

Absorption measurements of radiatively heated multi-layered Al/Ni foils

Abstract Mixtures of light and mid- Z elements have been used to measure the absorption of the mid- Z element Ni, the temperature is inferred from the K-shell absorption of the light element Al. Here we test this method by comparing the temperatures deduced from Al K α transitions and nickel L-shell absorption spectra in Al/Ni multilayers and bilayers. The ionisation state is obtained by comparison of the Al and Ni spectra with calculations assuming local thermodynamic equilibrium. The temperatures obtained from the experiment are compared with hydrodynamic simulations predictions. Simulation code results show that the density differs by a factor of 2 in the two elements. This has to be taken into account in the determination of the temperature.

Absorption of local thermodynamic equilibrium aluminum at different densities

Abstract Increasing the range of plasma parameters accessible for laboratory absorption coefficients measurements is of interest for astrophysical applications. Aluminum is of special interest as its 1s–2p inner shell absorption transitions permit one to precisely determine the ionization balance that is strongly dependent on the electron temperature. A method to increase the density of the probed sample was tested on aluminum confined by carbon tampers of different thickness (8– 70 μg / cm 2 ). This created a density increase in the aluminum of a factor of ∼10. Measurements showed that the aluminum ionization decreases substantially with increasing carbon thickness. Radiative hydrodynamic simulations showed that density and temperature gradients could not be neglected and had to be taken into account in calculating the absorption structures with the atomic physics code HULLAC. Very good agreement between theory and experiment was obtained by coupling HULLAC with hydrodynamic simulations.

Statistics of electric-quadrupole lines in atomic spectra

In hot plasmas, a temperature of a few tens of eV is sufficient for producing highly stripped ions where multipole transitions become important. At low density, the transitions from tightly bound inner shells lead to electric-quadrupole (E2) lines which are comparable in strength with electric-dipole ones. In this work, we propose analytical formulas for the estimation of the number of E2 lines in a transition array. Such expressions rely on statistical descriptions of electron states and J-levels. A generalized ‘J-file’ sum rule for E2 lines and the strength-weighted shift and variance of the line energies of a transition array nlN + 1 → nlNn′l′ of inter-configuration E2 lines are also presented.

The hybrid detailed / statistical opacity code SCO-RCG: New developments and applications

We present the hybrid opacity code SCO-RCG which combines statistical approaches with fine-structure calculations. Radial integrals needed for the computation of detailed transition arrays are calculated by the code SCO (Super-configuration Code for Opacity), which calculates atomic structure at finite temperature and density, taking into account plasma effects on the wave-functions. Levels and spectral lines are then computed by an adapted RCG routine of R. D. Cowan. SCO-RCG now includes the Partially Resolved Transition Array model, which allows one to replace a complex transition array by a small-scale detailed calculation preserving energy and variance of the genuine transition array and yielding improved high-order moments. An approximate method for studying the impact of strong magnetic field on opacity and emissivity was also recently implemented.