Jean-Christophe Pain

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.

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.

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.

Self-consistent approach for the thermodynamics of ions in dense plasmas in the superconfiguration approximation

Abstract We propose a new thermodynamic approach to ions in dense plasmas taking into account the screening by free electrons. The ions in fundamental and excited states are represented by a group of superconfigurations. Each superconfiguration containing an integer number of bound electrons is totally screened by free electrons in a Wigner–Seitz (WS) sphere. The minimisation of the plasma free energy with respect to the WS radii of the ions, under the condition that the specific mass of the plasma is preserved, leads to the equality of the electronic pressure for all ions. This pressure, as well as the WS radii and the distribution of ionic probabilities, are calculated by iteration. In this way, our approach not only gives the charge neutrality of the plasma, but also assures that the plasma environment is the same for each ion. In principle, the proposed approach allows one to apply the superconfiguration method to calculate radiative properties of plasmas for higher densities than those encountered in transmission experiments. Numerical examples for nickel, aluminium and samarium plasmas will be given. Comparisons with results from the previous statistical approach using the same WS radius for each ion charge state will also be discussed.

Quantum mechanical model for the study of pressure ionization in the superconfiguration approach

The knowledge of plasma equation of state and photoabsorption requires suitable and realistic models for the description of ions. The number of relevant electronic configurations of ions in hot dense plasmas can be immense (increasing with atomic number Z). In such cases, calculations relying on the superconfiguration approximation appear to be among the best statistical approaches to photoabsorption in plasmas. The superconfiguration approximation enables one to perform rapid calculation of averages over all possible configurations representing excited states of bound electrons. We present a thermodynamically consistent model involving detailed screened ions (described by superconfigurations) in plasmas. The density effects are introduced via the ion-sphere model. In the usual approaches, bound electrons are treated quantum mechanically while free electrons are described within the framework of semi-classical Thomas–Fermi theory. Such a hybrid treatment can lead to discontinuities in the thermodynamic quantities when pressure ionization occurs. We propose a model in which all electrons (bound and free) are treated quantum mechanically. Furthermore, resonances are carefully taken into account in the self-consistent calculation of the electronic structure of each superconfiguration. The model provides the contribution of electrons to the main thermodynamic quantities, together with a treatment of pressure ionization, and gives a better insight into the electronic properties of hot dense plasmas.

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.

Detailed computation of hot-plasma atomic spectra

We present recent evolutions of the detailed opacity code SCO-RCG which combines statistical modelings of levels and lines with fine-structure calculations. The code 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. The Zeeman line profile is modeled by fourth-order Gram-Charlier expansion series, which is a Gaussian multiplied by a linear combination of Hermite polynomials. Electron collisional line broadening is often modeled by a Lorentzian function and one has to calculate the convolution of a Lorentzian with Gram-Charlier distribution for a huge number of spectral lines. Since the numerical cost of the direct convolution would be prohibitive, we propose, in order to obtain the resulting profile, a fast and precise algorithm, relying on a representation of the Gaussian by cubic splines.

Opacity of germanium and silicon in ICF plasmas

Because germanium and silicon may be used as dopants in the ablator of ignition target, the knowledge of their opacities is crucial. We have calculated the opacity by using two approaches. The first one utilizes a detailed line calculation in which the atomic database is provided by the MCDF code. A lineshape code was then adapted to the calculation of opacity profiles. Because the calculation time is prohibitive when the number of lines is huge, a second approach, combining detailed line calculations and statistical calculations is used. This approach necessitates much smaller calculation than the first one and is then well suited for extensive calculations. The monochromatic opacity and the Rosseland and Planck mean opacities are calculated for various relevant densities and temperatures.

Regularities and symmetries in atomic structure and spectra

Abstract The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of levels and lines. In the past, much attention was paid to the distribution of energy levels (Wigner surmise, random-matrix model…). However, information about the distribution of the lines (energy and strength) is lacking. Thirty years ago, Learner found empirically an unexpected law: the logarithm of the number of lines whose intensities lie between 2kI0 and 2k+1I0, I0 being a reference intensity and k an integer, is a decreasing linear function of k. In the present work, the fractal nature of such an intriguing regularity is outlined and a calculation of its fractal dimension is proposed. Other peculiarities are also presented, such as the fact that the distribution of line strengths follows Benfords law of anomalous numbers, the existence of additional selection rules (PH coupling), the symmetry with respect to a quarter of the subshell in the spin-adapted space (LL coupling) and the odd–even staggering in the distribution of quantum numbers, pointed out by Bauche and Cosse.