Calcul des opacités de plasmas denses. Eclatement du spectre dû aux interactions électroniques dans le cas du fer

Radiative transfer is often the dominant energy transport channel in inertial confinement fusion experiments. It is a basic process needed in order to understand the behaviour of astrophysical plasmas, like stellar atmospheres and the inner parts of stars. Opacities account for photon absorption in matter. During decades, opacities have been numerically calculated on the basis of different atomic models. Before the nineties, no direct measurement of opacities spectra has been performed. The first experimental results were carried out by British and American groups after 1989. Especially interesting was the measurement of relative transmission spectra, obtained by Da Silva's group, of iron plasma at 25 eV temperature and 8-10-3 g/cm3 density. The features of experimental spectrum (main effects coming from bound-bound transitions, spectrum complexity due to relatively high atomic number) make it especially useful for verification of theoretic models. One of Our objectives is to obtain this spectrum via Our theoretical calculations. This work starts with a short review of the average atom model followed by derivation of photon absorption cross-section formula in the independent electrons approximation. Next, we introduce the Detailed Configuration Accounting approximation. This approximation describes the different ionicity and excitations states of an atom of the plasma in terms of electronic configurations. The absorption cross-section formula is derived in the Detailed Configuration Accounting approximation. This formula is based on configurations average energies and configurations probabilities. The average atom model allows us to determine the mean ionicity of atoms and the mean occupation numbers of atomic orbitals. It provides also the occupation numbers of the most probable atom in the plasma. From the fluctuation theory applied to occupation numbers, we get the probabilities of different electronic configurations. The probability formula results from the study of the second variation of the grand thermodynamic potential for a plasma atom. The Hartree-Fock theory for finite temperature is used to describe the atomic equilibrium. We show the effect of interactions between bound and free electrons on the bound levels correlations for a iron plasma of different temperatures and densities. For 10 eV or more and at solid density, the inclusion of interactions between bound levels may decrease by 60% the autocorrelation of the 3d level. The effect of free electrons is less important. The interactions between electrons decrease the variance of the ionic probability distribution for a iron plasma at 50 eV or 100 eV and at solid density. In the Detailed Configuration Accounting, the energies and the oscillator strengths of the N electron (where N stays for the number of bound electrons) atomic states are averaged for each electronic configurations. Without this approximation, the N electron states have to be explicitly calculated for each electronic configuration. This approach is called Detailed Term Accounting. If we neglect the spin-orbit coupling, the energies and the N electron eigenstates are calculated by simultaneous diagonalisation of the atomic hamiltonien H and the angular momentum operators L→2, Lz, S→2 and Sz. When the spin-orbit coupling is included, the H, J→2 and Jz are diagonalised. Finally, the absorption cross-section is calculated in this approximation. One of the main conclusions of this work, found in the case of Detailed Term Accounting, calculations, is a spectrum similar to the one obtained in the Da Silva experiment. For the same plasma, the Detailed Configuration Accounting calculation failed to recover a spectrum similar to the experimental one. The relevance of the Detailed Term Accounting model has been already pointed out in the American work of Iglesias and Rogers. Let us stress however that their code OPAL is using a different model for plasma equilibrium. The Rosseland mean opacity is calculated for a iron plasma at 0.01 g/cm3 and temperatures of 20, 40, 80 and 150 eV. The effects due to Detailed Term Accounting are less important for higher temperature.

Blenski, Tomasz Jan
Lausanne, EPFL


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