Olivier Peyrusse

Analysis of a non-LTE xenon spectrum by means of the model of superconfiguration temperatures

Abstract The method of superconfiguration (SC) temperatures is used for interpreting the experimental spectrum of a non-LTE xenon plasma with kT e =450 eV and n e =1.2×10 20 cm −3 . 109 SCs are selected for representing the eight relevant ions. The coefficients of the linear equations for the populations and the temperatures of these SCs are deduced from the rates of the atomic processes between the constituent configurations. The obtained ion balance is close to the results of previous calculations by other methods. The simulated spectrum agrees very well with the experimental spectrum.

Calculation of the charge state distribution of a highly ionized coronal Au plasma

We present the calculation of the charge state distribution of a highly ionized gold plasma in coronal conditions. The result is consistent with a previously published measurement done at the Livermore electron beam ion trap EBIT-II (Wong et al 2003 Phys. Rev. Lett. 90 235001) which raised many questions concerning the capabilities of the modelling codes to predict the charge state of a high-Z element under these conditions. By using a refinement procedure for the electronic description of these complex ions, we obtain a result which converges to a limiting value which agrees with the experimental results.

Density-induced continuum resonances and quasi-bound states in the collisional-radiative equilibrium of dense plasmas

The aim of this work is to improve the treatment of density effects in non-local thermodynamic equilibrium plasmas. The density effect on atomic structure (wavefunctions and energy levels) is modelled by an ion-sphere potential. The modification of the atomic potential, continuum lowering and appearance of resonances are presented. In particular, we show that the continuum resonances are linked to the electrons in the subshells passed into the continuum. Their presence determines the existence of partially bound configurations, which must be taken into account in the collisional-radiative model. We introduce in the set of rate equations a supplementary ionization process due to the plasma environment. This process (and its inverse) enters into the balance of all the other processes. It is equivalent to tunnelling ionization where an outer electron located above the ionization threshold (and trapped by the potential barrier) crosses the barrier. As an application, we studied the influence of temperature and density on the average ionization and the ionic populations of a carbon plasma. We compared these calculations with the traditional method based on the chemical picture with continuum lowering.

A superconfiguration approach to multi-electron ionization of Xe under strong x-ray irradiation

The production of highly ionized states in xenon under intense x-ray irradiation, is discussed with the help of specific calculations. The approach, which retains only one-photon absorption processes (photoionization and photoexcitation) as well as Auger and radiative relaxations, makes use of properly defined superconfigurations as a global ensemble of configurations. With a tractable number of (super)levels, we explain the occurrence of the highest charge states observed in experiments.

Superconfigurations and Super Transition Arrays

This chapter is a continuation of Chap. 6 in the sense that, for very complex ions, not only the number of levels is overwhelmingly large, but also the number of configurations. The concept of superconfiguration has been introduced for a proper gathering of configurations through the definition of supershells (collections of ordinary subshells). This concept relies on the notion of partial Local Thermodynamical Equilibrium, i.e., all the configurations belonging to a given superconfiguration are distributed according to a Boltzmann law at some temperature.

Static and dynamical equilibrium in plasmas

The plasma properties such as ionization, internal energy, emissivity or opacity depend on the populations of the energy levels, i.e., on the thermodynamical state of the plasma. The Local Thermodynamical Equilibrium (LTE) is the simplest state, but a non-LTE description is often necessary. The LTE laws are reviewed. The Saha-Boltzmann law is thoroughly derived in the framework of statistical mechanics. The most general description, however, requires considering all the microscopic processes (excitation, de-excitation, ionization, recombination, etc.) and building a rate equation for each atomic level. The system of coupled equations for the populations is called the collisional-radiative system. A major difficulty of this detailed level accounting (DLA) approach is the need to compute a large set of rates for all the processes between the energy levels. In each case, the link between the detailed balance principle and the microreversibility of the processes is discussed.

Distribution functions. Energy levels

The frequency distribution functions are universal quantities for describing the statistics of large ensembles. These functions are generally represented by their distribution moments, of various orders. In atomic physics, such moments are computed by means of the tensor-operator formalism, as sums of products of Wigner n-j coefficients. When the summation problem appears to be untractable, two methods may bring a decisive help: the second-quantization formalism developed in atomic physics by Judd, and the graphical methods elaborated by Jucys and his team. After a (limited) number of moment values have been obtained, one enters them into the distribution function of the “best” statistical model, which is a matter of choice (due to the limitation in the number of moments).

Global approach to plasmas in LTE equilibrium

The computation of a quantity such that the LTE opacity of a plasma by using a full detailed level accounting approach is, even in a limited spectral range, very demanding in terms of computational resources. For moderate- to high-Z plasmas, global concepts such as Unresolved Transition Arrays (between configurations) and Super Transition Arrays (between superconfigurations) can be very useful tools to handle large sets of radiative transitions. The relevance and the efficiency of these global methods are illustrated through the example of an absorption spectrum calculated in a line-by-line calculation and compared with the result of a superconfigurationaccounting approach. Also, the comparisons of these global calculations with experimental measurements of the plasma opacity in some selected energy ranges corresponding to specific nl - n´l´ transitions assess the usefulness of these methods. In particular, for moderate-Z plasmas, a UTA approach gives satisfactory results, notwithstanding the approximate accounting of the Boltzmann factors which can slightly alter the results at low temperatures. For higher-Z plasmas, the superconfiguration-accounting approach gives good results and makes tractable the treatment of very complex ions.

Applications to hot-plasma radiation

Some results of calculations using the methods proposed in the book are presented as examples. The plasma characteristics are needed either for studying its structure, or for computing its time evolution. Among the former, there are the free-electron temperature and density, and the chargestate distribution; among the latter, there are the radiative power losses, the cooling coefficients, and the Rosseland mean opacities. In the field of applications, several examples of fine experiments are addressed.

The central-field configurational model

In the central-field configurational model, the basis functions of the atomic states are products of a radial part, an angular part, and a spin part. They must obey the antisymmetry principle. They can be gathered into electronic configurations. The atomic states (wavefunctions) are the eigenvectors of the H Hamiltonian, which is essentially the sum of the electronic kinetic energies, of the electrostatic interactions between the nucleus and the electrons, and of those between the electrons, plus the magnetic interactions between the orbital and spin magnetic moments of the electrons. They are obtained by diagonalizing H over the basis functions of a single configuration (in intermediate coupling), or of several configurations (in configuration interaction). The (3p 2 + 3d 2) mixing is taken as an example.