Jacques Bauche

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.

Quenching of transition arrays through configuration mixing

In the atomic central-field model, the cancellation of some electric-dipole line strengths is a well known effect of configuration mixings. The authors study their global effects on transition arrays. A crucial quantity is the wavenumber mu 1 of the centre of gravity of two transition arrays when their upper or lower configurations mix. A closed formula is derived for the difference delta Emix between the values of mu 1 with and without the mixing effects. Two experimental examples are presented. In the first one, the value of delta Emix is a sufficient proof that one of the two arrays is almost completely quenched by the other. In the second one, the quenching is only partial, and the degree of quenching is evaluated. In conclusion using the unresolved transition array (UTA) formalism, it is possible to determine ab initio the centre of gravity of a mixed array, without any need for diagonalisation, and to deduce the main effects of configuration mixing.

Breakdown of jj coupling in spin−orbit-split atomic transition arrays

The global effects of configuration mixing on the total intensity of a transition array have been interpreted. The changes of the subarray intensities by the mixing of pure jj subconfigurations (breakdown of jj coupling) in heavy atomic ions can be calculated in the same way. The perturbed relative intensities are deduced from the eigenvectors of a 2 × 2 energy matrix. This matrix is not changed if the subarrays contain spectator electrons. The calculated values give the interpretation of some conspicuous features appearing, for instance, in highly ionized Ta, Pt and Hg x-ray spectra.

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.

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.

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.

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.

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).