Absorption and emission spectra in warm dense plasmas exhibit complex structures known as transition arrays of several types: “unresolved transition arrays” [C. Bauche-Arnoult, J. Bauche, M. Klapisch, Phys. Rev. A 20, 2424 (1979), Phys. Rev. A 25, 2641 (1982), Adv. At. Mol. Phys. 23 131 (1988)], “spin-orbit split arrays” [C. Bauche-Arnoult, J. Bauche and M. Klapisch Phys. Rev. A 31 2248 (1985)], or “supertransition arrays” [A. Bar-Shalom, J. Oreg, W.H. Goldstein, D. Shvarts and A. Zigler, Phys. Rev. A 40 3183 (1989)]. In addition to the complexity brought by the very large number of lines under consideration, one must take into account that such plasmas are often out-of local thermodynamic equilibrium (LTE), which means that the various levels populations do not follow Saha-Boltzmann distribution. Non-LTE conditions occur noticeably in X-ray or extreme-UV plasma sources, in astrophysics, in magnetic or inertial confinement devices for fusion, or in plasmas produced by interaction of a laser with a gas or solid target.
Then, electron-ion collisions or interactions of ions with an outer electromagnetic field are most often too weak to insure LTE. For a correct description of these media, one must resort to a detailed study of radiative and collisional processes responsible for the transitions between the ion levels. But to the necessity to use an accurate enough atomic model to compute the rate associated to each process adds the major difficulty of the solution of potentially very large linear systems: more than 103 equations, i.e., matrices with millions or even billions of elements. A model more efficient than the usual Gauss elimination is under development.
The
configuration average approximation [1] leads to a considerable simplification for the computation of the populations, because it shrinks the number of coupled equations, often by a factor of 10 or more. However one must evaluate the quality of this average. For instance in figure 1 we have plotted the average charge of a 10eV-neon plasma, computed with detailed levels and configuration average hypothesis [2]. In order to assess the validity of configuration average,
we propose here a new criterion based on the detailed balance principle on collisional rates .This average procedure turns out to be useful in a carbon plasma at 10 eV temperature but holds no more at 1 eV [1]. The new criterion is often better than the intuitive criterion according which the configuration average would be acceptable when the average energy dispersion inside a configuration is much less than the electronic temperature.
The above criterion based on the detailed balance or microreversibility of collisional processes may be generalized to radiative processes if one includes absorption, stimulated emission, photoionization and radiative recombination rates induced by a fictive electromagnetic field. The interest of this test is that it is complementary of the collisional-rates based one, because it deals with other rates. This criterion has been checked in detail in a non-LTE neon plasma [2].
[1] M. Poirier, F. de Dortan, J. Appl. Phys. 101, 063308 (2007).
[2] M. Poirier, J. Phys. B 41, 025701 (2008).
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