Statistical dielectronic recombination rates for multielectron ions in plasma
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CAL, NONLINEAR, AND SOFT MATTER PHYSICS
Statistical Dielectronic Recombination Rates for Multielectron Ions in Plasma A. V. Demuraa,*, D. S. Leont’ieva, V. S. Lisitsaa,b, and V. A. Shurygina a National b National
Research Center “Kurchatov Institute,” Moscow, 123182 Russia Research Nuclear University “MEPhI,” Moscow, 115409 Russia *e-mail: [email protected] Received December 29, 2016
Abstract—We describe the general analytic derivation of the dielectronic recombination (DR) rate coefficient for multielectron ions in a plasma based on the statistical theory of an atom in terms of the spatial distribution of the atomic electron density. The dielectronic recombination rates for complex multielectron tungsten ions are calculated numerically in a wide range of variation of the plasma temperature, which is important for modern nuclear fusion studies. The results of statistical theory are compared with the data obtained using level-by-level codes ADPAK, FAC, HULLAC, and experimental results. We consider different statistical DR models based on the Thomas–Fermi distribution, viz., integral and differential with respect to the orbital angular momenta of the ion core and the trapped electron, as well as the Rost model, which is an analog of the Frank–Condon model as applied to atomic structures. In view of its universality and relative simplicity, the statistical approach can be used for obtaining express estimates of the dielectronic recombination rate coefficients in complex calculations of the parameters of the thermonuclear plasmas. The application of statistical methods also provides information for the dielectronic recombination rates with much smaller computer time expenditures as compared to available level-by-level codes. DOI: 10.1134/S1063776117090138
1. INTRODUCTION The dielectronic recombination (DR) process plays an important role in formation of ionization equilibrium in the astrophysical and laboratory plasmas [1–34]. In recent years, DR of complex multielectron ions, which is interesting for the application of metals like tungsten in structural elements of thermonuclear fusion devices with magnetic confinement [13, 18, 21, 24–33] as well as for astrophysical studies [25, 34], has been analyzed especially actively. It is well known [1–34] that the dielectronic recombination rate can be expressed as the sum of different realizations of branching coefficients, which are associated with the competition of radiative decay and autoionization of doubly excited states of atoms or ions. Such level-by-level calculations for multielectron atoms or ions are quite complicated and laborious [1– 15, 17–21, 23–34]. At the same time, complex calculations of the transport and confinement of particles, which are accompanied by simultaneous calculation of ionization equilibrium, the kinetics of population of atomic energy levels, and radiation transport, as well as energy equilibrium and balance [21, 24], are required as applied to the thermonuclear plasma. In this connection, the calculations of ionization equilibrium of the
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