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A study of density effects in plasmas using analytical approximations for the self-consistent potential

M. Poirier 1, 2
1 MHDE - Matière à Haute Densité d'Energie
IRAMIS - Institut Rayonnement Matière de Saclay, LIDyl - Laboratoire Interactions, Dynamiques et Lasers (ex SPAM)
Abstract : Density effects in ionized matter require particular attention since they modify energies, wavefunctions and transition rates with respect to the isolated-ion situation. The approach chosen in this paper is based on the ion-sphere model involving a Thomas-Fermi-like description for free electrons, the bound electrons being described by a full quantum mechanical formalism. This permits to deal with plasmas out of thermal local equilibrium, assuming only a Maxwell distribution for free electrons. For H-like ions, such a theory provides simple and rather accurate analytical approximations for the potential created by free electrons. Emphasis is put on the plasma potential rather than on the electron density, since the energies and wavefunctions depend directly on this potential. Beyond the uniform electron gas model, temperature effects may be analyzed. In the case of H-like ions, this formalism provides analytical perturbative expressions for the energies, wavefunctions and transition rates. Explicit expressions are given in the case of maximum orbital quantum number, and compare satisfactorily with results from a direct integration of the radial Schrödinger equation. Some formulas for lower orbital quantum numbers are also proposed.
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https://hal-cea.archives-ouvertes.fr/cea-01245721
Contributor : Caroline Lebe <>
Submitted on : Thursday, December 17, 2015 - 3:26:58 PM
Last modification on : Monday, February 10, 2020 - 6:14:03 PM

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M. Poirier. A study of density effects in plasmas using analytical approximations for the self-consistent potential. High Energy Density Physics, Elsevier, 2015, 15, pp.12-21. ⟨10.1016/j.hedp.2015.03.008⟩. ⟨cea-01245721⟩

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