Ion Ellipsoid Model - A new model for atomic physics in hot dense plasmas

In this paper a new model is presented for calculating the atomic physics of atoms in hot and dense plasmas - the Ion Ellipsoid Model (IEM). The basic assumption of the model is that the ion is confined in an ellipsoid enclosure, with the total electric field vanishing on and beyond the ellipsoid surface. Ellipsoid shapes approximate the Voronoi cells of the ions. The present paper describes the statistical distributions of the ellipsoids' shapes and sizes, and the ion location relative to the ellipsoid center. Simple high accuracy semi-empirical formulas are presented for the probability densities of these quantities. The results indicate an increasing spherical symmetry around the ions and a significant reduction in the symmetry fluctuations as the plasma coupling constant, Γ, increases, in accordance with intuitive expectations. IEM predicts a fluctuating continuum lowering and thereby provides a realistic description of the situation in real plasmas. An explicit expression is provided for the distribution function of the continuum lowering. At high Γ's the average continuum lowering approaches the value given by the Ion Sphere Models. The electric fields at the ions, as computed with the IEM, turn out to be too low relative to those obtained directly from the Monte Carlo computations. A simple Γ-dependent scaling factor can, however, bring the IEM electric field distributions into good agreement with the Monte Carlo results.