Thomas Fermi Calculation of the Degree of Ionization in a Dense Plasma

Abstract

The knowledge of the average degree of ionization of a plasma plays a significant role both in inertial confinement experiments and in astrophysical situations. The Thomas-Fermi statistical model, combining relative simplicity, clarity and excellent qualitative descriptive capacity, has been proven to be a powerful method to calculate the average properties of the atomic system, such as the equation of state and the degree of ionization. A number of different versions of Thomas-Fermi model have been adopted to calculate the degree of ionization. Kobayashi (1959) solved the Thomas-Fermi equation for positive ions and calculated the degree of ionization for zero-temperature. For finite temperature, I.J. Feng, et al. (Feng, Zakowicz and Pratt, 1981) compiled a detailed study of the degree of ionization of a dense plasma in the Thomas-Fermi (TF) and the Debye-Huckel-Thomas-Fermi (DHTF) approximation. The results of Feng’s work are shown in Fig. 1. Note than an anomolous feature, viz., that the degree of ionization decreases as temperature increases, appears in both curves d and c, based on the DHTF model. In curve d, the bound electrons are defined as the electrons with a negative total energy and the number of bound electrons was calculated by integration. The dip in curve d is very obvious. In curve c, an attempt was made to remedy this defect. Here the bound electrons are restricted to be inside the sphere with the radius of mean distance between ions. The dip in the curve diminishes, but still exists.