Relaxation Theory of Spectral Line Broadening in Plasmas

Abstract

In this theory of spectral line broadening in plasmas, the radiation process is treated as the relaxation of an excited atom, weakly coupled to a thermal bath, to a state of lower energy. The theory presented here emphasizes the Liouville-operator formalism, as developed by Zwanzig, and may be considered an extension of Fano's theory of pressure broadening in neutral gases. It may further be considered an illustration of a case in which an observable quantity can be expressed in terms of a well-defined correlation function, which can be evaluated without resorting to a microscopic analysis of the interactions. A comparison is made with the impact theories of Griem, Kolb, and Baranger; specifically, it is shown that the assumption of binary collisions and the impact approximation are not necessary in the relaxation theory. Of special importance are frequency-dependent "width" and "shift" operators which produce asymmetries in the intensity profile that are not predicted by the previous plasma-broadening theories. These asymmetries are illustrated in an application of the relaxation theory to the Lyman-$\alpha$ line. The line shape is calculated to second order in the weak-coupling potential, and a comparison is made with experimental observations of this line.