Configuration Space Formulation and Implications for Approximation Schemes for Strongly Coupled Plasmas

Abstract

Some of the recent approximation schemes [Singwi, Tosi, Land and Sjölander, 1968 (STLS); Totsuji and Ichimaru, 1973 (TI), Golden, Kalman and Silevitch, 1974 (GKS)] for strongly coupled plasmas have been formulated in terms of integral equations in k-space for the pair correlation function, or the structure function, or other related quantities. The integrand, one observes, often has (almost) a convolution structure, which strongly suggests that a transition to the configuration space may simplify the problem and offer some specific advantages. We have so transformed [Bakshi, Kalman, Silevitch and Golden, 1976] the STLS and TI equations (Section II), which appear now as Poisson equations for the direct correlation function, with distinctive source terms involving the pair correlation function. This, in turn, suggests that the direct correlation function (properly normalized) must be an effective potential due to an effective charge density of the source. Indeed, the source terms, in both cases, obey the same normalization condition which essentially reflects the requirement of perfect screening. Various other physical requirements and their implications for the correlation functions and the source function are also noted in Section III.

Part of this work has been supported by AFOSR Grant 76-2960.