Linearized Superposition Theory of a Classical One-Component Plasma

Abstract

The equilibrium theory of a one-component nondegenerate charged gas, in a uniform continuum of a neutralizing charge, is studied on the basis of a linear-closure procedure for the BBGKY hierarchy which, in the present instance, corresponds to the use of the linearized Kirkwood superposition approximation, and leads to a second-order linear differential equation for the radial distribution function. Its solution is studied, numerically and analytically, for a wide range of the plasma parameter γ = e2/kTΛD, where ΛD is the Debye length. Results for γ ≪ 1 are compared with corrections to the Debye-Hückel theory derived by Abe and others. Solutions for γ ≫ 1, which approach an ordered state of the system as γ increases, are compared with two simple ``model'' calculations of the equilibrium theory of a body-centered cubic lattice of charges in a uniform background of compensating charge. The thermodynamic properties of these ``Coulomb lattice'' models are in qualitative agreement with those of the plasma as computed via our closure approximation for γ ≫ 1. The possibility is therefore suggested that, even for large γ, the linear closure approximation has a larger degree of validity than might be expected a priori.