The one-component plasma: a conceptual approach

TL;DR

This paper extends the Debye-Hückel theory to the one-component plasma, providing an analytic approach that yields thermodynamic functions and structure factors while maintaining physical consistency.

Contribution

It introduces a new analytic extension of Debye-Hückel theory specifically for the OCP, enhancing understanding of its thermodynamics and structure.

Findings

Analytic expressions for thermodynamic functions derived.

Structure factor calculations enabled.

Theory satisfies key sum rules, ensuring consistency.

Abstract

The one-component plasma (OCP) represents the simplest statistical mechanical model of a Coulomb system. For this reason, it has been extensively studied over the last forty years. The advent of the integral equations has resulted in a dramatic improvement in our ability to carry out numerical calculations, but came at the expense of a physical insight gained in a simpler analytic theory. In this paper we present an extension of the Debye-Hueckel (DH) theory to the OCP. The theory allows for analytic calculations of all the thermodynamic functions, as well as the structure factor. The theory explicitly satisfies the Stillinger-Lovett and, for small couplings, the compressibility sum rules, implying its internal self consistency.