One-Component Plasma: Going Beyond Debye-Hueckel

TL;DR

This paper employs field-theoretic methods to calculate the internal energy of the One-Component Plasma, extending previous Gaussian approximations by including non-Gaussian terms, and finds these higher-order effects are minimal across all plasma parameters.

Contribution

It introduces non-Gaussian corrections to the internal energy calculation of the OCP, improving the theoretical understanding beyond previous Gaussian-based models.

Findings

Higher-order non-Gaussian terms have minimal impact on the internal energy.

The extended theory does not significantly improve agreement with simulations.

Gaussian approximation remains adequate across the plasma parameter range.

Abstract

Using field-theoretic methods, we calculate the internal energy for the One-Component Plasma (OCP). We go beyond the recent calculation by Brilliantov [N. Brilliantov, Contrib. Plasma Phys. 38, pg. 489 (1998) / cond-mat/9805358] by including non-Gaussian terms. We show that, for the whole range of the plasma parameter Gamma, the effect of the higher-order terms is small and that the final result is not improved relative to the Gaussian theory when compared to simulations.