Theoretical Description of Coulomb Balls - Fluid Phase

TL;DR

This paper develops a theoretical model for the radial density profile of confined charged particles, incorporating correlations to accurately reproduce shell structures observed in experiments and simulations.

Contribution

It extends the hypernetted chain approximation to confined Coulomb systems, providing a more accurate theoretical description including charge correlations.

Findings

The theory reproduces shell structures seen in experiments and simulations.

Quantitative accuracy achieved with bridge function corrections.

The model applies across a wide range of temperatures and particle numbers.

Abstract

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained for the selected conditions by correcting the hypernetted chain approximation with a representation for the associated bridge functions.