Charge Correlations in a Harmonic Trap

TL;DR

This paper investigates charge correlations in a harmonic trap, revealing shell structures and ordering, and relates these correlations to uniform plasma and Thomson problem configurations.

Contribution

It introduces a detailed analysis of pair correlations in trapped Coulomb charges, connecting inhomogeneous and ordered states to known uniform and spherical arrangements.

Findings

Pair correlations in the fluid state relate closely to uniform OCP correlations.

Ordered states exhibit tiling patterns linked to Thomson problem ground states.

Density profiles are consistent with theoretical, simulation, and experimental results.

Abstract

A system of N classical Coulomb charges trapped in a harmonic potential displays shell structure and orientational ordering. The local density profile is well understood from theory, simulation, and experiment. Here, pair correlations are considered for this highly inhomogeneous system for both the fluid and ordered states. In the former, it is noted that there is a close relationship to pair correlations in the uniform OCP. For the ordered state, it is shown that the disordered "tiling" is closely related to the ground state Thomson sites for a single sphere.