Charge correlations in a harmonic trap

Complete text of publication follows. A system of N classical Coulomb charges trapped in a harmonic potential displays shell structure and orientational ordering. The shell structure can be accurately reproduced by using correlations from the bulk three dimensional one component plasma (3D OCP). In addition there are other relationships between the correlations of the trap system and the bulk OCP: the location free pair correlation function for the trap and the OCP are in agreement, and the orientational pair correlations within a shell agree with the bulk OCP when a specific length transformation is used (Euclidean distance replaced by arc length). This transformation leads to qualitative agreement with the 3D OCP and quantitative agreement with the 2D OCP, and is studied here with respect to the geometry and also the form of the Hamiltonians of the two systems. At stronger coupling the orientational correlations due to the ordering are in agreement with the single sphere Thomson problem, i.e. the Thomson sites represent a spherical 'lattice' for the individual shells of the trap system. A simple model of the charges at the Thomson sites predicts the behavior of the finite temperature orientational correlations of the trap system as determined by molecular dynamics simulation. Research supported by DOE award DE-FG02-07ER54946, and by the Deutsche Forschungsgemeinschaft via SFB-TRR24.