The structure of the cylindrically confined Coulomb lattice

Abstract

The structure of cold ions confined in a cylindrically symmetric static potential is explored by means of Molecular Dynamics calculations, as an approximation to a cooled ion beam in a storage ring. Ordered structures are obtained for the ratio of average Coulomb to thermal energies of Γ ⪢ 150. For low densities the ions arrange themselves in a linear string aligned along the axis of symmetry; above a critical density the ions repel each other away from the central axis by a distance that increases with linear particle density. First a zigzag pattern appears, then a helix with increasing number of particles per turn, then a tetrahedral structure of pairs of ions sitting opposite each other on a line perpendicular to the beam axis. With increasing density the average distance between nearest neighbours becomes constant. Above another linear density, ions begin to appear on the axis inside the shell formed by the helices and tetrahedra, with the number of shells increasing with linear particle density. On the surface of the cylindrical shells the particles form equilateral triangles arranged in a hexagonal structure characteristic of two-dimensional Coulomb solids. For the innermost helices the dependence of shell radii and of angles between particles are compared to analytic model calculations: at low densities the energies of these configurations are minimized with respect to the degrees of freedom, while for larger densities approximate geometrical models are used.