Crystalline beams

Ions in a storage ring are confined to a mean orbit by focusing elements. To a first approximation these may be described by a constant harmonic restoring force: F = -Kr. If the particles in the frame moving along with the beam have small random thermal energies, then they will occupy a cylindrical volume around the mean orbit and the focusing force will be balanced by that from the mutual repulsion of the particles. Inside the cylinder only residual two-particle interactions will play a significant role and some form of ordering might be expected to take place. The results of some of the first MD calculations showed a surprising result: not only were the particles arranged in the form of a tube, but they formed well-defined layers: concentric shells, with the particles in each shell arranged in a hexagonal lattice that is characteristic of two-dimensional Coulomb systems. This paper discusses the condense layer structure