Necessary Conditions for Attaining a Crystalline Beam

Molecular dynamics is employed to study the nature and magnitude of beam cooling that is required in order to achieve a crystalline beam. Analysis is presented of a number of cooling systems now in use, or whose use is contemplated, none of which has been shown to be able to achieve the crystalline state. However, for an adequately strong cooling system that produces on average a constant angular velocity among the particles, a crystalline state can be achieved. In this paper, we present numerical values for a particular example under typical experimental conditions; these values appear to be achievable in practice.