Confinement and stability of a Crystalline Beam

This technical report defines and describes a Crystalline Beam. This is an ordered state of matter made of electrically charged ions which are moving together in a storage ring with very high density and small velocity spread. In particular, the paper analyses the requirements for the confinement and the stability of the Beam. It is demonstrated that a storage ring made of one circular weak-focusing magnet, similar to a Betatron, is the most suitable for the confinement and stability of the Crystalline Beam. The disruptive effects of drift insertions have also been investigated. Requirements on final densities and velocity spreads are also calculated and reported. A matrix formalism is developed for the design of the storage ring. The important issue of the disruption caused by the curvature of the closed trajectory is not here discussed; it is the subject of a subsequent paper