The Low-Energy State ofCirculating Stored Ion Beams: Crystalline Beams

Molecular dynamics is employed to study the low energy states of a beam of charged particles subject to circumferentially varying guiding and focusing forces and with Coulomb forces between the particles. In a constant gradient ring, the lowest energy state is never ordered, but in an alternating gradient structure, operating below the transition energy, the lowest state is ordered. The nature and characteristics of the ground state depends upon the beam density and the ring parameters. For zero temperature the crystal remains intact for a very long time, but at nonzero temperatures it gains energy from the lattice. A critical temperature exists above which the crystal melts rapidly