Low-Energy States of Circulating Stored Ion Beams: Crystalline Beams

The low-energy states of a beam of charged particles subject to circumferentially varying guiding and focusing forces is studied by first deriving a Hamiltonian and then using molecular dynamics methods. In an alternating gradient structure, operating below the transition energy (but not in a constant gradient ring), the lowest state is ordered. The nature of the ground state depends upon the beam density and the ring parameters. For very low temperature, the crystal remains intact for a long time, but as the temperature increases it rapidly gains energy from the lattice.