Diverse topics in crystalline beams

Equations of motion are presented, appropriate to interacting charged particles of diverse charge and mass, subject to the external forces produced by various kinds of magnetic fields and radio-frequency (rf) electric fields in storage rings. These equations are employed in the molecular dynamics simulations to study the properties of crystalline beams. The two necessary conditions for the formation and maintenance of crystalline beams are summarized. The transition from ID to 2D, and from 2D to 3D is explored, and the scaling behavior of the heating rates is discussed especially in the high temperature limit. The effectiveness of various cooling techniques in achieving crystalline states has been investigated. Crystalline beams made of two different species of ions via sympathetic cooling are presented, as well as circulating ``crystal balls`` bunched in all directions by magnetic focusing and rf field. By numerically reconstructing the original experimental conditions of the NAP-M ring, it is found that only at extremely low beam intensities, outside of the range of the original measurement, proton particles can form occasionally-passing disks. The proposed New ASTRID ring is shown to be suitable for the formation and maintenance of crystalline beams of all dimensions.