Single-particle orbit equation in crystalline beams

Abstract

This paper presents a set of equations that describe the closed orbits of individual particles in a crystalline beam. A mean-field model is employed under the condition that single-particle trajectories in a crystalline ground state are proportional to each other. It is shown that the solution to the orbit equations can almost uniquely be determined once the lattice design of a storage ring is made. The theoretical predictions are compared with molecular dynamics simulation results in order to confirm the validity of the present formalism. The orbit equations can be used, e.g., to study the intrinsic stability of crystalline beams in an arbitrary storage-ring lattice and to calculate the optimum tapering factor of a beam cooling force.