Single-Particle Nonlinear Beam Dynamics

Abstract The investigation of single-particle dynamics in circular particle accelerators can be traced back to pioneering works in the 1950s. Traditionally, the design of new circular accelerators has focused on optimizing linear dynamics in ways that minimize nonlinear effects. When encountered, these effects were managed using suitable correction techniques. However, this methodology has undergone significant reconsideration, leading to a more favorable view of nonlinear beam dynamics. Notably, several new concepts have been promoted to improve the description and modeling of nonlinear beam dynamics. Furthermore, new proposals have emerged that leverage the extensive potential of nonlinear beam dynamics to enhance the control and manipulation of the characteristic features of charged particle beams.