On dynamic aperture (SSC accelerator)

An analytical method is presented to study the beam stability in large accelerators such as the SSC (Superconducting Supercollider) and an alternative to using the kick approximation (particle tracking) over large time intervals. This includes the stability factor f, which determines the convergence of the superconvergent perturbation theory, and the behavior of the system, e.g. stable if f>1, and unstable if f<1. The critical point where the system makes the transition from stable (F>1) to chaotic (f<1) behavior corresponds to f=1, the point at which the size of the beam is defined as the dynamic aperture in accelerators.<>