Advanced nonlinear theory: Long‐term stability at the SSC

 The SSC is supposed to be one of the most stable dynamic systems. The luminosity lifetime of one day means that particles have to be in a regular, stable, bounded motion for 10⁸ revolutions. This is only an order of magnitude less than the lifetime of the solar system. The problem of beam stability, one of the main problems in the theory of accelerators, has many aspects: one‐particle dynamics, and intrabeam, beam‐environment, and beam‐beam interactions. We address here only the first problem—the dynamics of a single particle.  (AIP)