DYNAMIC APERTURE ESTIMATES AND PHASE-SPACE DISTORTIONS IN NONLINEAR BETATRON MOTION

Symplectic mappings that model the four-dimensional betatron motion in a magnetic lattice are considered. We define the dynamic aperture in terms of the connected volume in the phase space of initial conditions that are bounded for a given number of iterations. Different methods for a fast estimate of this quantity are given; the analysis of the as sociated errors and the optimization of the integration steps are outl ined. A comparison of the accuracy of these methods is given for both simple models and more realistic lattices.