CONSTRUCTION OF SYMPLECTIC MAPS FOR NONLINEAR MOTION OF PARTICLES IN ACCELERATORS

We explore an algorithm for the construction of symplectic maps to des cribe nonlinear particle motion in circular accelerators. We emphasize maps for motion over one or a few full turns, which may provide an ec onomical way of studying long-term stability in large machines such as the Superconducting Super Collider (SSC). The map is defined implicit ly by a mixed-variable generating function, represented as a Fourier s eries in betatron angle variables, with coefficients given as B-spline functions of action variables and the total energy. Despite the impli cit definition, iteration of the map proves to be a fast process. The method is illustrated with a realistic model of the SSC. We report ext ensive tests of accuracy and iteration time in various regions of phas e space, and demonstrate the results by using single-turn maps to foll ow trajectories symplectically for 10(7) turns on a workstation comput er. The same method may be used to construct the Poincare map of Hamil tonian systems in other fields of physics.