Construction of symplectic maps for nonlinear motion of particles in accelerators

J. S. Berg, R. L. Warnock, R. D. Ruth, É. Forest
1994 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We explore an algorithm for construction of symplectic maps to describe nonlinear particle motion in circular accelerators. We emphasize maps for motion over one or a few full turns, which may provide an economical way of studying long-term stability in large machines such as the Superconducting Super Collider (SSC). The map is defined implicitly by a mixed-variable generating function, represented as a Fourier series in betatron angle variables, with coefficients given as B-spline functions of
more » ... spline functions of action variables and the total energy. Despite the implicit definition, iteration of the map proves to be a fast process. The method is illustrated with a realistic model of the SSC. We report extensive tests of accuracy and iteration time in various regions of phase space, and demonstrate results by using single-turn maps to follow trajectories symplectically for lo7 turns on a workstation computer. The same method may be used to construct the Poincari map of Hamiltonian systems in other fields of physics.
doi:10.1103/physreve.49.722 pmid:9961266 fatcat:zo2ztelzg5hkzn3ktbmbjda47a