Symplectic full-turn maps in a Fourier representation

A method that uses an arbitrary sympletic tracking code to generate an exactly symplectic full-turn or multi-turn map has been developed. The map is obtained from a generating function, which is a finite Fourier series in the final angle coordinates, the Fourier coefficients being represented as a B-spline series in the initial action coordinates. The authors achieve fast iteration of this implicitly defined map, and good accuracy. As a first application, a simplified model of arcs of the SSC (Superconducting Super Collider) is treated.<>