Full-turn symplectic map from a generator in a Fourier-spline basis

Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables, It is constructed by using results of single-turn tracking from many initial conditions. The method has been applied to a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10⁷ turns on an IBM RS6000 model 320 workstation, in a run of about one day