Construction of symplectic full-turn maps by application of an arbitrary tracking code

It is pointed out that a map to describe propagation of particles through any section of a nonlinear lattice can be represented as a Taylor expansion about the origin in phase space. Although the technique to compute the Taylor coefficients has been improved recently, the expansion may fail to provide adequate accuracy in regions where nonlinear effects are substantial. It is suggested that a representation of the map in angle-action coordinates, with the angle dependence given by a Fourier series and the action dependence by polynomials in I ^1/2, may be more successful. Maps of this form are easily constructed by taking Fourier transforms of results from an arbitrary symplectic tracking code. Examples are given of one-turn and two-turn maps for the SLC (Stanford Linear Collider) North Damping Ring in a strongly nonlinear region. Results for accuracy and speed of evaluation of the maps are quite encouraging. It seems feasible to make accurate maps for the SSC (Superconducting Super Collider) by this method