Comment on the Healy's Symplectification Algorithm

摘要

For long-term tracking, it is important to have symplectic maps for the various electromagnetic elements in an accelerator ring. While many standard elements are handled well by modern tracking programs, new magnet configurations (e.g., a helical dipole with a superimposed solenoid) are being used in real accelerators. Transport matrices and higher terms may be calculated by numerical integration through model-generated or measured field maps. The resulting matrices are most likely not quite symplectic due to numerical errors in the integrators as well as the field maps. In his thesis, Healy presented a simple algorithm to symplectify a matrix. While the method is quite robust, this paper presents a discussion of its limitations.