Accurate and fast computation of high order fringe-field maps via symplectic scaling

The fringe fields of particle optical elements often have a significant influence on particle motion, particularly on the higher order aberrations of instruments. Using DA methods, it is possible to compute high order transfer maps of the fringe-field region exactly by integration, but compared to the determination of the main field effects, the method is rather time consuming. Here we introduce an approximate calculation scheme which is very accurate and fast and is therefore particularly useful for efficient optimization of field parameters. It works to arbitrary order and yields order by order symplectic Taylor maps. With this method, the speed of computing fringe-field maps is typically increased by up to two orders of magnitude.