High-order maps with acceleration for optimization of electrostatic and radio-frequency ion-optical elements

A method has been developed to calculate accurate high-order ion-optical maps for electrostatic and radio-frequency accelerating elements. The method has been incorporated into the arbitrary-order map-based beam optics code COSY Infinity. The treatment is restricted to the case of negligible magnetic fields, as is typical of heavy-ion accelerating cavities, and does not include space charge. For validation purposes, the beam dynamics calculated for these elements is compared against ray tracing for typical beam and cavity parameters. Different from the ray-tracing approach, parameter changes of individual components typically require only recalculation of the maps of the particular components and not the entire system, and thus the method is particularly suitable for optimization. The approach developed for accurate analytical representation of the on- and off-axis electric fields of cylindrically symmetric electrostatic lenses and radio-frequency cavities is described. Some of the many possible applications for using accurate high-order map representations of Einzel lenses, electrostatic accelerating gaps, and radio-frequency accelerating structures are discussed.