Optimization of Heavy Ion Focussing Systems with Large Numbers of Magnets

A method is presented for efficiently optimizing heavy ion focussing systems consisting of large numbers of magnets. The method is based on a technique for computing gradients of performance functions in systems where the transfer fuction at each point depends only on the state (trajectory) and control function (magnet strength) at that point. A computer program developed to implement this method is also described. The program can be used to minimize final spot size together with maximum bore radius for systems with both quadrupole and sextupole components. Geometric and chromatic abberations are included, with chromatic ones computed nonperturbatively. The results of some initial studies done for ideal quadrupole systems with large momentum spread (±1.5%) are presented. Also, some results for systems that can simultaneously focus several beams, each with different momentum or charge, are presented.