A Computer Program for Optical Matching Systems

A computer program has been developed for finding an optical matching system of particle beams in the transverse (x-x´, y-y´) phase space. It is well-known that the two sets of symmetric quadrupole triplets could be easily obtained for this purpose starting from a thin lens approximation. However, a system composed of only four lenses (with a fixed geometry) is often desirable in order to save the available space. Four simultaneous algebraic equations for four unknowns (magnet strength) are solved numerically starting from a thin lens approximation and the solutions are improved successively. In general, the program finds the strength of each magnet in less than one minute. (IBM 7094.) Maximum beam excursion is also computed to find the best solution when there are several possible combinations.