Phase Selection in the K500 Cyclotron and the Development of a Non-Linear Transfer Matrix Program

A method has been developed for the rapid calculation of particle orbits in a cyclotron with spiral-shaped dees. The method uses second order matrix transfer methods and has been implemented in the FORTRAN program "SOMA", (Second Order MAtrix). SOMA has been checked against the slower orbit integration program SPRGAPZ. A combination of SPRGAPZ and SOMA has been used to investigate the phase selection process in the Michigan State University K500 cyclotron. This study led to the design of hardware necessary for phase selection and the ancillary beam diagnostic equipment. Finally SOMA calculations and the phase selection calculations are compared to experimental results.