Optimized multi-particle central region for the Michigan State University isochronous cyclotron

Centered orbits are highly desirable in a cyclotron since problems with resonances are minimized and beam stability is greatly improved. The Michigan State University Cyclotron, as originally designed, produces accurately centered orbits in first harmonic operation and performs acceptably on second harmonic. Third harmonic operation, on the other hand, has never been adequate due to very large centering errors. The basic origin of these centering problems is the gap crossing resonance, and the effect of this resonance is highly sensitive to the angular width of the dees. Studies herein show that with a proper selection of both the central region geometry and the dee angle this centering problem can be effectively eliminated. Appropriate configurations have been worked out for harmonics H=1, 2, and 3, using 138°, 90°, and 60° dees respectively, and confirmed in electrolytic tank studies. To implement this new design, a major cyclotron improvement program has been initiated based on a system of interchangable dees. Basic features of this new design and computational results for the optimized geometries are discussed.