Beam Optics for a 12-GeV Isochronous Ring Cyclotron

This paper discusses the tolerances required for isochronous cyclotrons accelerating protons to kaon and p¿ producing energies. The beam traverses many more imperfection resonances and low order intrinsic resonances than in existing cyclotrons since the isochronous radial tune ¿r¿¿. We anticipate an incoherent radial amplitude of 1 mm at extraction. The turns will overlap and the net accelerating voltage must be flat-topped to ensure that all particles make the same number of turns. With these conditions a 1 G imperfection at the final integer resonance develops 3 mm coherent amplitude, and although some non-linear stretching takes place, a clear space of 0.8 mm permits insertion of a septum. To preserve 1 mm amplitude the operational imperfection fields and gradients at other resonances must, be less than 0.10 G and 0.10 G/cm. A third order intrinsic resonance will cause some filamentation and impair extraction efficiency, although this can be partially controlled.