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 ν
_r
≈γ. 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.