Stability and Tolerances of the Separated Orbit Cyclotron

The physical arrangement of the magnets and rf cavities in a Separated Orbit Cyclotron are described, and the equations of motion and their solution are discussed. The stability limits are determined for triplet and singlet lens systems, and the choice of operating values to give maximum acceptance are examined. The treatment of random misalignment errors of the magnets is described; the six types of errors whose relative strengths are compared lead to bench alignment errors of ~l mil. The alignment of adjacent lenses and alignment over a distance long compared with a betatron oscillation wavelength are shown, however, to have relatively relaxed tolerances.