Effects of Axial Misalignment of the Dees and Their Correction

Abstract
Axial misalignment of the dees near the centre of a cyclotron can lead to the build‐up of large coherent axial oscillations. Numerical computations made for the TRIUMF cyclotron are shown to be in agreement with an analytic treatment of the problem. General formulae are given, applicable to all cyclotrons. In the case of TRIUMF the tolerance allowed on the vertical positions of the dee lips in order to maintain beam quality is ±0.25 mm, quite tight considering the size of the cyclotron. Various methods of reducing the effects of dee misalignment are considered. For TRIUMF a system of specially shaped electrostatic deflecting plates acting over the first few turns has been proposed; these could relax the misalignment tolerance by a factor four. Other advantages and disadvantages of this scheme are discussed, including its effects on the radial motion.