CXXXVIII. Non-linear regenerative extraction of synchrocyclotron beams

Abstract

To extract a beam of a maximum energy from a synchrocyclotron, the deflector must be placed at the edge of the magnet, where the magnetic field falls off very rapidly and non-linearly with radius. This presents an analytical problem of coupled non-linear differential equations with periodic coefficients which is solved approximately. The results have been checked by electronic .computation. It is concluded that a nonlinear deflector can extract the beam with higher energy and perhaps greater theoretical efficiency than the linear one at present working at Liverpool. The new method is mechanically simpler than the old for it has no peeler, only a regenerator. The mathematics has interest apart from this application, for the difficulty of handling these coupled cyclotron equations is a major obstacle to the development of new particle accelerators of the fixed field type.