Transition revisited

The standard derivations of the energy and phase of the synchronous particle in a proton accelerator assume, as if by definition, that said synchronous particle lies on the central orbit of the machine. This is manifestly unjustified in the particular case of the acceleration near transition of a mixture of ions, when a small difference in charge-to-mass ratio can produce a Iarge radial separation of the different ion species. The development of a simple derivation of the parameters of the synchronous particle that involves no such o priori constraint has yielded some surprises; not least, a belated explanation for an apparent anomaly encountered in 1987, when a mixture of oxygen and sulphur ions was accelerated in the PS for the first time. These ideas are supported by measurements performed during the latest ion run.