The Definition and the Use of the Central Position Phase in Cyclotrons

The high frequency phase (HF phase), normally used in cyclotrons, is replaced by the central position phase (CP phase). This CP phase gives a proper description of the behaviour of energy and phase of the particle motion and enhances the insight in the total motion (longitudinal and radial) in the median plane, especially when high harmonic acceleration is involved. The use of the CP phase is illustrated with numerical calculations. A very important consequence for injection systems in cyclotrons is treated. Also a proper interpretation of the HF phase behaviour, measured with HF pick-up probes is given.