Phase Oscillations in High Current Synchrotrons

The theory of phase oscillations in the synchrotron, first given by Bohm and Foldy, is extended to cover the case where the amplitude of the accelerating voltage is not constant and where the accelerated bunch is itself sufficiently large to produce an appreciable part of the accelerating voltage. It is found that the phase oscillation is more stable when the driving frequency is less than the natural frequency of the accelerating electrode system, and that the plate characteristic of the driving amplifier has a negligible effect on the phase stability.