Longitudinal tune control in synchrotrons

Abstract

Dual RF systems that use fundamental and higher‐harmonic cavities can be used to control the longitudinal tune in synchrotrons. The equations of motion and the Hamiltonian are defined for particle motion using dual RF systems. An example is considered using a second‐harmonic system—it is shown, that as φs is increased, a substantial gain in bucket area over a single RF system can be realized by proper relative phasing of the first‐ and second‐harmonic voltages.