Interaction of the RF system of storage rings and linacs with longitudinal bunch oscillations

Summary

The RF amplifier feeding a synchrotron, a storage ring or a linac is the source not only of the beam energy, but also of the energy of mismatch oscillations, which lead to emittance growth if they are not damped. The steering mechanism for the energy flow is a first of all particle dynamics and resistivity of the beam environment. Also the properties of the amplifier play a role; the Robinson criterion is an example. Longitudinal mismatch can be excited as well by cavity as by amplifier properties. The mechanism can be very easily demonstrated and understood in case of a storage ring with a one-gap RF cavity. In case of a linac of finite length, the effect is evaluated statistically. Excitation of mismatch occurs already below the «Robinson threshold». At the Robinson threshold it becomes catastrophic: the beam vibrates. We discuss measures to suppress the growth of mismatch.