Modeling and control of longitudinal single-bunch oscillations in heavy-ion synchrotrons

This contribution is of interest for engineers, physicists, and scientists working in the fields of control systems and accelerator technology or interested in the modeling and analysis of longitudinal radio frequency (RF) feedback systems in heavy-ion synchrotrons. Among other objectives, the stabilization of the particle beam before and during the acceleration is desirable to preserve the beam quality and stability. The work deals with the modeling of longitudinal coherent oscillations of a bunched beam. The main focus is on the usability of the models for the analysis and design of digital RF feedback loops. The analysis of these models with methods from control theory leads to new insight into the possibilities of RF feedback with regard to the longitudinal beam stabilization. In particular it is shown that the nonlinearity of the beam dynamics plays a major role in the damping of coherent oscillations of higher order. An analysis of a specific RF feedback setup and the comparison with experimental data shows the practical relevance of the models.