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Longitudinal oscillations of bunched beams in synchrotrons have been analyzedby accelerator physicists for decades, and a closed theory is well-known [1].The first modes of oscillation are the coherent dipole mode, quadrupole mode,and sextupole mode. Of course, these modes of oscillation are included in thegeneral theory, but for developing RF control systems, it is useful to workwith simplified models. Therefore, several specific models are analyzed in thepaper at hand. They are useful for the design of closed-loop control systems inorder to reach an optimum performance with respect to damping the differentmodes of oscillation. This is shown by the comparison of measurement andsimulation results for a specific closed-loop control system.

Modeling Longitudinal Oscillations of Bunched Beams in Synchrotrons