A system-theoretic formulation of the bunch train cavity interaction

The bunch train cavity interaction is an accelerator physics problem, for which a system-theoretic model is lacking. A form of modal analysis has been used to characterize the system dynamics, and this model has been used for control system design. Correspondingly, control design has been done using input-output classical frequency-domain-based control, including several nested loops. Several shortcomings of this control-design method are highlighted, all of which are remedied by a new time-domain, system-theoretic model developed herein. The new formulation is a periodic, discrete-time system, amenable to state-space control-design methods.