A General Control Model for Designing Beam Control Feedback Loops* A General Control Model for Designing Beam Control Feedback Loops

Abstract

Abstract To control the beam in the synchrotron there may be six different primary feedback loops interacting with the beam at a given time. Three loops are local to the rf cavity. They are: high bandwidth cavity phase and amplitude loops used to minimize the effects due to beam loading and a low bandwidth cavity tuning loop. The loops global to the ring accelerating system are: a radial loop to keep the beam on orbit, a beam phase loop to damp the dipole synchrotron oscillations, and a synchronization loop to essentially lock with the succeeding machine. There are various ways in which these loops may be designed. Designs currently in use in operating machines are based on classical frequency domain techniques. To apply modern feedback controllers and study the interaction of all the feedback loops, a good mathematical model of the beam is extremely useful. In this paper we show the derivation of a non-linear tracking model in terms of differential equations obtained from a set of time varying finite difference equations. The model compares well with the results of thin element tracking codes