INTERACTION BETWEEN BEAM CONTROL AND RF FEEDBACK LOOPS FOR HIGH-Q CAVITIES AND HEAVY BEAM LOADING

An open-loop state space model of all the major low-level rf feedback control loops is derived. The model has control and state variables fo r fast-cycling machines to apply modern multivariable feedback techniq ues. A condition is derived to know when exactly we can cross the boun daries between time-varying and time-invariant approaches for a fast-c ycling machine like the Low Energy Booster (LEE). The conditions are d ependent on the Q of the cavity and the rate at which the frequency ch anges with time. Apart from capturing the time-variant characteristics , the errors in the magnetic field are accounted in the model to study the effects on synchronization with the Medium Energy Booster (MEB). The control model is useful to study the effects on beam control due t o heavy beam loading at high intensities, voltage transients just afte r injection especially due to time-varying voltages, instability thres holds created by the cavity tuning feedback system, cross coupling bet ween feedback loops with and without direct rf feedback etc. As a spec ial case we have shown that the model agrees with the well known Peder sen model derived for the CERN PS booster. As an application of the mo del we undertook a detailed study of the cross coupling between the lo ops by considering all of them at once for varying time, Q and beam in tensities. A discussion of the method to identify the coupling is show n. At the end a summary of the identified loop interactions is present ed.