Reduction of the Apparent Impedance of Wide Band Accelerating Cavities by RF Feedback

In the CERN SPS proton synchrotron the four accelerating cavities are of the travelling wave structure type. At the 10 GeV/c injection energy the cavities present to the beam an impedance very similar to that of a detuned RLC cavity with the result that strong dipole and quadrupole instabilities occur. The SPS accelerated beam current was limited by the combined action of these two effects to 2.5 X 10/sup 13/ protons which resulted in capture losses increasing with the injected beam intensity. Among the solutions possible for this problem, the RF feedback, which would alleviate both transient beam loading and instability effects, looked to the authors to be the most promising. In such a system the total voltage seen by the beam is reinjected into the feedback cavity via its power amplifier. Without any delay in the system the cavity impedance seen by the beam could be greatly reduced. Unfortunately the long delay in the system severely limits the bandwidth and the RF feedback could hardly correct more than the n = O beam loading component. The authors circumvented this problem by observing that they needed a large gain only in the vicinities of the RF frequencies. Outside these bandsmore » the phase rotation due to the long delay is unimportant if the gain is made low enough. If, in addition, the total delay of the system is made exactly equal to one machine turn, the open loop phase of the feedback system is always zero for each RF frequency. The two ingredients needed to make the RF feedback work for n not too small are therefore a transfer function with comb filter shape and a total delay of one machine turn. In this paper these ingredients are derived.« less