Beam Loading Effects in the CERN PS Booster

At intensities > 1.5 × 1012 protons per ring, and at reduced RF voltage, fast growing beam loading instabilities occur in the Booster (PSB) with loss of beam bunching. The observed thresholds are reported; they are different from those given by Robinson´s1 criterion and occur with a different frequency. To explain this and other observations, a model of the beam loading interaction including the feedback loops controlling RF amplitude, phase and cavity tuning, is presented. In the general case, beam loading causes cross-coupling between all three loops, which for high beam loading makes the system unstable. For low beam loading, which was assumed for the basic systems design, the loops are practically independent. The Robinson criterion is a limiting case of this model (no feedback loops). A method for designing better loops taking into account the cross-coupling is described. It has the advantage over other cures, such as lowering of the cavity Q or feeding the cavity with a current equal to the beam current but of opposite phase, that it does not require extra RF power.