Fundamental-mode rf design in e+e- storage ring factories

The difficulties arising in the design of the rf system for a factory-type storage ring lie mainly in two areas. First, a gap in the circulating beam current is required for ion clearing. Because of the high beam loading current, this gap produces a strong transient variation in the rf cavity voltage, which can in turn lead to a significant shift in the synchronous phases between bunches on either side of the gap. This phase shift would produce an unacceptable shift in the collision point, unless compensated by a corresponding shift in the bunch phases in the other ring. In order to work out the details of this compensation, the transient beams loading effects produced by the gap must be calculated quite carefully. A major goal of this chapter is to provide the insight and the basic analytic tools necessary for this analysis. The second major problem for the fundamental mode rf design is also a consequence of the high average current needed for a storage ring particle factory: longitudinal multibunch beam instabilities at sideband frequencies within the passband of the accelerating mode. These instabilities can be damped by an appropriate feedback system, as discussed elsewhere in these proceedings. However, as background for this problem, we need to understand the phase and amplitude variations produced in the cavity voltage when the bunches undergo small-amplitude synchrotron oscillations. In the final section, the cavity voltage variation induced by such oscillations is calculated and applied to compute the Robinson damping time. The emphasis throughout this paper will be to provide a thorough understanding of beam loading effects