The Effect of Phase Slippage in Multicell Cavities on Longitudinal Beam Dynamics

In modern linear accelerators it is often convenient to use multicell cavities which are designed for a constant particle velocity.These cavities are then employed over a certain velocity range until the next cavity type, designed for a higher ß, further accelerates the beam. For superconducting cavities this approach has become mandatory due to the high R&D costs of such devices. Using multicell cavities at velocitiesdifferent from their design value yields phase slippage in the single cells, thereby reducing energy gain and longitudinal focusing. In this paper we derive some simple analytical formulas in order to demonstrate the implications of phase slippage on longitudinal dynamics. It is shown that for large phase slip values the longitudinal focusing is not only reduced by lower transit time factors but also by an additional "slip factor ", that can drive particles into unstable regions of parameter space.