Smooth approximation with acceleration in an alternating phase focusing superconducting linac

In this paper, we present a smooth approximation method to calculate the effective potential in a longitudinal RF accelerating and focusing system. Comparing with the smooth approximation without acceleration, this method gives a more accurate calculation of the zero-current phase advance and effective potential when the energy gain through a period is not negligible. Using such a smooth approximation, we have studied an alternating phase focusing structure in a proposed accelerator-driven test facility superconducting linac. A self-consistent macroparticle simulation for one asymmetrical alternating phase focusing structure shows that beyond a beam current of 50 mA, there will be significant particle losses. This will put a limit on the future machine operation based on the alternating phase focusing concept.