Transient beam loading effects in standing wave cavities of linear accelerators

In modern high energy accelerators, with the increase of charge in a bunch or a bunch train, the induced transient beam loading voltages become higher and higher when the beams pass through the standing wave cavities. But in the usual analysis, people usually pay more attention to the steady state instead of the transient state beam loading. In this paper, the transient nature of beam loading and the cavity's frequency changing behavior seen by the RF power generator are studied, and then the optimum detuning conditions in two cases are derived. In the first case, the resonant cavity's frequency can be tuned to meet the in-phase condition between the RF power generator current and the cavity voltage during the passage of beams. While in the second case, only few bunches in the bunch train and the cavity's resonant frequency is fixed during the passage of the bunch train. At last, the beam loading effects in the prebuncher of BEPC II pre-injector and the two SHBs of BEPC II future pre-injector are studied.