MULTI-BUNCH ENERGY SPREAD INDUCED BY BEAM LOADING IN A STANDING-WAVE STRUCTURE

The interaction of a relativistic beam with the modes of the TM(010) p ass-band of a multicell cavity does not cause any problem: although al l the modes are excited by the RF generator, resulting in different ce ll excitations during the cavity filling and the beam pulse, the net a ccelerating field exhibits negligible fluctuations from bunch to bunch . However, when the beam is not fully relativistic, this is no longer true. The phase slippage occurring in the first cells, between the non relativistic beam and the lower pass-band modes, produces an effectiv e enhancement of the shunt impedances, which is usually negligible for a relativistic beam in a well tuned cavity. Moreover, the voltage jum ps (amplitude and phase) occurring at each bunch passage, as well as t he beam detuning caused by the off-crest bunches, vary from cell to ce ll. These effects enhance dramatically the fluctuation of the accelera ting voltage, with a dominant beating provided by the pass-band mode n earest to the pi-mode. The induced beam energy spread has been estimat ed by the help of two distinct codes, developed at Frascati and Saclay , with results in good agreement. While an interaction integral is com puted at each bunch passage, the cavity refilling is calculated by sol ving coupled differential equations of the ''modes'' of the pass-band, driven by a generator linked to one end-cell. It is also shown that t he intermode coupling arises from the external Q of the drive end-cell , and not from the wall losses. For illustration, we applied the metho d to the beam-loading problem in the SC capture cavity of the low char ge injector of TESLA Test Facility installed at DESY.