Calculating RF ’ Profiles for Beam Loading Compensation of Arbitrary Current Profiles

In the NLC, the energy variation along the multi-bunch beam pulse will be controlled by preloading the structure with a ramped rf profile which is followed by constant amplitude rf. The rf amplitude modulation will be achieved by combining the outputs of pairs of oppositely phase-modulated klystrons through a hybrid. Such agile phase modulation is currently used in the NLCTA[ I]. The duration of the required ramp is nominally the fill time minus the structure length divided by c. This is illustrated in Figure 1, which shows qualitatively the rf pulse shape and (with different shading) how it fills the structure at beam injection, at steady state, and at a point inbetween. The increasing gradient from the injected rf cancels the increasing retarding field due to beam loading build-up.