Multi-bunch energy compensation in the NLC bunch compressor

The task of the NLC bunch compressor is to reduce the length of each bunch in a train of 90 bunches from 4 mm, at extraction from the damping ring, to about 100 {mu}m, suitable for injection into the X-band main linac. This task is complicated by longitudinal long-range wake fields and the multi-bunch beam loading in the various accelerating sections of the compressor. One possible approach to compensate the multi-bunch beam loading is to add two RF systems with slightly different frequencies ({prime} {Delta}f{prime} scheme) to each accelerating section, as first proposed by Kikuchi. This paper summarizes the choice of parameters for three such compensating sections, and presents simulation results of combined single- and multi-bunch dynamics for four different NLC versions. The multi-bunch energy compensation is shown to be straightforward and its performance to be satisfactory.