Multi-bunch energy compensation

To obtain a luminosity of 1034 cm/sup /minus/2/ sec/sup /minus/1/ in a TeV Linear Collider (TLC), it will probably be necessary to accelerate many bunches in one filling of the rf structure. This has the effect of extracting more energy from the structure and thus enhances the overall efficiency of the accelerator. However, this leads to many problems. First, the train bunches is subject to cummulative beam breakup transversely. This can be controlled by damping the transverse modes with slots in the irises coupled to waveguides. In addition, the energy of the bunches must be kept the same to high precision. For the fundamental mode, this entails adjusting the timing of the rf fill and also the bunch spacing. The higher longitudinal modes, although they do not induce instability, also may lead to bunch-to-bunch variations in energy. However, it also seems possible to damp these modes to cure this problem. Of course, there are also problems associated with damping a train of bunches in a damping ring. In this paper we discuss some of the issues of multi-bunch energy compensation. In the first two sections, we review some basics about energy extraction by a single bunch, and then, multi-bunch energy compensation is treated. We discuss various tolerance issues associated with deviations of amplitude and phase of the rf away from the ideal