General Beam Loading Compensation in a Traveling Wave Structure

The well-known beam loading in a traveling wave structure is in fact a resistive beam loading which bunches travel on the crest. This type of beam loading could be compensated by increasing RF feed power. But generally, bunches could travel on each phase. General beam loading compensation is well-known for a single cell cavity and it is done by changing the RF feed power and detuning the structure together. In this paper, the concept of detuning for a TW structure will be shown and the evolution of fundamental mode beam-induced field will be derived and finally, it will be shown how to compensate beam loading by changing the phase velocity in comparison to the beam velocity.