AC space charge effects on beam loading of a cavity

A calculation of the loading of a resonant cavity by an electron beam is presented. This calculation is the first to include all effects of ac space-charge. The fields in the cavity are determined in the presence of the beam, including the effects of higher order structure modes. The formulation also explicitly includes Ramo's space-charge waves of all ranks. The result reduces to the conventional ballistic beam loading result for low beam current. Comparison of the complete theory developed here with the ballistic result demonstrates that the ballistic theory is sufficiently accurate, typically accounting for the quality factor to within 5%, and the resonant frequency to within 1%. In addition, the theory is shown to agree well with particle-in-cell simulations.