Study of the energy gain and the beam loading of the detuned structure with a simple model

A circuit model for the longitudinal case from which to study the field pattern, energy gain and beam loading of a detuned structure is derived from Maxwell's equations. The results obtained with the model are compared to numerical results of the code PROGON. The model gives reasonable scaling of the group velocity and voltage with geometric parameters. The energy gain and beam loading are compared and are shown to depend on the same factor. This is true even for periodic variations of the boundary. Finally, a way to find the shape of the rf pulse envelope for the beam loading compensation is suggested