Analysis of the Field Shape and Mode Competition for the Higher Order Modes in the Oversized Multigap Resonant Cavity With Coplanar Beams

We present a theoretical study on the mode competition for the planar multiple-beam extended-interaction circuit. The circuit consists of a multigap resonant cavity which is also oversized in the transverse direction, leading to a complex mode distribution. We found that the mode competition is highly relevant to the synchronous characteristics between the multigap resonant cavity and the beams, which depends on the standing-wave field distribution along the interaction paths rather than the dispersion curves. It is demonstrated that the interaction electric field of higher order modes can be characterized by a pure shape factor with a set of complex coefficients. In this way, the interaction between the higher order transverse modes and the coplanar multiple beams can be modeled. As a result, a beam-loading model was developed, which is capable of predicting the stability for the modes in higher passbands. Numerical results are presented, benchmarked against the 3-D particle-in-cell simulations.