Eigenmode Solution for Beam-Loaded Slow Wave Structures Based on Particle-In-Cell Simulations

We present a method to model hot slow wave structures based on finding the unit-cell's transfer matrix. The method considers the small-signal interaction between the electromagnetic guided field and the electron beam via three-dimensional (3D) particle-in-cell (PIC) simulations. We calculate the complex-valued wavenumbers of the hot modes in a serpentine waveguide near the synchronization point. The distribution of the calculated complex-valued wavenumbers agrees with the one predicted by the Pierce model. The results show that the gain calculated based on the proposed model very well matches the one calculated from 3D PIC simulations of the whole structure. The results also show that the proposed model is superior to the Pierce model on predicting the gain of long structures.