Traveling Wave Tube Eigenmode Solution for Beam-Loaded Slow Wave Structure Based on Particle-in-Cell Simulations

A scheme to characterize and model the dynamics of the electron beam–electromagnetic power exchange along a traveling-wave tube (TWT) is proposed. The method is based on defining a state vector at discrete periodic locations along the TWT and determining the transfer matrix of the unit cell of the “hot” (i.e., beam loaded) slow wave structure (SWS) that considers the small-signal interaction between the electromagnetic guided field and the electron beam via 3-D particle-in-cell (PIC) simulations. Once the estimate of the unit-cell transfer matrix is obtained, we show how to find the hot guided eigenmodes in the interactive system made of an electromagnetic wave in the SWS coupled to an electron beam by using Floquet theory. In particular, we show how to determine the complex-valued wavenumbers of the hot modes and the eigenvectors associated with them. We focus on finding the hot modes supported by a TWT amplifier with a serpentine SWS operating at millimeter waves. We show the dispersion relation of the modal complex-valued wavenumbers of the hot modes when varying frequency; near the synchronization point, the results are in agreement with the Pierce theory. Finally, we show how the proposed scheme is also useful to estimate the gain performance of a long TWT amplifier by cascading the transfer matrices estimated from PIC simulations of a shorter hot SWS. The results show that the gain calculated based on the proposed model very well matches the one calculated from 3-D PIC simulations of the whole structure. The technique is general and can be applied to any SWS geometry where electromagnetic modes interact with an electron beam. The model we proposed can be a very powerful tool to understand the physics of TWTs and can be used for optimization purposes.