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A scheme to characterize the dynamics of the electron beam-electromagneticpower exchange along a traveling wave tube (TWT) is proposed. The method isbased on defining a state vector at discrete periodic locations along the TWTand determining the transfer matrix of the unit-cell of the "hot" slow-wavestructure (SWS) that takes into account the interaction between theelectromagnetic guided field and the electron beam via particle-in-cell (PIC)simulations. Once the estimate of the unit-cell transfer matrix is obtained, weshow how to find the hybrid, beam-electromagnetic, eigenmodes in the hot SWS,i.e., where the electromagnetic guided field interacts with an electron beam,by using Floquet theory. In particular, we show how do determine thecomplex-valued wavenumbers of the hybrid modes and the eigenvectors associatedto them. The method is applied to find the hot modes with complex wavenumberthat can be supported in a TWT amplifier with a helix SWS. We show dispersionrelations of the modal complex wavenumbers of the hybrid modes when varyingfrequency and beam voltage; the results are in agreement with Pierce theory.The method is also applied to find the complex-wavenumber modes in a hot SWS ofa millimeter wave TWT amplifier based on a serpentine waveguide. The techniqueis general and can be applied to any SWS geometry where electromagnetic modesinteract with an electron beam.

Traveling Wave Tube Eigenmode Solver for Interacting Hot Slow Wave Structure Based on Particle-In-Cell Simulations