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

Abstract

An eigenmode solver based on particle-in-cell simulations is proposed to find the hybrid beam-electromagnetic eigenmodes in a "hot" slow-wave structure (SWS), i.e., where the electromagnetic mode interacts with an electron beam. The proposed scheme is based on the determination of the transfer matrix of the unit-cell of the hot SWS that takes into account the interaction of the electromagnetic mode with the electron beam, followed by the determination of its eigenvalues and eigenvectors using Floquet theory. The proposed method is applied to find the hot modes, with complex wavenumber, in a traveling wave tube (TWT) amplifier with helix SWS. We show dispersion relations of the modal complex wavenumber of the electromagnetic wave interacting with the electron beam when varying frequency and beam voltage, with results in agreement with Pierce theory. The method is also applied to find the complex-wavenumber modes of the hot SWS of a millimeter wave TWT amplifier based on a serpentine waveguide. The technique is general and can be applied to any SWS geometry where the electromagnetic modes interact with an electron beam.

An Accurate Analytic Model for Traveling Wave Tube Dispersion Relation

“…In reality, the energy of the electrons in the beam does not have a single value at each z point. The energy usually depends on each electron transverse location, hence it is convenient to deal with the average of all electrons' energies at each transverse z-dependent cross section such that at each point z the electrons' energy is represented by a single value representing their average, as was done for the beam electrons' speed in [15,Eqn. 6].…”

“…Other studies have extended the work by Pierce to theoretically model TWTs as in [10], [14]. Recently, a numerical eigenmode solver for hot eigenmodes in TWT systems was introduced based fully on PIC simulations in [15], that is however more complicated than the method proposed here since in this work we constrain the dispersion to follow the physics predicted by an analytical model. In spite of being excellent tools for the initial design of TWTs, theoretical models are often not reliable, and the actual TWT performance is determined by accurate and time consuming partricle-in-cell (PIC) simulations.…”