Exceptional Degeneracies in Traveling Wave Tubes with Dispersive Slow-Wave Structure Including Space-Charge Effect

The interaction between a linear electron beam and a guided electromagnetic wave is studied in the contest of exceptional points of degeneracy (EPD) supported by such an interactive system. The study focuses on the case of a linear beam traveling wave tube (TWT) with a realistic helix waveguide slow-wave structure (SWS). The interaction is formulated by an analytical model that is a generalization of the Pierce model, assuming a one-dimensional electron flow along a dispersive single-mode guiding SWS and taking into account space-charge effects in the system. The augmented model using phase velocity and characteristic impedance obtained via full-wave simulations is validated by calculating gain versus frequency and comparing it with that from more complex electron beam simulators. This comparison also shows the accuracy of our new model compared with respect to the non-dispersive Pierce model. EPDs are then investigated using the augmented model, observing the coalescence of complex-valued wavenumbers and the system's eigenvectors. The point in the complex dispersion diagram at which the TWT-system starts/ceases to exhibit a convection instability, i.e., a mode starts/ceases to grow exponentially along the TWT, is the EPD. We also demonstrate the EPD existence by showing that the Puiseux fractional power series expansion well approximates the bifurcation of the dispersion diagram at the EPD. This latter concept also explains the "exceptional" sensitivity of the TWT-system to changes in the beam's electron velocity when operating near an EPD.