The interaction between a linear electron beam and a guided electromagnetic wave is studied in the context of exceptional points of degeneracy (EPD) supported by such an interactive system, focusing on 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. The augmented model using phase velocity and characteristic impedance obtained via full-wave simulations is validated by calculating gain vs 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 nondispersive 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.

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We propose a scheme to calculate the reduced plasma frequency of a cylindrical-shaped electron beam flowing inside of a cylindrical tunnel, based on results obtained from Particle-in-cell (PIC) simulations. In PIC simulations, we modulate the electron beam using two parallel, non-intercepting, closely-spaced grids which are electrically connected together by a single-tone sinusoidal voltage source. The electron energy and the beam current distributions along the length of the tunnel are monitored after the system is operating at steadystate. We build a system matrix describing the beam's dynamics, estimated by fitting a 2 × 2 matrix that best agrees with the first order differential equations that govern the physics-based system. Results are compared with the theoretical Branch and Mihran model, which is typically used to compute the plasma frequency reduction factor in such systems. Our method shows excellent agreement with the theoretical model, however, it is also general. Our method can be potentially utilized to determine the reduced plasma frequencies of electron beams propagating in differentlyshaped beam tunnels, where no theoretical model yet exists, such as the case of a cylindrical or elliptical electron beam propagating inside of a metallic beam tunnel of cylindrical, square, or elliptical cross-section. It can be applied also to electron beams composed of multiple streams.