  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.
