  Traveling wave tube (TWT) is a powerful vacuum electronic device used to
amplify radio-frequency (RF) signals with numerous applications, including
radar, television and telephone satellite communications. TWT design in a
nutshell comprises of a pencil-like electron beam (e-beam) in vacuum
interacting with guiding it slow-wave structure (SWS). In our studies here the
e-beam is represented by one-dimensional electron flow and SWS is represented
by a transmission line (TL). The interaction between the e-beam and the TL is
modeled by an analytic theory that generalizes the well-known Pierce model by
taking into account the so-called space-charge effects particularly
electron-to-electron repulsion (debunching). Many important aspects of the
analytic theory of TWTs have been already analyzed in our monograph on the
subject. The focus of the studies here is on degeneracies of the TWT dispersion
relations particularly on exceptional points of degeneracy and their
applications. The term exceptional point of degeneracy (EPD) refers to the
property of the relevant matrix to have nontrivial Jordan block structure.
Using special parameterization particularly suited to chosen EPD we derive
exact formulas for the relevant Jordan basis including the eigenvectors and the
so-called root vector associated with the Jordan block. Based on these studies
we develop constructive approach to sensing of small signals.
