  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. 
Exceptional points of degeneracy in traveling wave tubes