  We propose a new principle of operation in vacuum electron-beam-based
oscillators that leads to a low beam current for starting oscillations. The
principle is based on super synchronous operation of an electron beam
interacting with four degenerate electromagnetic modes in a slow-wave structure
(SWS). The four mode super synchronous regime is associated with a very special
degeneracy condition in the dispersion diagram of a cold periodic SWS called
degenerate band edge (DBE). This regime features a giant group delay in the
finitelength SWS and low starting-oscillation beam current. The starting beam
current is at least an order of magnitude smaller compared to a conventional
backward wave oscillator (BWO) of the same length. As a representative example
we consider a SWS conceived by a periodically-loaded metallic waveguide
supporting a DBE, and investigate starting-oscillation conditions using Pierce
theory generalized to coupled transmission lines (CTL). The proposed super
synchronism regime can be straightforwardly adapted to waveguide geometries
others than the periodically-loaded waveguide considered here since DBE is a
general property that can be realized in a variety of structures.
