Absolute instability near TWT band edges

Using the Briggs-Bers criterion, we find that the lower band edge of linear beam TWTs is not subjected to absolute instability. At the upper band edge, we find a threshold beam current beyond which absolute instability is excited. In general, an absolute instability would occur in a linear beam tube if the cold-tube circuit dispersion curve in the frequency-wavenumber (ω-k) plane is locally convex and would not occur if the cold-circuit dispersion curve is locally concave, whenever the group velocity of the circuit mode is in the same direction as the beam mode. These results are used to examine the recent studies on the start current of a Smith-Purcell source.