TWT stability for frequencies near a band edge

Using a simple model we derive a universal condition for oscillation in a traveling wave tube for frequencies near a band edge, when the adjacent band gap is small. The condition is expressed graphically as a value for the maximum allowable (stable) small signal gain as a function of the size of the band gap. As an example of the application of the general condition, a simple upper bound on the E-plane offset of a beam tunnel in a folded-waveguide TWT is obtained.