Start-oscillation conditions of tapered backward-wave oscillators

Abstract

Coupled-mode theory is employed to describe the interaction between nonuniform electron beams and circuits. It is then applied to determine the start-oscillation conditions of a tapered backward-wave oscillator. It is shown that under high space-charge operating conditions where the coupling to the fast space-charge wave is negligible and for weak circuit tapers, an approximate closed form solution of the coupled-mode equations can be obtained through a Wentzel-Kramers-Brillouin-Jeffreys approximation. The start-oscillation conditions are then determined approximately from such a solution.