Approximate treatment near resonance of backward and traveling wave tubes in the Compton regime

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Abstract
Backward and traveling wave tubes are devices in which the kinetic energy of an electron beam is converted into electromagnetic radiation through interaction with a slow wave structure. In the low‐current, or Compton, regime of operation, the linear instability leading to microwave generation is the result of a three‐wave process involving the two space‐charge waves on the beam and a normal mode of the slow wave structure. The three‐wave character of this resonance is explored qualitatively and quantitatively by deriving an approximate, cubic dispersion relation valid near the resonance. Although the approximate dispersion relation is derived from the full relation for a specific system, the method of analysis is quite general and can easily be applied to other configurations. The approximate dispersion relation is employed to find expressions for the growth rates in these devices, to place this electromagnetic analysis into correspondence with Pierce’s circuit analysis, and to arrive at a proof that the instability in the backward wave device is absolute, while that in the traveling wave tube is convective.

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