BWO power holes and unstable interaction with the fast space charge wave

Summary form only given. Slow wave circuits used in forward wave amplifiers like helix TWTs also support backward waves. A backward wave can interact with the slow and fast space charge waves of an unmodulated electron beam at frequencies at which the phase velocities of the waves are nearly equal. Under small signal conditions, the interaction of a backward wave with the slow space charge wave produces positive backward wave gain that becomes infinite at the threshold for oscillation, while the interaction of the backward wave with the fast space charge wave produces negative backward wave gain. When a large forward wave signal is present - as in an amplifier - we have found that the backward wave gain due to the slow-wave interaction is reduced, while the gain due to the fast wave interaction is increased, and can even change sign. An example is shown, which was obtained using the large signal helix TWT code, CHRISTINE 3D. We have found that this phenomenon is not sensitive to the frequency of the drive signal. We have identified the positive backward wave gain due to the interaction of the fast wave and the first backward wave space harmonic in a helix TWT as being the primary physical mechanism responsible for so-called ´power holes´ - dips in the output power vs. frequency curves in TWTs observed under large signal conditions. We find that the frequency difference between the small signal BW gain region and the power hole region may be (artificially) reduced in the simulation by reducing the space charge reduction factor, which is consistent with the identification of the interaction of the fast space charge wave with the circuit wave as the cause of the power holes.