A modal description of intermodulation injection in a klystron

Understanding the generation and mitigation of harmonic and intermodulation distortion in microwave devices is currently an active area of research. One popular technique for amplifier linearization is the injection of harmonics and other frequencies into the amplifier to reduce the unwanted spectrum at the amplifier output. In a klystron, the bandwidth of the input cavity prohibits using harmonic injection, but it has been shown that intermodulation injection can be used to control the output intermodulation content. As an elementary example we consider a velocity modulated electron beam as would be found in a two cavity klystron. If the current modulation at the intermodulation frequency is canceled, then there would be no cavity voltage at this frequency. The harmonic and third order intermodulation (3IM) charge density perturbations are composed of several complex exponential modes. In this paper, while constructing solutions to the aforementioned, we have ignored small contributions from secular modes, and modes at the 3IM that result from the 3IM being included as a drive frequency.