Nonlinear space charge wave theory of distortion in a Klystron

We present a new view of nonlinear distortion in a klystron based on an analytically solvable nonlinear Eulerian model. The nonlinear contributions to the analytic solutions for the beam modulations are "nonlinear space charge waves" in the sense that they are produced by the nonlinear mixing of the linear space charge waves. For a single-frequency input, amplitude and phase distortion are shown to be results of "self-intermodulation" at the drive frequency, or mixing of harmonic distortions with the fundamental. The self-intermodulation contributions add out of phase with the linear space charge waves to produce gain compression and phase distortion. By comparing the results to a conventional large-signal Lagrangian model we find this physical picture is accurate for drive levels up to 1.2 dB of gain compression. For a two-frequency input we predict the third-order intermodulation distortion generation and suppression with the nonlinear space charge wave theory.