Oscillation thresholds in coupled-cavity TWTs

Summary form only given. We present a new approach to the computation of thresholds and oscillation frequencies for drive induced oscillation (DIO) and DC oscillation (DCO) in coupled-cavity TWTs. DIO is frequently observed in broadband CC-TWTs under high drive conditions; its occurrence limits the attainable power and/or bandwidth in these tubes. DCO develops under zero drive conditions; its occurrence may generally be avoided by increasing the beam voltage and/or reducing the beam current. Our approach is based on a linearization of the 1-dimensional frequency-domain model used in CHRISTINE-CC, a multi-frequency, large signal, CC-TWT simulation code. The onset of oscillation is predicted by analyzing the spectrum of a certain linear operator whose singularity (non-invertibility) corresponds to a condition of infinite gain. The oscillation threshold is obtained using a global parametric search over beam current, beam voltage, and signal frequency, followed by a local iterative Newton-type method for converging to the respective threshold value. The electron-beam equations of motion used in CHRISTINE-CC generally give rise to a non-linear relation between the gap voltages and the currents induced in the cavities. In the case of DIO we linearize this relation around the single-tone equilibrium gap voltages. DC oscillations are a special case in which the single-tone equilibrium gap voltages are assumed to be identically zero. The matrix of the resulting linear operator is combined with the impedance matrix from the coupled-cavity circuit model to produce a composite matrix which becomes singular at the onset of oscillation. Our numerical simulation framework uses CHRISTINE-CC to evaluate the linearized model corresponding to any particular set of input parameters. The output data provides feedback to the external spectral analysis tools that we have implemented to track proximity to the oscillation threshold.