Parametric analysis of electron beam–wave interaction in linear beam devices: A tutorial on gap coupling factor and scaling to high frequency

Electron beam–wave interaction is essential for particle acceleration, radiation generation, microwave and millimeter-wave communications, and fusion research. In this work, we first provide a tutorial review on the gap coupling factor, the key parameter to characterize beam cavity–gap interaction in linear beam devices, by using Carter’s simple model and the disk model. We then conduct a parametric analysis of the gap coupling factor considering large signals. The gap coupling factor is investigated for different beam and tunnel radius, gap length, RF current, and anode voltage, aiming to provide guidance for the design of higher frequency devices. The effects of space charge in a large signal interaction are particularly examined, as the space charge force is responsible for energy loss and instabilities. The electron velocity change through the beam interaction gap is studied under different cavity parameters. The analysis is exemplified in a high-efficiency RF power amplifier based on an inductive output tube. The results are compared favorably against experiments and particle-in-cell simulations. We demonstrate the design of device parameters for scaling up in high frequency operations.