A simulation study of beam loading on a cavity

Beam loading exerts a strong influence on the operation of high-power and medium-power microwave sources. This paper reports a simulation study of beam loading on a cavity using the two-dimensional particle-in-cell code, MAGIC. We vary the beam voltage, the beam current, the degree of current modulation on the dc beam before the beam enters the cavity, and the degree of charge neutralization on the beam. We deduce the beam-loaded quality factor Q and the beam-loaded resonant frequency from a Lorentzian fit of the numerical data on the gap voltage response as a function of the driving frequency. The MAGIC simulations have revealed several unanticipated results. The beam loading is observed to be a function of perveance. Constant perveance beams, of varying voltage and current, exercise about the same degree of beam loading on the model klystron cavity (except, of course, for the cases with very small beam current). The inclusion of an ac component on the dc beam current has no effect on the degree of beam loading; neither does the neutralization of the electron beam. Many of these simulation results cannot be explained by existing theories that ignore ac space charge effects.