Predictions from the van der Pol equation applied to high power microwave phase-locking experiments at Physics International

Summary Form only given, as follows. The van der Pol equation has been evaluated as a model for an experiment in which a high-power cavity vircator was driven by a relativistic magnetron. It has been found that Adler´s inequality gives a necessary but not sufficient condition for achieving phase locking between the driving magnetron and the driven vircator oscillations. The amplitude of the entrained oscillations has been determined as a function of the injected magnetron power, the initial frequency detuning, and other system parameters. The stability of these oscillation is examined. It has also been found that not all entrained states are stable. Boundaries between stable and unstable states are given. Moreover, the driven oscillator can operate as a beatwave source. Comparison of predictions to measurements has validated the model. A similar analysis has been extended to two coupled van der Pol equations that model phase-locked relativistic magnetron experiments.<>