Investigation of nonlinear dynamics and chaos in magnetrons

In the operation of microwave oscillators or amplifiers, the electron beam is acted as a medium to converted DC energy into the RF energy. This kind of conversion is based on an interaction process between the electrons and its surrounding electromagnetic field, which is quite nonlinear and provides sufficient conditions to generate complicated dynamics, even chaos. In the crossed-field devices, such as magnetrons, the electrons move in a cycloidal trajectory from the cathode to the anode due to the axially applied magnetic field. It was demonstrated in the experiments that very complicated oscillations, even chaotic oscillations, can be excited in the magnetron under certain conditions. This paper presents our investigation into the nonlinear dynamics, especially chaos in magnetrons by using an equivalent-circuit model. An equivalent-circuit model mainly consists of three parts: (a) the complex admittance representing electron-wave interaction, (b) RLC-circuit for resonant cavity, and (c) the admittance for an external load. The model has been evaluated through both analytical approach and circuit simulation. The nonlinear dynamics of the magnetron has been demonstrated by changing the control parameters, such as the anode current and the external load.