The chaotic character of ion relaxation oscillation in microwave tubes

The noise caused by ion relaxation oscillation becomes a research focus in the field of microwave tubes recently because of the improvement of radars and communications requirements. In this paper, electron beam is described by beam envelope equation, and ions generated from ionization of the background gas in microwave tubes are treated as discrete macro-particles. One dimensional particle-in-cell (PIC) simulation code was developed, and time series of ion relaxation oscillation are obtained by the presented method. The ion relaxation oscillation is treated as the response of a complex nonlinear dynamical system, and the time series is analyzed by power spectrum; restructure phase diagram and Lyapunov exponent. From the analysis results, we find that the ion relaxation oscillation has chaotic character at the first time. The reason of chaos was attributed to the dissipative structure of the system. This would be useful for depressing relaxation oscillation and processing signal with relaxation oscillation noise.