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Nonlinear characteristics (chaos) of high-power microwave (HPM) sources

Recent advances in the understanding of dynamical systems and chaotic behavior have resulted in the investigation of HPM source design issues. Modern dynamical systems theory can improve our understanding of the dynamics of space charge dominated beams and the RF waveforms generated by them. This paper will review the work done to date using time series analysis techniques to study the state space dynamics of high power microwave sources using simulation (particle-in-cell) code results. Low-dimensional chaos has been observed in simulation results from a variety of HPM sources, including the MILO (Magnetically Insulated Line Oscillator). Additionally, the particle behavior within the diode portion of HPM tubes can have chaotic characteristics. Knowing when these features occur and how they develop are important first steps in our ability to control and/or eliminate them. Central to understanding source behavior is the initial use of joint time frequency analysis to assess whether the dynamics are stationary or not. Subsequently we use delay coordinate embedding techniques to reconstruct an effective state space global dynamics. From this, Poincare sections are examined. Lyapunov exponents are then calculated to determine whether the behavior of the source is noise or deterministic chaos.