Self-modulation and chaos in delayed-feedback klystron oscillators

Summary form only given. Non-stationary and chaotic generation of microwave radiation is important for numerous applications such as communication and radar systems, plasma heating, etc. In this paper, we summarize the results of investigation of nonlinear dynamics in klystron delayed feedback oscillators. Several models of oscillators with two or more cavities have been developed. Detailed theoretical analysis of self-excitation conditions, system eigenmodes, self-oscillation conditions and basic features of stationary generation modes have been done. Self-excitation threshold has a form of discrete "oscillation zones" that are 2/spl pi/-periodic in the feedback phase parameter. Each zone corresponds to one eigenmode of an oscillator. Near the boundaries of two adjacent zones there is a region of bistability and oscillation hysteresis where either of the two eigenmodes can survive as a result of a mode competition process. Numerical simulation of non-stationary processes has been carried out. Modeling of self-modulation regimes has revealed an existence of a variety of limit cycles of different shapes corresponding to regimes of periodical self-modulation. The studied systems demonstrate continuous complication of shapes of limit cycles and hard transitions between them. Latter is attended with a hopping of frequency of self-modulation. Scenario of transition to chaos was studied in details. It depends on whether we are at the center of a zone or at its edge. In the center, period-doubling Feigenbaum scenario dominates. Near the boundaries the dynamics is more complicated due to mode competition effects. Transition to chaos occurs either via Feigenbaum, or via Ruelle-Takens (quasiperiodic) scenario.