Automodulation and chaotic regimes of generation in a two-resonator gyroklystron with delayed feedback

Topic and aim. The dynamics of a double-resonator gyroklystron of the 93 GHz band with delayed feedback is studied. A comparative analysis of the dynamical regimes of amplifier generation obtained in the numerical experiment both on the basis of averaged equations and in the framework of direct numerical simulation by the «particle-in-cells» method using the KARAT code is carried out. Method. To identify the dynamical properties of system behavior we apply the spectrum of of statistical methods from the theory of chaos: the calculation of fractal dimensions, Lyapunov exponents, etc. To find the Lyapunov exponents we apply a method of estimating them from dynamical time series. This method is extremely convenient, since it requires only the single scalar time realization in a fixed in space point of spatially distributed system, for example, the amplitude of output radiation. Moreover, this method imitates the processing of the data that can be obtained in natural experiment. Results. The analysis of the time series obtained in numerical simulation showed the existence of hyperchaotic regimes for both approaches to the modeling of gyroklystron. Such regimes correspond to attractors with a high correlation dimension and more than one positive Lyapunov exponents. It was found that mentioned hyperchaotic regimes occur, for example, with an increase in the transmission factor for the feedback loop. The multimode «strong» hyper-chaos arises from chaos resulting from the sequence of period doubling bifurcations of the periodic automodulation mode intensity of output radiation gyroklystron. Discussion. UHF chaotic and noise generators are extremely important for various technical applications. One can note, for example, radars and wideband communication. Thus, the production of multimode, chaotic and hyper-chaotic regimes of gyro-amplifiers generation is a priority branch of microwave electronics. Being proposed in this paper the mathematical modeling methods allow to detect complex regimes for gyroklystron. Being proposed in this paper the approaches to amplifier generations analysis can be applied in a physical experiment.