Valeriy V. Emelyanov

Synchronization of two coupled multimode oscillators with time-delayed feedback

Abstract Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires many new features not inherent to finite-dimensional ones. A picture of oscillation modes in cases of identical and non-identical coupled oscillators is studied in detail. Periodical structure of amplitude death and “broadband synchronization” zones is investigated. Such a behavior occurs due to the resonances between different modes of the infinite-dimensional system with time delay.

Time-Domain Particle-in-Cell Modeling of Delayed Feedback Klystron Oscillators

Time-domain modeling of vacuum tubes is important for theoretical analysis of spurious oscillation, amplification and generation of short pulses and complex multifrequency, or chaotic signals. In this paper, a time-domain model of a klystron delayed feedback oscillator is presented. The model is based on the nonstationary Vainshtein theory of cavity excitation and the 1-D particle-in-cell method for simulation of electron beam dynamics. The results of simulation are presented for an S-band four-cavity klystron with delayed feedback, as well as for a miniaturized sub-terahertz reflex klystron. The developed code allows sufficiently fast and accurate calculation of output characteristics of klystron-type oscillators.

Time-domain PIC-modeling of the multiple cavity klystron oscillator with delayed feedback

The results of time-domain numerical simulation of a four-cavity klystron oscillator with external delayed feedback using a 1.5D PIC-code are presented. Basic properties of oscillation regimes are studied. With the increase of the beam current self-modulation and transition to chaos via the sequence of period-doubling bifurcations are observed. The results are in good agreement with the theoretical predictions obtained previously for approximate model of the oscillator based on a system of time-delayed differential equations.

Theory and simulation of a two-stage W-band multiple cavity klystron oscillator

We present the results of theoretical analysis and numerical simulation of a two-stage multiple cavity klystron oscillator in W band. Small-signal theory of the oscillator is developed and start-oscillation current and oscillation frequency are calculated. Output power and efficiency is determined from large-signal time-domain particle-in-cell simulation. Oscillators with different number of cavities are compared.

Time-domain PIC-modeling of suppression of self-modulation in the multiple cavity klystron oscillator with delayed feedback

The results of time-domain PIC-modeling of suppression of self-modulation in a four-cavity klystron oscillator with external delayed feedback are presented. The method is based on using an additional feedback loop with properly chosen delay and phase shift. The application of the method increases the self-modulation threshold beam current. This results in significant increase of the output power and efficiency in comparison with the oscillator with a single feedback.

Mutual synchronization of two coupled klystron oscillators

We present the results of numerical simulation of synchronization of two coupled delayed-feedback S-band klystron oscillators. A 1.5-D time-domain particle-in-cell code is used for simulation. Optimal parameters of an isolated oscillator are evaluated. We investigate the pattern of synchronization on the frequency mismatch - coupling strength parameter plane. Periodical set of zones of synchronization which separate domains of amplitude death and quasi-periodic beating regimes is observed. Synchronization of interacting oscillators allows increase of the total output power.

Simulation of a W-band kW-power two-stage klystron oscillator

We demonstrate the results of theoretical analysis and numerical simulation of a two-stage multiple-cavity klystron oscillator. We develop the small-signal theory of the oscillator, which predicts start-oscillation current and oscillation frequency. Results of 1.5-D particle-in-cell simulation of the oscillator with different number of cavities are presented. The numerical results are in good agreement with the small-signal theory. Optimal parameters of oscillator are evaluated. The simulations predict over 1.3 kW output power with nearly 650 mA beam current.

A study of dynamics of a five-cavity klystron with delayed feedback

The results of numerical modeling of a five-cavity S-band klystron oscillator with delayed feedback are presented. The main oscillation regimes are numerically investigated. An increase in the electron beam current leads to the transition to chaos through the consequence of self-modulation period-doubling bifurcations.

Amplitude death and broadband synchronization in the coupled delayed-feedback electronic oscillators

Effects of interaction of two ring-loop electronic oscillators with time-delayed feedback are investigated. Nearly periodical zones of amplitude death and beating regimes separated by the “broadband synchronization” domains are revealed. Similar synchronization picture is observed in a system of two coupled klystron vacuum-tube oscillators.

P1–16: Generation of hyperbolic chaos in the system of coupled klystrons

A schematic of the generator of hyperbolic chaos in the microwave band consisting of two klystrons coupled in a ring circuit is proposed. The first klystron doubles the frequency of the input signal. The second klystron mixes the second harmonic of signal with the reference signal that is a periodic sequence of pulses with third harmonic carrier frequency. In the output cavity of second klystron the signal on the differential frequency is separated. As a result, the transformation of the phase of signal for the period of following of pulses of the reference signal is described by the chaotic Bernoulli map. The results of numerical simulation show that generation of structurally stable hyperbolic chaos is possible.