#### For citation:

Adilova A. B., Ryskin N. M. Study of synchronization in the system of two delay-coupled gyrotrons using a modified quasilinear model. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2018, vol. 26, iss. 6, pp. 68-81. DOI: 10.18500/0869-6632-2018-26-6–68-81

# Study of synchronization in the system of two delay-coupled gyrotrons using a modified quasilinear model

Topic. The paper is devoted to the study of mutual synchronization of two gyrotrons coupled with delay. As a rule, a theoretical study of synchronization of gyrotrons and other microwave oscillators is usually carried out by numerical simulations using certain well-established models of microwave electronics. Using this approach, it is difficult to provide a fairly complete synchronization pattern, using methods and ideas of nonlinear dynamics. Aim. The aim of the paper is to develop a modified quasilinear model based on the approximation of the electron susceptibility. Methods. The study is based on a bifurcation analysis of the system, which is applicable to this model. A comparison is also made with numerical simulation using the non-stationary theory of a gyrotron with a fixed high-frequency field profile. Results The model proposed in this work allowed us to construct synchronization areas on the plane of parameters of the coupling coefficient – the frequency mismatch for various synchronous modes, the number of which increases with increasing delay time. The model also makes it possible to compute the most important practical parameters (power, efficiency, oscillation frequency). Discussion. An important advantage of the proposed modified quasilinear model is the ability to use modern automated bifurcation analysis packages for studying synchronization modes.

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