численное моделирование

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.

The investigation of operation regimes of CW/263 GHz/1kW gyrotron, developed at IAP RAS/GYCOM Ltd., was made by various numerical methods. The influence of the azimuthal inhomogeneity (such as electron beam radial misalignments and tilt) has been studied. The method of average equations and 3D PIC codes (CST Studio Suite and KARAT) were used. Results, achieved by different methods, are in agreement with experimental data.

Three-dimensional electromagnetic numerical simulation is carried out of «squeezed» state of the electron beam in two-section vircator system with drift tubes of different diameters. We have studied the influence of two-section system geometric parameters on the nonlinear dynamics of electron beam. We have obtained an effective plasma frequency depending on the system parameters.

This paper is devoted to the three­dimensional numerical simulation of the «compressed» state of the relativistic electron beam in two­section vircator system with drift tubes with different diameters. We have discovered the mechanism of formation of the «compressed» state of the relativistic beam through the formation of two virtual cathode near the anode grid and between connected sections, which will eventually merged into one distributed in the drift space virtual cathode (compressed state of the beam).

Numerical model of long fiber Raman laser is proposed. The model based on the equations, describing the propagation of pump and Stokes waves, linear coupling of oppositely running waves due to scattering and its nonlinear interaction. The derivation of equations for slowly varying pulse envelopes uses the field decomposition in terms of spatial harmonics rather then commonly used temporal harmonics, which allows to avoid the two­point boundary conditions, and to employ the numerical scheme of Courant–Isaakson–Rees.

With the help of 2D numerical model it has been investigated the nonlinear dynamics and generation of wideband chaotic signals in the generator based on electron beam with the virtual cathode. It has been discovered the strong influence of the external non­uniform magnetic field on the nonlinear dynamics of the virtual cathode in the system. It has been analyzed the physical processes responsible for the discovered dependency of dynamics of the electron beam with the virtual cathode on the parameters of the external non­uniform magnetic field.

The influence of external additive homogeneous isotropic field of Gauss fluctuations to evolution of competition processes, which described by Lotka–Volterra equations, where taking into account the mobility of weak population individuals and spatial and temporal fluctuations of resource, has been researched. The numerical simulation of considered model was performed.

The new method for the calculating of the spectrum of the Lyapunov exponents from data series is proposed. The already known methods of the same thematic are investigated. The Roessler system is given as an example for describing the proposed method. The results of numerical modeling are presented.

We study synchronization in ensembles of locally diffusive coupled Bonhoeffer–van der Pol oscillators. Individual elements frequencies influence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this effect are numerical modeling data and analytical research.