numerical simulation

Topic. The paper is devoted to the study of synchronization of a gyrotron by an external harmonic signal. A theoretical study of gyrotron synchronization processes by means of a computational experiment based on certain traditional models of microwave electronics does not provide a complete description of the synchronization pattern. Therefore, the goal of the paper is to develop a modified quasi-linear model based on an approximation of the electron susceptibility by rational functions. Methods.

Aim. The aim of the work is the numerical study of the oscillations of two-phase medium (a mixture of gas and a dispersed phase of solid particles) which caused by electric charge of the dispersed component, and the reciprocal effect of the dynamics of gas and solid particles, as well as the effect of linear size of dispersed particles on the dynamic processes. Methods. With the help of numerical models of electrically charged suspension was modeled in different modes of oscillatory dynamics in a dusty environment.

A new model of neurons like elements is suggested in the paper. The model is based on the generalized Lottka–Volterra model with excitatory coupling. The study is motivated by the fact that the excitatory couplings are the dominating type of interactions between neurons in the human brain. It is shown in the paper that there are two regimes exist in such ensemble of oscillators in dependence on the coupling between the elements: the regime with stable heteroclinical cycle and the regime with stable limit cycle.

The results of preliminary 3D fully electromagnetic simulation of microwave generator with virtual cathode and external feedback loop (virtode) are discussed in this paper. The feedback is realized by the velocity modulation of electron beam in the accelerating gap of electron gun with the electromagnetic signal taken with output cavity placed in the virtual cathode area.

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 non-uniform 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.

It was stated in the paper the mathematical model and its numerical realization for the investigation of wideband chaotic oscillations and of physical processes in the electron beams with virtual cathode at the generators with electron feedback. Also it was briefly described the developed program package for the modeling of non­stationary nonlinear physical processes at the electron generators with virtual cathode and for calculating of output characteristics of devices.

The influence of additive homogeneous isotropic field of Gauss fluctuations of dynamical variables of Gierer–Meinhardt model to formation of dissipative structures in soft mode regime was investigated. The system of equations for description of undamped modes interaction was received. It was shown that fluctuations of dynamical variables are widening the instability region. The numerical simulation of considered model with different boundary condition was performed.

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.

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).