A. P. Privezentsev’s scientific contributions

Fractal properties of attractors representing self-induced oscillation modes of electron flows with a virtual cathode are investigated by numerical simulation. Correlation dimensionalities of attractors as functions of the immersion space are compared for vircators and reflex klystrons.

Possible oscillatory modes of the virtual cathode in a planar or cylindrical transit gap are studied by a numerical modeling with an account of the high-frequency field excited by the current. The possibility for effective generation in a nearly monochromatic or a nearly two-frequency mode is demonstrated. Mutual conversion between the chaotic and the regular oscillation components is shown to be possible.

A mechanism of microwave radiation generation in a vircator of the triode type is studied using the computer simulation method. Analysis of autocorrelation functions of the averaged and local flow characteristics shows that the vircator operation is based on forming a coherent dissipative structure.

Computer modeling of the dynamics of a space charge interacting with an RF circuit is carried out by means of point transformations. Synchronization of the flux oscillations at the frequencies of two regular attractors is analyzed. The initial flux distributions with complete transit and partial reflection produce such attractors. A critical dependence of the character of such oscillations on the injection current is demonstrated together with the possibility for chaotic states to exist.

The modes of oscillation which occur when unstable steady states of the electron beam cease in a plane, equipotential space are discussed in the present paper. The Hamiltonian form of the plane-sheet model can be used in this case, with the same dimensionless variables and parameters. The model of plane sheets enables us to explain the basic features of the space charge dynamics in systems with one-dimensional current flow configuration and, in spite of its obvious limitations, yields results which are in good agreement with experiment.

Present paper represents the results of theoretical and experimental in - vestigation on studying a generation mechanism and improving a radiation efficiency in a virtual cathode triode. It shows the possibility to produce a new type of a high-frequency monochromatic radiation generator with a frequency tuned.

The numerical modeling method is used to investigate the interaction of a virtual cathode in a high-intensity beam with the high-frequency field in a multimode resonator. The possibility of synchronization in the beam-resonator system is considered, leading to the formation of close-to-sinusoidal oscillations with a fairly high efficiency of transfer of beam energy to the electromagnetic field. It is established that the synchronization mechanism has a nonlinear character, and the formation of an oscillation regime with a narrow spectrum depends critically on the coupling coefficients of the beam with the resonator modes. It is shown that when the coupling is reduced, the synchronization regine is interrupted and a mode competition regime is established when the dynamics of the system are close to chaotic.

The results of an investigation of the oscillations of a virtual cathode and the hysteresis of the state for a one-dimensional electron stream in a flat drift space are given. It is shown that in the case of a given mean space charge density and a given injection current different oscillatory regimes can exist in a stream with a virtual cathode.

Digital simulation of electron-beam dynamics in a microwave triode system is carried out on the basis of the flat-sheet method. It is demonstrated that one of the factors determining the intensity of the virtual-cathode oscillations is the symmetry of the system forming the virtual cathode. For a triode system, the oscillation amplitude increases with a decrease in the decelerating field in the anode-screen gap and with a decrease in the anode transparence.

In connection with an increasing interest in the generation of high-power microwave radiation using intense-current relativistic beams, consideration is given to the electron flux oscillating in the field of its own space charge, focusing on the nonlinear stage of interaction with a high-frequency field. An optimization of the parameters of a triode reflecting system reveals that less than 10 periods of electron oscillation between the cathode an the virtual cathode are required for the system to begin operation in the stationary generation mode with an efficiency of 8 percent. Theoretical results are compared with available experimental data.