# Review of Actual Problems of Nonlinear Dynamics

## About current state high frequency vacuum electronic and microelectronic devices with field emission

Some results of researches and development of devices with ?eld emission (TWT, BWO, carcinotrode, klystrons and X-ray tubes, ?eld emission displays, etc.) have been brie?y presented in the article. Lines of development of its theory have been designated. Also the vacuum microwave electronics programs o?ered in Europe and USA have been considered. They are directed on using new technologies in coping with the terahertz frequency range, re?ecting the trend of recent years.

## Terahertz vacuum electromagnetic radiation sources: evolution zigzag from klynotron to klynoorbictron

Investigation and development of e?cient electromagnetic oscillations sources are one of the topical issues in the ?eld of terahertz radiophysics and electronics. A frequency region is regarded as an explored for which oscillating, amplifying and measurement devices have not been developed. The exploration of the terahertz frequency range is at the initial state. In a review paper, published in one of the USA scienti?c journal [1], which was devoted to the terahertz radiation vacuum sources there is some reminder of using, a «klynotron e?ect» in the BWO developed at the IRE NASU.

## Radiative processes, radiation instability and chaos in the radiation formed by relativistic beams moving in three-dimensional (two-dimensional) space-periodic structures (natural and photonic crystals)

We review the results of studies of spontaneous and stimulated emission of relativistic particles in natural and photonic crystals.We consider the di?raction of electromagnetic waves in a crystal, and the resonance and parametric (quasi-Cherenkov) X-ray radiation, the radiation in the channeling of relativistic particles in crystals, di?raction radiation in conditions of channeling, di?raction radiation of a relativistic oscillator, induced radiation in multidimensional space-periodic resonators (natural or arti?cial (electromagnetic, photonic) crystals).

## By the theory of the electron waves and the discrete electron- wave interaction in the stopbands of the slow-wave systems

The role of the discrete description of electron-wave interaction in high-power traveling wave tubes is shown. Deals with the development of this trend on the basis of the theory of interaction of the di?erence equation excitation waveguides. The validity of the linear theory and developed a universal characteristic equation of electron waves, using the di?erence equation excitation waveguides in stopbands of slow-wave systems.

## Determining the value of the structure water-containing environment of living tissue in biomedical radio-electronic nanotechnologies millimetric and terahertz ranges

The article contains the short review of the main results on research of a role of structuration of the water-containing environment in the living tissues. These tissues are used as the objects of research in biomedical radio-electronic nanotechnologies of the extremely high-frequency and terahertz ranges. The experimental devices and technique of researches of the water containing environment structuration under the in?uence of electromagnetic radiation are described. The results of pilot studies are given.

## Phenomenon of the van der pol equation

This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radioengineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters. • The biography of van der Pol, history of his equation and supposed precursors. • The contribution of A.A. Andronov in the theory of selfoscillations.

## Progress and prospect of wavelet transform application to the analysis of nonstationary nonlinear dates in contemporary geophysics

The presented paper is an analytical review of the methods and examples of applications of the continuous and discrete wavelet transform in geophysical study. The possibility of the extension of application of the waveletbased methods in geophysics is also considered.

## Theory of waveguides excitation

The theory of waveguide excitation is presented, based on expansions of the electromagnetic ?eld by proper waves of waveguide. Necessary properties of smooth and periodic waveguides, including the conditions of orthogonality of plane and the volume of the waveguide are given. Main properties of pseudo-periodic waveguides are described. Thisis a new class of waveguide systems. Di?erent forms of the waveguides-excitation theory are considered.

## Development and improvement of field emitters containing carbon materials

Achievements and problems in creation of ?eld emitters for vacuum microwave devices are described. The main attention is devoted to the emitters made of containing carbon materials for high-voltage devices operating at technical vacuum conditions 10?6–10?8 Torr. The brief review of existing works is presented. Results of investigations performed in SPbSPU are described.

## Unique properties of open cavities and wavegiudes containing layered metamaterial

The review of works on studying arti?cial media with negative refractive index and their unique application is given. We make a point of negative refraction and lens e?ects in plan-parallel layers of such metamaterials. The properties and stability conditions of waveguide modes in layered structures and open cavities are considered in terms of the e?ective di?raction and dispersion lengths.