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Subject and Purpose. Results are presented of the solar corona investigations performed with the world famous Ukrainian radio telescopes. The work has been aimed at offering a consistent review of recent achievements in observations of a variety of low-frequency radio emissions from the Sun. Methods and Methodology. The studies of the quiet (thermal) and sporadic (burst-like) radio emissions from the Sun have been carried out with the decameter-wavelength radio telescopes UTR-2, GURT and URAN-2. Specific features of the low-frequency solar radio emissions from a variety of sources are presented, with characterization of the optimized techniques that were applied in each case for evaluating physical parameters of the corona in the areas of decameter-wavelength radio wave generation. Results. The analysis of temporal, frequency and spatial characteristics of solar radio emissions has allowed suggesting a number of models for the coronal electron density distribution, and evaluating magnetic field strengths in the corona. Also, our experimental results have proven to be consistent with the observational data obtained in different frequency ranges and with the use of both ground based and space-borne instruments. Conclusions. The radio observations performed with Ukrainian radio telescopes have permitted studying, with high temporal, frequency and spatial resolutions, solar radio frequency emissions from various localized sources. Along with the large effective area and high sensitivity of the antennas, this permits application of a wide range of methods and tools aimed at detecting and analyzing solar bursts, of both strong and weak intensity, against the background of terrestrial interference of natural or artificial origin.

Subject and Purpose. The paper is aimed at suggesting ways for implementing electromagnetic devices that would involve a nonlinear dielectric inside the structure for concentrating electromagnetic field within it at relatively low intensities of the excitation field. A representative example is offered by a Fabry-Pérot resonator with semi-transparent mirrors and a nonlinear dielectric inside. Methods and Methodology. The paper presents a fundamentally new approach to controlling the frequency response of a metasurface, and a method for protecting electronic modules from high excitation powers. The method is based on the use of nonlinear properties of a Fabry-Pérot "resonator-capacitor" containing a nonlinear dielectric in its volume. Thus, we propose a method for creating spatial filters and antenna protecting fairings capable of active reconfiguration. Results. Analysis of the results has shown that by changing the voltage across the resonator-capacitor plates it is possible to control the degree of electromagnetic field localization in the resonator volume. The frequency response of the metasurface based on the Fabry-Pérot resonator with a nonlinear dielectric inside can be reconfigured by changing the voltage applied to the resonator mirrors. The advantages provided by electrical control of the frequency-selective characteristics include an increased efficiency and possibility of integrating digitally controllable systems into antennas. Conclusions. The use of a Fabry-Pérot "resonator-capacitor"model, with a nonlinear dielectric inside, in the capacity of a reconfigurable metasurface, else as a power limiter in a variety of devices, has sufficient prospects for application in microwave transmitting systems. A special area of application for the reconfigurable Fabry-Pérot resonators is creation of broadband receive antenna systems for direction- finding. In essence, the proposed Fabry-Pérot resonator is a reflective antenna array with an ability to exhibit, conceal or alter its electrodynamic properties according to a certain algorithm. This opens up prospects for its application in "friend-or-foe" recognition systems, reflective beacons, navigation systems, etc.

Subject and Purpose. Considered in the paper is diffraction of a plane wave by a structure involving a half-plane and two disks. The disks and the half-plane, lying within parallel planes, are assumed to be infinitely thin and perfectly conducting. The problem is to be analyzed for two cases, namely for that of both disks located on the same side with respect to the half-plane, and for the other where they are placed on opposite sides against the half-plane. The purpose of the paper is to develop a suitable operator method for performing the analysis of the structure described. Methods and Methodology. The solution to the problem has been sought for within the operator method suggested. The electric field components tangential to the half-plane and the disks are expressed, with the aid of Fourier integrals, via some unknown functions having the sense of amplitudes. The unknown amplitudes shall obey the operator equations formulated in terms of wave scattering operators for individual disks and the sole half-plane. Results. When subjected to certain transformations, the operator equations allow obtaining integral equations relative amplitudes of the spherical waves involved. The integral equations permit investigating scattered wave fields for the cases where the disks stay in the shadow region behind the half-plane or in the penumbra, or else in the region which is illuminated by the incident wave. As has been shown, in the case of plane wave scattering at the edge of the half-plane the resulting cylindrical waves possess non-zero amplitudes even with the disks placed totally in the shadow region, hence not illuminated by the incident plane wave. Conclusions. Making use of an operator method, an original solution has been obtained for the problem of plane wave diffraction by a structure consisting of a perfectly conducting, infinitely thin half-plane and two disks. The operator equations of the problem have been shown to be reducible to integral equations, further solvable numerically with the use of discretization based on quadrature rules. The behavior of far and near fields relative to the disks has been studied for a variety of values of the disk radii and their positions relative to the half-plane.

Subject and Purpose. The transformation peculiarities that the electromagnetic pulses get when heading towards a boundary that performs uniformly accelerated relativistic motion are the present paper concern. A smooth non-stationarity case when the boundary velocity gradually changes from zero to the pulse velocity value is considered, with a focus on the spacetime distribution and evolution of the electromagnetic Airy pulse field. Methods and methodology. The study and analysis are carried out by the method of Volterra integral equations which can describe electromagnetic wave propagation in a heterogeneous time-varying medium. In terms of this method, the basic initial boundary value electrodynamical problem on the electromagnetic source radiation in a heterogeneous time-varying medium is formulated, taking into account the boundary and initial conditions. The resolvent method for solving the Volterra integral equation of the second kind is described. Its advantage is analytical solution capabilities and a versatility as to the primary field choice. Results. Analytical solutions to the original integral equation have been obtained. By analysis, it has been found that the secondary field expressions have singularities that can be controlled well enough by a proper choice of numerical modeling parameters. The revealed singularities have been analytically studied. Their action on the Airy pulse was examined and illustrated through simulation modeling using the starting parameter that locates the Airy pulse at any moment in time. Conclusions. In this work, the electromagnetic Airy pulse interaction with a boundary perfoming uniformly accelerated relativistic motion was examined using the Volterra integral equations method. The obtained analytical solutions revealed significant spacetime changes in the Airy pulses. Our analysis indicated possibilities for controlling the secondary field characteristics by a proper choice of modeling parameters. The results have been confirmed by numerical simulations. They provide a basis for further research in this area.

Subject and Purpose. The paper investigates the accuracy of measurements of the elevation angles of targets located near the surface of a disturbed sea in the area from the upper limit of their extremely small values to the free space zone. The main part of the study concerns measurements using the root-MUSIC method based on the analysis of the eigenvalues of the autocorrelation matrix of signals received from the target. Under the same conditions, the accuracy of measurements using the amplitude sum-difference (monopulse) method was obtained. The purpose of the work was to determine the upper limit of the location angles up to which the accuracy of the root-MUSIC method exceeds the accuracy of the monopulse method measurements, and thereby determine the area of its eff ective use. Methods and Methodology. The study was conducted using computer modeling of the measurement of elevation angles by two types of radio direction finders. The first one used the root-MUSIC measurement method, and the second one used the monopulse method. Both operated at a wave of 3.2 cm and had the same receiving antenna aperture of 2.5 m. The modeling was performed for sea waves from calm to heavy. In addition to interference from the sea, interference caused by internal noise of the direction finders’ receiving channels was taken into account. The modeling calculated the distance dependencies of the measurement errors of the target’s position angles moving at a constant height of 20 m at a distance from 2 to 0.5 km. This ensured the overlap of the position angles in the range of 0.57...2.28 of the width of the sum directional pattern of the monopulse direction finder. Results. Under the same sea waves and using equal apertures of the receiving antennas, the values of the errors in measuring the target elevation angles by both methods were obtained. Recommendations for choice the a priori parameters of the root-MUSIC method have been developed, which ensure high measurement accuracy in diff erent interference conditions. Conclusions. It was found that the root-MUSIC method has a higher accuracy of measuring the elevation angles of low-altitude targets over the sea compared to the widely used monopulse method up to position angles equal to twice the width of the sum directional pattern of the monopulse direction finder antenna.

Subject and Purpose. The troposphere is a natural channel for the propagation of meter- and shorter wavelength radio waves. Studying the impact of solar activity (SA) on the condition of the troposphere is important for improving the accuracy of weather forecasts and understanding the state of the tropospheric radio channel. The present paper has been aimed at identifying and comprehending the solar-tropospheric interactions resulting from the 27-day cycles of solar activity. Methods and Methodology.The study was conducted through twenty 27-day cycles of solar activity, over an interval of latitudes between 0 and 80°N, and at four east longitudes, specifically 30, 180, 240 and 330°E. The atmospheric data used were quoted from the NOAA Physical Sciences Laboratory list (https://psl.noaa.gov /data/timeseries/daily/) and concerned sea level pressure, temperature in the troposphere at the height level with a 1000 hPa pressure, stratospheric temperature at the height corresponding to 50 hPa, and zonal wind speed. Results. Reliable estimates have been obtained for the atmospheric parameters varying over 27-day cycles, that revealed maximum amplitudes at middle and high latitudes,: in particular the sea level pressure up to 12 hPa, temperature in the troposphere up to 5.3 K, and up to 3.5 K in the stratosphere . The relative amplitudes (about 1.3%) of these variations correlate with the 27-day changes in the solar UV radiation of a 205 nm wavelength. Anti-phase changes have been observed between the troposphere and stratosphere temperatures over the continents in the Western and Eastern hemispheres, as well as anti-phase changes in pressure over the continents and the oceans. The change in the sign of temperature variation with height occurs near the tropopause, being accompanied by a ~ 1 km change in the tropopause height. At the latitude of 60°N, the 27-day changes in the zonal wind speed in the stratosphere may reach tens per cent. A persistent solar effect is observable not in winter time alone, but in summer as well, while of a smaller amplitude. Conclusions. Owing to stratosphere-troposphere interaction effects, the troposphere demonstrates a high sensitivity to 27-day variations of the solar UV radiation. The main properties of the 27-day variations of atmospheric parameters testify to the important role of planetary and meteorological- scale Rossby waves in the realization of solar influence.

Subject and Purpose. The paper presents results of numerical simulation of a composition patch antenna with a complex form factor. The design combines two structures, specifically, a disc and an annular resonator. The annular resonator is fed via a coplanar structure that involves cut-ins of different geometries. The feed connections are effectuated pointwise, such as to provide for galvanic contact between the central conductor of the coplanar line and the annular resonator, owing to the distributed electromagnetic coupling of the annular resonator and the aperture of the coplanar line’s outer conductor. The work has been aimed at finding an optimized set of antenna parameters. Methods and Methodology. The antenna design features a combination of two resonators and an open circuit represented by the external conductor of the coplanar line. A variety of form factors were proposed for the circuit breaking slit, including such of a straight line and of a triangle. The angular parameter of the triangular slit was a variable value. Numerical simulations were carried out within a semi-open resonator model, with proper account of all the boundary conditions as specified in the finite-element method. The form of the amplitude-frequency response was optimized according to the required values of the return loss level. Results. The frequency and power characteristics of a composition patch antenna have been analyzed and optimized over a broad frequency range. The optimal values of the main parameters of the structure, affecting the functionality of the antenna have been determined, including form factors of the slits (cut-ins), angular characteristics of the triangle-shaped slit, the dielectric constant of the substrate, and the separation from the ground level. Conclusions. The frequency, spectral and power characteristics of a complex patch antenna based on a combination of annular and disc resonators, sitting above a grounding base, have been investigated over a wide frequency range. Numerical simulation was performed within a methodology combining the finite-element methods and the approaches pertinent to semi-open resonators. Principal dependences of the antenna’s electrodynamic parameters upon the geometry and characteristic dimensions of the structure and material constants thereof have been identified and studied.

This paper is devoted to the memory of Volodymyr Methodyevich Yakovenko, an outstanding scientist in the field of solid-state radio physics, Honored Worker of Science and Technology of Ukraine, Full Member of the National Academy of Sciences (NAS) of Ukraine, Honorary Director of the O.Ya. Usykov Institute for Radiophysics and Electronics (IRE) within the NAS. At the IRE, Dr. Yakovenko founded a scientific school that is well-known for its studies of charged particles’ interaction with electromagnetic fields in inhomogeneous conducting media. In addition, he initiated research in a new branch of today’s solid state physics, specifically investigation of plasma instabilities in semiconductors that occur because of heating of conduction electrons by the existing elecromagnetic fields.

Purpose: The overview of the scientifi c papers devoted to the study of the solar decameter radio emission with the world’s largest UTR-2 radio telescope (Ukraine) published for the last 50 years. Design/methodology/approach: The study and analysis of the scientifi c papers on both sporadic and quiet (thermal) radiation of the Sun recorded with the UTR-2 radio telescope at the decameter wavelength range. Findings: The most signifi cant observational and theoretical results of the solar radio emission studies obtained at the Institute of Radio Astronomy of the National Academy of Sciences of Ukraine for the last 50 years are given. Conclusions: For the fi rst time, at frequencies below 30 MHz, the Type II bursts, Type IV bursts, S-bursts, drift pairs and spikes have been recorded. The dependences of these bursts parameters on frequency within the frequency band of 9 to 30 MHz were obtained. The models of their generation and propagation were suggested. Moreover, for the fi rst time the fi ne time-frequency structures of the Type III bursts, Type II bursts, Type IV bursts, U- and J-bursts, S-bursts, and drift pairs have been observed due to the high sensitivity and high time-frequency resolutions of the UTR-2 radio telescope. The super-fi ne structure of Type II bursts with a “herringbone” structure was identifi ed, which has never been observed before. New types of bursts were discovered: “caterpillar” bursts, “dog-leg” bursts, Type III bursts with decay, Type III bursts with changing drift rate sign, Type III-like bursts, Jb- and Ub-bursts, etc. An interpretation of the unusually high drift rates and drift rates with alternating signs of the Type III-like bursts was suggested. Based on the dependence of spike durations on frequency, the coronal plasma temperature profi le at the heliocentric heights of 1.5–3RS was determined. Usage of the heliographic and interferometric methods gave the possibility to start studies of the spatial characteristics – sizes and locations of the bursts emission sources. Thus, it was shown that at the decameter band, the Type III burst durations were defi ned by the emission source linear sizes, whereas the spike durations were governed by the collision times in the source plasma. It was experimentally proved that the effective brightness temperatures of the sources of solar sporadic radio emission at the decameter band may reach values of 1014–1015 K. In addition, it was found that the radii of the quiet Sun at frequencies 20 and 25 MHz are close to the distances from the Sun at which the local plasma frequency is equal to the corresponding observed frequency of radio emission in the Baumbach–Allen model.

This paper presents theoretical developments of some issues in the physics of space intrusions. We report the discovery of a new effect – variations in brightness and “wobbling” in the meteor trail. The frequency of the variations of brightness (f_c) and wobbling (f_m) that can be measured is important information parameters that allow us to obtain estimates all the characteristics of the meteor if its height and speed are known. Basic two-side intrusion observations automatically determine both the height and speed of the intrusion. We offer a new “tuning technique” that allows determining the meteor characteristics during one-side observations. The essence of a new technique is to fine-tune the initial parameters of the simulation model of intrusion until the calculated and measured frequencies f_c, f_m coincide. We found that rotation plays an important role in the dynamics of meteors; in particular, they can burst in due to centrifugal forces that exceed the strength of the material. In the case of one-side observations, we construct a grid of intrusion models using the Impact 4A software program on the plane of the primary “mass–speed” meteoroid. As a result of modelling, we find the height at which the frequency ratio f_c/f_m coincides with the value found from measurements for exploding meteoroid. The paper describes the characteristics of the space intrusion of a meteor in Kyiv on August 12, 2019, 22:52:57 UT. The amplitude of the brightness fluctuations was found about 0.1 magnitudes, the amplitude of the wobbling of about 4 arc seconds. Using the Impact 4A software program the preatmospheric velocity was evaluated ∼40 km/sec; the mass of the meteoroid was evaluated approximately 0.45 kg. This meteoroid reached maximum light at 82.2 km and ablated partially. We find estimates of a residual mass of about 10 grams and a residual speed of about 20 km/s. We found that the radius of the helical path of the meteor at this height is about 1.5 meters. The meteoroid reached a critical value of the speed of rotation on the surface. At this moment, a meteoroid exploded and destroyed.

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Subject and Purpose. This paper presents numerical simulation results on the transmission spectra of a split-ring resonator (SRR) loaded with a thin film of yttrium iron garnet (YIG). The application of a magnetic core in the SRR is proposed for increasing the photon-magnon (P-M) coupling strength. The anticrossing effect in the frequency dispersion behavior of the SRR modes and YIG film ferromagnetic resonance modes, namely SRR-YIG coupled modes, is identified. The dimensional parameters of the SRR with a magnetic core are calculated, taking care to preserve the design compactness and striving to obtain a maximum possible spin-number-normalized coupling strength for such a system. The work has been aimed at evaluating the efficiency of applying the magnetic core as a part of the planar microwave resonator to enhance the P-M coupling strength. Methods and Methodology. The transmission coefficient |S21| spectra of electromagnetic waves propagating through the planar resonator with the YIG film under the ferromagnetic resonance condition are numerically studied using the CST Studio Suite package in the frequency domain. The spatial distribution function of the magnetic field strength is calculated for the two scenarios of YIG film location: near the magnetic core (between the SRR and the feeding stripline) and inside the magnetic core (in the SRR center). Also, for each of these two scenarios, the transmission coefficient |S21| spectra of the wave propagation through the feeding stripline in the region of SRR-YIG coupled modes are simulated with and without the magnetic core. The dispersion curves of the SRR-YIG coupled modes are obtained in analytical terms. Results. It has been shown that the magnetic core application increases the P-M coupling strength 2.0 times in the scenario of YIG film location near the magnetic core (between the SRR and the feeding stripline). When the YIG film is inside the magnetic core (in the SRR center), the P-M coupling strength rises 2.3 times compared to similar cases without the magnetic core. Conclusions. The suggested magnetic core application can be used to increase the P-M coupling strength in the SRR — magnetic film resonant system, striving to develop effective microwave-to-optical converters and create efficient information exchange between quantum computers.

Subject and Purpose. Сonsidered are the natural modes and their correspondent eigenfrequencies of a composite structure which is nonuniform along one of the coordinates and consists of a lossy ferromagnetic layer placed in a static magnetic field. The layer involves a perfectly conducting strip grating at one of its boundaries and a graphene monolayer at the other. Methods and Methodology. The above stated problem can be approached within the analytical regularization procedure developed for dual series equations. The latter concern a broad class of diffraction problems which include, in particular, the diffraction of monochromatic plane waves on strip gratings placed at the boundary of a gyromagnetic medium. The amplitudes of the electromagnetic eigenmodes can be obtained from the infinite set of homogeneous linear algebraic equations solvable within a truncation technique. The roots of the system’s determinant represent complex-valued eigenfrequencies of the system under investigation. The material parameters adopted in our computations for the ferromagnetic layer correspond to such of yttrium iron garnet. Results. A number of numerical programs have been developed which permit analyzing the dependences of wave field eigenfunctions and complex eigenfrequencies upon geometrical parameters of the structure (such as grating slot width and period, and thickness of the lossy layer), as well as on electrodynamic parameters of the ferromagnet and graphene characteristics, specifically the chemical potential and relaxation energy of electrons. A number of behavioral regularities have been established, as well as the effect of non-uniformity of ferrite layer parameters upon the structure’s eigenfrequencies and wave field eigenfunctions. Conclusions. The structure under study has been shown to be is an open oscillatory system with a set of complex-valued natural frequencies demonstrating finite points of accumulation. The real parts of these eigenfrequencies lie in a certain interval determined by characteristic frequencies of the ferrite layer, while the imaginary parts are negative, such that the correspondent natural modes show an exponential decay with time. The grating edges represent the mirrors which the natural surface oscillations are reflected from, being supported at that by the ferromagnetic medium. The results obtained in this paper can be useful for creating the elemental base for microwave devices and the devices themselves.

This paper is an attempt of paying tribute to the memory of Leonid Mykolayovych Lytvynenko (LML), an outstanding Ukrainian scientist, Full Member of the National Academy of Sciences who worked most fruitfully in the fields of radio science and radio astronomy. Starting of 1985, Dr. Lytvynenko was, over a 30-plus years period, at the head of the Institute of Radio Astronomy, Acad. Sci. of the Ukrainian SSR (currently the National Academy of Sciences of Ukraine) that had been established owing to his vigorous and direct participation in the process. In 1996 LML promoted foundation of a new scientific journal, namely the "Radio Physics and Radio Astronomy", which he devotedly served for, in the Editor-in-Chief capacity, during the 25 years that followed. Dr. L. Lytvynenko was one of the brightest representatives of the school of theoretical radio physics that had developed within the O. Usikov Institute for Radio Physics and Electronics in Kharkiv and further flourished within the Institute of Radio Astronomy. He is known as the founder of a new branch of radio science, specifically theory of electromagnetic wave diffraction and propagation through composite and multilayered periodic structures.

Purpose: The subject of the paper is discussion of reflected radiation from the neutron star surface. Such radiation, as was shown earlier by S. V. Trofymenko and one of the authors, occurs when reflects the radiation of relativistic positrons flying from the magnetosphere to a star in the accelerating electric field of the polar gap. This gave an explanation of both the interpulse shift in the Crab pulsar (mirror reflection in an inclined magnetic field) and the appearance of additional HF components (diffraction on the periodic structure excited by the incident radiation) discovered by Moffett and Hankins. The aim of the paper is to study the effect on the HF components of a resonance with a surface electromagnetic wave. Design/methodology/approach: Since the HF components occur at the same frequencies as the interpulse shift, we believe that they are a consequence of the same physical process. Such a process is the reflection from the surface of a neutron star of the radiation of the return positrons. The appearance of HF components is considered as a manifestation of stimulated scattering by surface waves. For comparison, the data of laboratory experiments on the diffraction of laser radiation on a metal diffraction grating are presented. They demonstrate the appearance of a bright near-surface wave under resonance conditions, which can serve as an analog of the HF component in the Crab pulsar. Findings: In the formation of HF components, such phenomena as Wood’s anomalies are significant, leading to considerable essential increase of the increment of stimulated scattering at the resonance with the surface electromagnetic wave. The surface wave excited with the resonance leads to reflected Raman scattering of higher frequencies of the continuous spectrum of the incident radiation. Conclusions: The radiation of a pulsar is determined, among others, by the reflecting properties of the surface of the neutron star, i.e. its conductivity (surface impedance). The resonance substantially reduces the stimulated scattering threshold. The continuous spectrum of the radiation incident on the surface provides a large width of the HF-components.

Subject and Purpose. The present paper is concerned with sea wave diagnostics by signals from artificial satellites in a bistatic radar scheme using the grazing radio-wave propagation and a diffuse component of the signal reflected off the sea surface. The possibility is considered to expand the range of sea state diagnostics by using satellite emissions in different frequency regions. Methods and Methodology. The research is based on the data of field experiments using over-the-horizon navigation satellites of the first (Transit) and second (GPS) generations. The data processing is by the methods of moving average and moving mean square deviation adopted because of the dynamic character of the experiments given the moving source presence. The sea surface state in a particular experiment is estimated by the diffuse component extracted from the total experimental signal. A comparative analysis of the diffuse component parameters is carried out by computer modeling at various wavelengths, source elevation angles and root- mean-squared wave heights. Results. For both satellite systems GPS and Transit, the experimental results show that in the calm and moderate states of the sea surface, the diffuse component intensity of signal fluctuations caused by sea waves differ significantly and fit in with the model upon the Rayleigh Roughness Criterion. On this basis, an advantage can be taken from the satellite emissions in various frequency ranges to expand the scale of sea state diagnostics. The higher-frequency region therewith offers a more accurate yet more limited scale of the sea state measured. The addition of lower-frequency emissions expands the scale of sea state diagnostics towards the severe states. Conclusions. It has been determined that the range of sea state diagnostics can be expanded by using satellite emissions in different frequency regions.

Subject and Purpose. In this paper, an algorithm is developed to improve the spectrum image resolution in the atomic emission spectrum registration using multi-element detectors and taking multiple exposures with image shifting by a fractional part of a pixel. Methods and Methodology. Mathematical modeling techniques are employed in the coordinate representation dictated by the prior information. The modeling results are checked by experiment. Results. The importance of the resolution value of spectral image registration systems and its impact on the quality of the obtained results have been highlighted. The spectral informativeness of the regularly (matrix- or linearly) structured multi-element detectors has been evaluated against the irregular-structure sensors, such as photographic emulsions. As it has been found that the process of pixel size reduction is demanding, an alternative approach through subpixel image shifting has been proposed. Unlike the case of the corresponding instruments implemented as a rule in the frequency domain, here the relevant theoretical problem reduces to the over- determined system of linear equations. The proposed solution algorithm employs the least squares method having regard to the prior data specificity posed by the isolation of the spectral lines and a smooth flow of the background between them. The digital simulation results and the real experimental evidence from the atomic emission spectral analysis have been presented, illustrating the algorithm operation. The experimental research was carried out for one-dimensional spectrum images registered with linear charge-coupling photodetectors. The so gained resolution was twice the spatial resolution of the photodetector. Conclusions. It has been demonstrated that controlled image shifting not only improves the photometry accuracy but also significantly enhances the detector resolution. The general comparisons of the theory with the experiment have proved the feasibility of bringing the proposed methodology into atomic emission analysis.

Subject and Purpose. In Part 2 of the current paper, we seek to analyze the observational results of decameter carbon radio recombination lines (RRLs) detected near the frequency 26 MHz through the UTR-2 radio telescope towards the S140 emission nebula and the GSH 139-03-69 super shell. These lines have proven themselves as a highly effective tool for cold, rarefied interstellar medium (ISM) diagnostics. The aim is to determine an association of line-forming regions (CII regions) with other ISM components and study physical conditions (electron temperature Te and electron density Ne) in these regions. Methods and Methodology. By iterative comparison of detected and modeled integral intensities of decameter carbon RRLs, we determine physical state ranges where recorded experimental data best fit the model values for various combinations of Te,Ne, and path lengths s. Results.It has been found that the characteristics of the detected decameter carbon RRLs are consistent with the higher-frequency data for both the S140 line of sight and other Galactic plane directions, including the GSH 139-03-69 direction. Ranges of physical conditions where recorded data and model values are in the best agreement have been determined, being Te = 50÷ 100 K, Ne = 0.01 cm–3, and s= 10 pc — for the S140 nebula direction and its vicinity and, also, Te = 50÷ 100 K, Ne =0.01 cm–3, and s = 5÷ 7 pc — for the GSH 139-03-69 super shell direction. Conclusions. The obtained results indicate that the detected decameter carbon RRLs originate from CII regions associated with clouds of diffuse neutral hydrogen HI in the Galactic plane. The lines are seen against a background Galactic radio emission whose brightness temperature increases as frequency decreases.

The article presents the results of the authors’ research on the cosmological views of Johannes Keppler in his Latin treatise Harmonices Mundi. The authors discuss the background of composing the treatise concerning the philosophical, religious, and cultural contexts of that period, and give a brief overview of the structure of the treatise, Kepler’s theory and his third law of harmony. The paper demonstrates the connection and reception of philosophical ideas on the harmony of the world in Kepler’s treatise and ancient philosophers, such as Pythagoras, Plato, and Proclus. This shows that Kepler’s philosophical and scientific views largely depended on his theological background. The authors discuss the perception of ancient cosmological ideas in Kepler’s Harmonices Mundi relating to Pythagorean tetractys, five Platonic solids or regular polyhedral, and cosmic harmony as well as Proclus’ theoretical mathematics.

Subject and Purpose. Since decameter carbon radio recombination lines (RRLs) were detected for the first time more than forty years ago, they have significantly extended our knowledge of the physics, kinematics and chemistry of the cold rarefied interstellar medium (ISM). A large number of these lines have been observed towards various Galactic radio sources. The present paper describes our studies of decameter carbon RRLs in such Galactic directions as the sight-lines to the S140 emission nebula and to the large volume of cold neutral hydrogen known as the GSH 139-03-69 super shell. Methods and Methodology. Observations within a 1-MHz frequency band centered at 26 MHz were performed using the UTR-2 radio telescope and a multi-channel digital correlator. The UTR-2 is still the world largest and the most sensitive low-frequency radio telescope. Results. We report the detection of decameter carbon RRL series C627α – C637α from the medium lying towards the S140 nebula. The extents of RRL forming regions have been estimated. It is suggested that RRLs in the S140 direction are formed in the local ISM lying along the line of sight. The RRL-forming region is probably associated with omnipresent diffuse neutral HI gas in the Galactic plane rather than with S140 nebula itself. Toward the GSH 139-03-69 super shell, decameter RRLs have been detected as well. Likewise, they apparently originate from the local medium lying along the sight-line. Yet, the spectrum contains a RRL component corresponding to the absorption of the cold gas of the GSH 139-03-69 itself in the ISM. Conclusions. The obtained results indicate great possibilities of decameter carbon RRLs not only for cold ISM probing but also for making a good auxiliary tool for studying large complexes of extremely cold hydrogen HI in the Galaxy.

Subject and Purpose. This part of the paper continues presentation of results of the solar radio emission studies performed with Ukrainian radio telescopes over the past 20 years. The importance is stressed of developing adequate instruments and methods for identifying the nature of decameter-wavelength radio emissions from the Sun. Methods and Methodology. The low frequency Ukrainian radio telescopes UTR-2, GURT and URAN-2 have been used in the project along with other ground- and space based instruments in order to achieve a comprehensive understanding of physical conditions in the solar corona. Results. Special methods and tools have been developed for studying radio frequency burst emissions against the background of strong interference. Unique data have been obtained concerning sources of sporadic radio emissions from the Sun, as well as the contribution from wave propagation effects and the impact of the ionosphere on the results of observations. The most significant observational and theoretical results are presented, obtained in the study of solar low frequency emissions over the past 20 years. Solar radio emissions are shown to be efficient sounding signals not for the solar corona alone but for the Earth’s ionosphere as well, which allows identifying its impact on the results of radio astronomy observations. Conclusions. The Ukrainian radio telescopes of the meter and decameter wavebands currently are unrivaled tools for investigating the Universe in the low-frequency range of radio waves. Owing to their advanced characteristics, they make a significant contribution to the progress of world’s solar radio astronomy.

Subject and Purpose. The thermal energy of the Tonga volcano reached 3.9 ·10¹⁸ J, its power amounted to 9.1 ·10¹³ W. The energy and power of the blast waves approached (6.7...7.5) ·10¹³ J and 1011 W, respectively. Ionospheric effects caused by the explosive eruption of the Tonga volcano on January 15, 2022 have received due attention. It was established that the ionospheric disturbances spread over global distances, with the greatest disturbances occurring in the near zone. The aim of the present paper is to describe aperiodic and quasi-periodic disturbances started by the Tonga volcano explosion and occurring in the near ionospheric zone. Methods and Methodology. To detect ionospheric disturbances generated by the volcanic eruption, temporal variations of the total electron content (TEC) in a vertical column in the ionosphere were analyzed. The total error of the TEC estimation did not exceed 0.1 TECU. Results. The quantitative characteristics of ionospheric disturbances caused by the explosive eruption of the Tonga volcano have been obtained. It was proved that the appearance of the ionospheric "hole" was caused directly by the volcanic explosion. With distance away from the volcano, the TEC deficit in absolute values decreased from ~10 to ~2.5 TECU. As that was happening, the time taken to form the ionospheric "hole" increased from ~20 to ~100 min. Three groups of disturbances were observed. One group picks out disturbances having an N-shaped profile and caused by a blast wave with a speed exceeding ~1 000 m/s. Another group includes disturbances with a propagation speed within ~340...620 m/s, which is characteristic of atmospheric gravity waves at ionospheric heights. The last group is specified by the disturbance propagation speed within ~110 to 320 m/s. The disturbances of the kind can be generated by tsunamis, Lamb waves and atmospheric gravity waves. The wave disturbance periods varied within ~ 5 to 20 min, the disturbance amplitudes were within 0.5...1.0 TECU. Conclusions. It has been proven that aperiodic and quasiperiodic ionospheric disturbances in the near zone were caused directly by the explosion of the Tonga volcano

Subject and Purpose. Accuracy of the material recognition using radio wave methods in the ultra-high frequency band for substanc- es with dielectric properties is the present paper concern. To estimate a total error arising in material measurements by the radio wave method and determine constituents of the error is the aim of the work. Methods and Methodology. The material recognition accuracy is estimated by the method of statistical analysis in terms of average statistical deviation and dispersion. Results. Advantages and disadvantages of the waveguide method in which a test material sample is placed inside a metal waveguide have been traced, suggesting an obvious drawback that the material recognition process of the sort is difficult to be automated. In the remote inspection procedure, the test material is in free space (e.g. on a conveyor) where it is illuminated with a microwave transmitting antenna. The receiving antenna is located on the other side of the test sample and transfers the received signal to the apparatus for determining material parameters. There, the attenuation coefficient is measured as the electromagnetic wave passes through the sample. The measurement results show a correlation dependence of the wave attenuation coefficient on the quality of the substance, enabling us to use frequency dependences of the material to reveal its unknown quality. The remote method makes it possible to automate the recognition of materials with dielectric properties. For these methods mentioned right above, random error values arising during the material recognition were estimated by the method of statistical analysis. Conclusions. The analysis of errors in the material recognition shows that the total error ranges from 7.28 to 12.74% with corresponding constituent errors including faults of today’s microwave measuring devices, inappropriate application of the method or unsuitable type of the structural model of the parameter determination, and errors in data calculations.

Subject and Purpose. The sporadic radio emissions coming from the Sun in a broad frequency range contain a lot of important information concerning the solar corona, parameters of the radio frequency sources therein, and the parameter variations resulting from active processes on and about the Sun. These have been the reasons for recent launches of the space missions intended for stud- ying the Sun and its corona, such as the Parker Solar Probe (PSP) and the Solar Orbiter. The present work is aimed at demonstrating effectiveness of the ground-based support for the space missions, the PSP before all, which is provided by the large Ukrainian radio telescopes of the decameter wavelength range. Another purpose has been cross-calibration of the space-borne radiometer against calibrated data from a ground-based instrument. Methods and Methodology. One of the remote diagnosis techniques widely used with respect to the solar corona is to analyze parameters of the radio frequency emissions from sources lying at a variety of altitudes within the corona. The methodology of such joint, space-borne/terrestrial investigations suggests simultaneous observations of certain individual events during closest approach of the space probe PSP to the Sun, with analysis over a widest possible frequency range. The data obtainable within overlapping fre- quency bands are proposed for calibrating the on-board radio receivers of the space probe. Results. The methodology proposed for joint, space-based / terrestrial observations has been substantiated. Data from the UTR-2 and URAN-2 radio telescopes and the space probe PSP have been used to plot the dynamic and the polarization spectra of the June 9, 2020 solar bursts, with identification and comparison of the relevant individual events. A joint dynamic spectrum of these bursts has been obtained for the frequency band of 0.5 to 32 MHz. The calibrated data from the ground-based radio telescopes have allowed performing cross-calibration of the HF receiver in the FIELDS-PSP data taking module within the frequency band of 10 to 18 MHz. Conclusions. The paper has provided evidence of an effective ground-based support for the space mission PSP on the part of large Ukrainian radio telescopes. Examples of joint observations have been given, and a methodology described which is employed for cross-calibrating the HF receivers of the FIELD-PSP module. Prospects are outlined of further ground-based support for solar space research missions.

Subject and Purpose. The study deals with the dual-frequency radio interferometry technique, which is based on the employment of two fairly close frequencies with the aim to remove ambiguity of the radar target elevation estimation using 2D-radar and eliminate 2 pm-uncertainty of the signal phase difference measurement. Analysis of random noise action on the accuracy of the elevation angle estimation by the dual-frequency radio interferometry and assessment of practical applicability of the method make up the purpose of the paper. Methods and Methodology. The noise action on the elevation angle measurement accuracy is examined through a series of analytical calculations with the use of statistical analysis methods. The noise in each receiving channel is modeled in terms of additive, statistically independent stationary Gaussian processes with zero mean values and equal variances. The calculation results are checked via computer simulations with statistics estimations for 106 random noise realizations. Results. A correct condition has been developed for the sector width where the target elevation angle is unambiguously estimated depending on the space separation of the antennas (baselines) and the frequency ratio. Expressions for elevation angle estimation errors have been obtained, showing that the error is mainly contributed by the faults in the determination of the ambiguity interval number. A probability of the correct determination of the ambiguity interval number has been derived depending on the signal- to-noise ratio and the frequency difference, indicating that almost one hundred per cent probability of the correct determination of the ambiguity interval number is only achieved when the signal-to-noise ratio exceeds 30 dB. A comparative analysis has been performed between the methods of dual-frequency interferometry and conventional phase-difference direction finding in the case of close X-band frequencies and the same sectors of survey. Conclusions. The dual-frequency radio interferometry technique with close frequencies has been shown to outperform the standard phase-difference direction-finding method only when the signal-to-noise ratio is sufficiently high (over 30 dB). In principle, the accuracy of the technique seems possible to improve by taking significantly different frequencies selected with regard to the scale negotiation condition. However, it should be mentioned that the implementation of the relevant algorithm in practice is much more complicated than the conventional scheme with a single frequency and several antenna baselines.

Subject and Purpose. The subject of this paper is to review the principal methods of fractal and multifractal analysis of signals and processes, in combination with a detailed consideration of the algorithms that can provide for a successful practical implementation of the methods described. Methods and Methodology. The results presented concern modeling of both deterministic and stochastic fractal and multifractal signals and processes. The corresponding practical methods of analysis are considered, with discussion of their essential features, advantages and disadvantages, as well as of the problems of application that may exist. Results. Several approaches have been discussed as to categorizing the signals and processes within the notion of fractality. A few tens of models of deterministic and stochastic fractal or multifractal signals and processes have been analyzed in detail. Over twenty methods of monofractal analysis have been analyzed, with identification of their features, advantages or disadvantages, and limits of applicability. The expediency of resorting to complex methods of monofractal analysis has also been discussed. Those methods are not based upon application of fractal analysis techniques alone but rather combine them with linear and nonlinear integral time-frequency transforms. The effectiveness of the ten most popular multifractal analysis techniques has been confirmed, with consideration of their special features, advantages and drawbacks. Conclusion. The mathematical foundations have been presented which underlie modern methods of analysis and modeling of fractal and multifractal signals and processes. The methods discussed may allow revealing a great amount of unique hidden information on the world around us.

The paper is dedicated to the memory of V.P. Shestopalov, an outstanding scientist known for his great contributions to radio physics, electronics, theoretical and mathematical physics. While being a holder of many formal academic degrees and titles, like PhD, DSc (Phys.-Math.), Professor, and Fellow Member of the Academy of Sciences, he was particularly honored as the founder of a scientific school vigorously developing diff raction theory and diffractional electronics. Th at school has been associated with the O.Ya. Usikov Institute for Radio Physics and Electronics where Dr. Shestopalov was Director till 1993. Today, we are marking the 100-th anniversary of Victor P. Shestopalov.

This paper is dedicated to the 90-th anniversary of Vadym Borysovych Razskazovsky, an outstanding scientist in the fields of radio engineering and radio science, holder of the titles and positions like DSc (Engineering), Professor, and Head of the Statistical radio physics department at the O.Ya. Usikov Institute for Radio Physics and Electronics within the Academy of Sciences of Ukraine.

Subject and Purpose.Methods for computer processing of radio astronomical signals observed with space objects at low frequencies are given. The aim of this paper is to improve the current methods and use their combinations for cleaning records from radio interference of natural and artificial origin in the frequency-time domain, as well as to discuss advantages and disadvantage of the methods. Methods and Methodology.In the study of records obtained with radio astronomical observations there is a common feature of received signals from space sources, which consists in a significant contribution of radio interference. Having sufficient experience on possible types of interference and distortion of signals on the way of their propagation, the efficiency of suggested procedures, clearing radio signal interference in the frequency-time domain by a combination of different approaches in dependence from typical features of signals withinvestigated space objects, is shown. Results. The developed methods of extracting space signals against the background of interference allow one to get unique data on the sources of radio emission in astrophysical phenomena. On the one hand, software tools make it possible to detect very weak events against the background of radio frequency interference. On the other hand, they allow one to measureemission parameters based on the most statistically complete set of events. Conclusions.The results obtained in this work manifest that there is no universal way to overcome any obstacle in the records of radio astronomical observations because of radio interference. In addition, even if the most appropriate method is applied, it often requires pre-adjustment of the corresponding parameters on which the analysis of physical parameters of radio emission in the area of generation depends. But if such a space signal at the radio records is not very spoiled by interference, the use of considered methods can be successful and useful.

Subject and Purpose. The subject of research is the flicker noise present in informant signals of search-and-rescue radars, specifically its properties and the effect it may have on algorithms for detecting and identifying manifestations of human breath and heartbeat processes during rescue operations. The work has been aimed at creating a suitable description of flicker noise for developing optimal algorithms of digital signal processing for quick detection and identification of informant signals during rescue missions. Method and Methodology. The low-frequency flicker noise has been modeled within the polynomial equations technique, proceeding from an analysis of real data on noise components in the output signals from a coherent search-and-rescue radar. A comparative analysis is done for a variety of approximating functions suggested for representing the low frequency portion of the spectrum observed. Results. For the low-frequency range wherein spectral components of the informative signal owing to respiration and heartbeat of humans are concentrated, an adequate model of the fluctuating interference is the flicker noise model built on the basis of polynomial equations. The problem of optimized model representation of the noise in digital signal processing algorithms has been analyzed for the case of a coherent search-and-rescue radar. A model of the fluctuating process has been suggested, based on a polynomial approximation for the spectral function in the low-frequency range of the signals observed at the radar output. Conclusion. Spectral characteristics of both interference and informant signals have been investigated. A structural diagram has been proposed for a high sensitivity, coherent search-and-rescue radar implementing a signal storage algorithm based on the polynomial model of the fluctuating process. The advantages and disadvantages of the radar are discussed, with examples given of real signal implementations and of noise spectrograms. Methods of effective estimation of Doppler signal phases are presented. The paper suggests an analysis of basic requirements as to parameters and performance characteristics of the rescue radar.

A bundle of papers dealing with functionally stable systems requires the necessity of analyzing of obtained results and their understanding in a general context of cybernetic's development and applications. Description of this field of science, main results and perspectives of the new theory of functionally stability of dynamical systems concerning the problem of remote-piloted aircrafts engineering using pseudosatellite technologies are proposed in the paper.

Subject and Purpose. Considerable attention has traditionally been given to the interaction of high-power radio-frequency emissions with the ionosphere. The great many physical effects taking place within the limits of a powerful (heating) facility’s antenna pattern are subjected here to a thorough and detailed analysis. Also, the application of high-power radio emissions provides a convenient means for studying subsystem coupling in the Earth-atmosphere-ionosphere-magnetosphere system, as well as of generation and propagation of disturbances well beyond the antenna pattern of the transmitter. The present paper has been aimed at analyzing the features revealed by the large-scale ionospheric disturbances as these are generated under the impact of either monopulse or periodic radio-frequency emissions from an HF heating facility. Methods and Methodology. In the course of the experiments, the ionosphere was affected with high power radio frequency emission from the heating facility Sura. The disturbances were diagnosed at a distance of 960 km from the heater, with the aid of a vertical incidence Doppler radar. Results. It has been found that through the period of minimal solar activity the ionospheric disturbances observable at a range about 103 km from the heater did arise as the effective radiated power of the latter approached to 25 MW. The duration of the ionospheric response to the impact of an incident monopulse was equal to the length of that latter, while the quasi-periodic variations shown by the Doppler frequency shift just started to appear. The apparent horizontal speed of the propagating disturbances was found to vary from about 300 m/s to 420 m/s. Note that speed to increase at higher altitudes. The periodic mode of heater operation was accompanied by generation of quasi-periodic disturbances in the electron density, of relative amplitudes about 1% and periods close to the Brunt–Väisälä period. Conclusions. The basic features of Doppler spectrum variations, contained in the signals from a diagnostic radar, have been identified in connection with high-power HF radiation incident on the ionosphere

The paper is dedicated to the memory of Pavel V. Bliokh, an outstanding Ukrainian scientist in the fields of theoretical and radio physics, on the occasion of his 100th anniversary. P.V.Bliokh (PhD, D.Sc, Professor, Honored Scientist of Ukraine) was one of the founders of the ‘space radiophysics’ branch of research. While working in that direction, he created a well-known scientific school at the O.Ya. Usikov Institute of Radiophysics and Electronics and the Institute of Radio Astronomy, National Academy of Sciences of Ukraine.

Subject and Purpose. The paper presents results of numerical modeling and experimental studies of a disk-shaped microstrip antenna involving ‘meander’ type slotted inhomogeneities. The work has been aimed at optimizing the operating range of the antenna and matching it to external circuits through the use of additional structural elements and appropriate feeding techniques. Methods and Methodology. The design features a circular disk-shaped microstrip resonator containing within its plane groups of slotted inhomogeneities which form a segmented meander line, with the segments oriented relative one another at an angle of 120°. The antenna could be fed through a segment of a screened coplanar line. The location of the screening plane of the coplanar line, as well as its dimensions, were variable. Numerical simulation was carried out within the ‘semi-open resonator’ technique using the finite element method. The degree of optimization of the operating range was estimated, based on analyzing spectral characteristics of the antenna, for a variety of its geometric parameters, and the magnitude of the return loss over a given frequency range. Measurements of the VSWR were carried out with reflectometers. Results. Frequency and power characteristics of a monopole, disk-shaped microstrip antenna have been analyzed and optimized over a wide frequency range. Mechanical dimensions of the additional shielding plane and location thereof have been identified as factors having significant influence upon the frequency-dependent, polarizational and power characteristics of the antenna. Conclusions. The operating frequency range, spectral and power characteristics of a monopole, disk-shaped microstrip antenna have been studied both theoretically and experimentally. Numerical simulations were carried out with the use of the fi nite element method. Experimental studies of the frequency characteristics were performed using reflectometry techniques. The antenna considered can find practical application over a wide frequency range, either as a single radiating element in a device or system, or a constituent part of an antenna array.

Subject and Purpose. Proceeding from a mathematical model of the electronically tunable autodyne oscillator (Part І of this paper), essential features of the signal formation / signal processing procedure are considered, as implementable in an autodyne radar that may reveal nonlinearity in its modulation characteristic. The work is aimed at suggesting a digital technique to enable introduction of corrections to the frequency modulation law of the sounding signal and effectuate processing of the data from the close-range autodyne radar (improving its spatial resolution and accuracy of target range measurements). Methods and Methodology. The present analysis of the radiated signal formation and processing of the data from the autodyne radar has been carried out as numerical modeling of spectral, frequency and amplitude characteristics of the radar signals expected, as well as spectral processing of the experimental data from the frequency modulated autodyne radar. Results. An effective law of temporal variations has been suggested for the corrective control voltage of the Gunn diode-based Ka-band autodyne transceiver with a linear law of frequency modulation. The correspondent experimental studies were conducted with an autodyne close-range radar system of Ka-band employing an asymmetric linear frequency modulation with a 500 MHz band of frequency tuning. The use of digital methods for correcting the frequency modulation law has permitted improving the accuracy of target ranging and range resolution up to 0.3 ÷ 0.6 m, which figures correspond to the theoretical limit for the close-range homodyne radar with a 500 MHz tuning band. Conclusion. By linearizing the modulation characteristic of the oscillator and applying digital processing to the autodyne signal in the close-range radar system with a linear frequency modulation law it proves possible to reach ultimately high estimates for the accuracy and resolution of target range measurements. The results obtained can be helpful for developing radar sensors and radiofrequency meters with enhanced parameters and characteristics.

Subject and Purpose. The paper is an effectiveness study of the root-MUSIC technique as applied to elevation angle measurements of low-altitude radar targets over the sea, specifically with account of the radio waves’ phase front sphericity. The purpose is to find out whether and how much can the measurement accuracy be improved through account of the phase front sphericity, as compared with the classical approach assuming a plane phase front. Methods and Methodology. The work proceeds from computer simulation, considering a variety of sea roughness levels, and covers a range of radio wave reflection conditions from a nearly specular return to strong diff use reflection from the sea surface. The simulation involves a wide range of target distances within the far-field region with respect to the receive array. Results. A new approach has been suggested for taking into account the phase-front sphericity of the radio waves arriving from the target. The level of errors of elevation angle measurements has been estimated and compared with such shown by the conventional root-MUSIC method which assumes a plane phase front for the waves reflected from the target. The comparison concerns a wide range of sea roughness levels and target separations. Conclusion. It has been established that the proposed version of the root-MUSIC technique which takes wave front sphericity into account can significantly reduce the errors in elevation angle measurements for low-altitude targets.

It is follows from the observation data that the nonthermal radio source Sgr A* at the Galactic Center must be identified with a supermassive compact object with mass 2.6 x10^6 M_Sun. In paper (Verozub L.V., Kochetov A.Y, 2001) the existence of stable configurations of degenerated Fermi-gas without events horizon with masses 0^6 M_Sun - 10^9 M_Sun was argued. A spherically symmetric hydrodynamical accretion onto the object in the Galactic Center is considered in this paper. The profiles of the velocity, temperature and density in the falling gas have found taking into account of two-flow regime, dissipation processes, pressure of radiation and strong gravitation effects. The spectrum of the bremsstrahlung radiation is calculated. It is shown that the our results do not contradict the observation data.

Subject and Purpose. In Part 1 of the paper, a mathematical model of an autodyne self-oscillator with frequency tuning by varactor capacitance varying is built and thoroughly analyzed for the features of signal formation in autodyne radar with a wide frequency-modulation bandwidth and a nonlinearity in the modulation characteristic. The aim of the study is to appreciate the action that the nonlinearity of the oscillator modulation characteristic exerts on the spectral characteristics of signals from frequency-modulation autodyne radar. Methods and Methodology. The research method is a mathematical analysis of the operation of an autodyne oscillator with electronic frequency tuning. To examine formation processes of emitted autodyne signals, the spectral, frequency and amplitude characteristics of signals from frequency-modulation autodyne radar are constructed with the use of numerical modeling techniques. Results. Numerical modeling of autodyne response signal spectra has been performed for various distances to the reflecting object and different modulating voltages across the varactor. It has been shown that a nonlinear dependence of the generator frequency on the varactor voltage makes for the broadening of the autodyne response signal spectrum. It has been found that as the object distance increases, the frequency of the autodyne response signal moves towards the higher frequencies, while the nonlinearity makes the spectrum broaden. The obtained calculation results refer to an 8-mm Gunn diode autodyne. Conclusion. The performed research of the spectral characteristics and into the features of signal formation in autodyne transceiver devices with a wide frequency tuning has shown that in order to achieve high resolution figures from autodyne radar, certain methods are needed to be developed for adjusting the laws of frequency modulation and for the processing of response signals from reflecting objects. Such a method and ways to solve these problems will be presented in Part 2 of the work.

Subject and Purpose. The paper is concerned with the behavior of a nonlinear dynamic system that has two degrees of freedom and whose joint nonlinearity is established by all the nonlinear coupling between the degrees of freedom. The purpose is to find out if the Krylov—Bogolyubov—Mitropolsky (KBM) method is applicable to a system of partial differential equations. Methods and Methodology. The consideration of the problem is by the Krylov—Bogolyubov—Mitropolsky method in the first approximation. Then the results are treated using numerical methods. Results. An electromechanical system with two degrees of freedom and a known parametric resonance has been studied using the Krylov—Bogolyubov—Mitropolsky method in the first approximation. The phase space of the system has been described. It has been shown that the obtained solution covers an energy periodic transfer between the two degrees of freedom. The difference between the considered oscillation system and its analogs discussed in the literature lies in that the considered circuit is parametrically excited by an internal force rather than external one. In a similar system of two circuits connected through a diode, the coupling includes a linear component. In the system of present concern, the coupling is all-nonlinear. Conclusion. The obtained results are of interest for the research into internal nonlinear resonances between degrees of freedom in an oscillation system that has two degrees of freedom and whose joint nonlinearity is due to all the nonlinear coupling between the degrees of freedom. The considered system can serve a test example in the development of programs implementing the Krylov—Bo- golyubov—Mitropolsky method as applied to an oscillation system with numerous degrees of freedom and a small nonlinearity.

Purpose: Solar eclipses pertain to high-energy sources of disturbance in the subsystems of the Sun–interplanetary-medium–magnetosphere–ionosphere–atmosphere–Earth and the Earth–atmosphere–ionosphere–magnetosphere systems. During the solar eclipse, the coupling between the subsystems in these systems activates, and the parameters of the dynamic processes become disturbed. Investigation of these processes contributes to understanding of the structure and dynamics of the subsystems. The ionospheric response to the solar eclipse depends on the season, local time, magnitude of the solar eclipse, phase of the solar cycle, the observation site, the state of space weather, etc. Therefore, the study of the effects, which each new solar eclipse has on the ionosphere remains an urgent geophysics and radio physics problem. The purpose of this paper is to describe the radio wave characteristics and ionospheric parameters, which accompanied the partial solar eclipse of 10 June 2021 over the City of Kharkiv. Design/methodology/approach: To make observations, the means of the HF Doppler measurements at vertical and oblique incidence available at the V. N. Karazin Kharkiv National University Radiophysical Observatory were employed. The data obtained at the “Lviv” Magnetic Observatory were used for making intercomparison. Findings: The radiophysical observations have been made of the dynamic processes acting in the ionosphere during the solar eclipse of 10 June 2021 and on the reference days. The temporal variations in the Doppler frequency shift observed at vertical and oblique radio paths have been found to be, as a whole, similar. Generally speaking, the Doppler spectra over these radio propagation paths were different. Over the oblique radio paths, the number of rays was greater. The solar eclipse was accompanied by wave activity enhancement in the atmosphere and ionosphere. At least three wave trains were observed. The values of the periods (about 5–12 min) and the relative amplitudes of perturbations in the electron density (δN≈0.3–0.6 %) give evidence that the wave disturbances were caused by atmospheric gravity waves. The amplitude of the 6–8-min period geomagnetic variations has been estimated to be 0.5–1 nT. Approximately the same value has been recorded in the X component of the geomagnetic field at the nearest Magnetic Observatory. The aperiodic effect of the solar eclipse has appeared to be too small (less than 0.01 Hz) to be observed confidently. The smallness of the effect was predetermined by an insignificant magnitude of the partial eclipse over the City of Kharkiv (no more than 0.11). Conclusions: The features of the solar eclipse of 10 June 2021 include an insignificant magnitude of the aperiodic effect and an enhancement in wave activity in the atmosphere and ionosphere.

Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operator method for the axially symmetric structures placed in free space. Design/methodology/approach: The problem is considered in the spectral domain. The scattered field is expressed in terms of unknown Fourier amplitudes (spectral functions). The annular slot is given as a unity of two simple discontinuities, namely of a disk and a circular hole in the plane, which interact with each other. The Fourier amplitude of the scattered field is sought as a sum of two amplitudes, the Fourier amplitude of the field of currents on the disk and Fourier amplitude of the field of currents on the perfectly conducting plane with circular hole. The operator equations are written for these amplitudes, which take into account the electromagnetic coupling of the disk and the hole in the plane. The equations use the reflection operators of a single isolated disk and a single hole in the plane. They are supposed to be known and can be obtained for example by the method of moments.The reflection operators can have singularities. After transformations, the equations are obtained, which are equivalent to the Fredholm integral equations of second kind and they can be solved numerically. Findings: The operator equations relative to the Fourier amplitudes of the field scattered by the discussed structure are obtained. The far zone scattered field for an annular slot and a ring for different values of parameters are studied. Conclusions: The rigorous solution of the problem of the electromagnetic wave diffraction by an annular slot in the plane and by a circular ring is obtained. The problem is reduced to the Fredholm integral equations of second kind. The far field distribution for different parameters is studied. The developed approach is an effective instrument for a number of problems of antenna technique to be solved.

Purpose: Experimental results and numerical simulations are presented, concerning effects of microwave generation in coaxial transmission lines which are fed with unipolar, high voltage electric pulses. The work is aimed at clarifying the relative importance of several mechanisms that could be responsible for the appearance of microwave-frequency oscillations in the course of pulse propagation through the guiding structure. Design/methodology/approach: Dispersive and filtering properties of coaxial waveguides that involve three structural sections are discussed. These latter follow one another along the axis of symmetry. Two identical sections at the input and output are filled with an isotropic liquid dielectric, while the middle part may, in addition, be either partially or fully filled with a non-conductive gyrotropic material. The inserted core represents a set of ferrite rings showing a nonlinear response to the initial high voltage, pulsed excitation. Throughout the series of measurements, the diameters of the inner conductor and of the ferrite core were kept constant. The outer conductor’s diameter was varied to permit analysis of the effect of that size proper and of the degree to which the cross-section is fi lled with ferrite. The gyrotropic properties of the ferrimagnetic material were realized through application of a magnetic bias field from an external coil. The measurements were made for a variety of pulsed voltage magnitudes from the range of hundreds of kilovolts, and magnetic bias fields of tens kiloamperes per meter. Findings: As observed in our experiments, as well as in papers by other writers, a unipolar pulse coming from the radially uniform front-end section, further on gives rise to quasi-monochromatic voltage oscillations. These appear as soon as the pulse has advanced a sufficient distance into the radially nonuniform portion of the guide. The oscillations may consist of a small number of quasi-periods, which suggests a large spectral line width. However, by properly selecting geometric parameters of the wave guiding line and the characteristics of the initial pulsed waveform it proves possible to obtain output frequencies of about units of gigahertz and pulse powers at subgigawatt levels. Conclusions: The frequencies and amplitudes of the appearing oscillations, as well as their spectral widths, are governed by the complex of dispersive and non-linear properties of the guiding structure. The diameters of the inner and outer coaxial conductors in the line, diameter of the ferrimagnetic insert and its intrinsic linear dispersion determine the set of waveguide modes capable of propagating through the line. An oscillating part of the waveform may appear and get separated from the main body of the pulse if it has originated at a higher frequency than the cut-off value for a different mode than the initial TEM.

Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper is to develop the operator method to the structures, which scattered fields have both discrete and continuous spatial spectra. Design/methodology/approach: In the spectral domain, in the domain of the Fourier transform, the scattered field is expressed in terms of the unknown Fourier amplitude. The field reflected by the considered structure is represented as a sum of two fields of currents on the strips of semi-infinite gratings. The operator equations are obtained for the Fourier amplitudes. These equations use the operators of reflection of semi-infinite gratings, which are supposed to be known. The field scattered by a semi-infinite grating can be represented as a sum of plane and cylindrical waves. The reflection operator of a semi-infinite grating has singularities at the points, which correspond to the propagation constants of plane waves. Consequently, the unknown Fourier amplitudes of the fi eld scattered by the considered structure also have singularities. To eliminate these latter, the regularization procedure has been carried out. As a result of this procedure, the operator equations are reduced to the system of integral equations containing the integrals, which should be understood as the Cauchy principal value and Hadamar finite part integrals. The discretization has been carried out. As a result, the system of linear equations is obtained, which is solved with the use of the iterative procedure. Findings: The operator equations with respect to the Fourier amplitudes of the field scattered by the structure, which consists of two semi-infinite gratings, are obtained. The computational investigation of convergence has been made. The near and far scattered fields are investigated for different values of the grating parameters. Conclusions: The effective algorithm to study the fields scattered by the strip grating, which has both discrete and continuous spatial spectra, is proposed. The developed approach can be an effective instrument in solving a series of problems of antennas and microwave electronics.

Purpose: The main most pronounced events, which occurred in the initial period of the pulsars’ study at the decameter wavelength range, are presented. The example of the main scientific problems, which were formulated at the very beginning of pulsar research, shows how the emphasis and priorities of these studies have been changing over time, which tasks have finally been solved, and which are still waiting to be solved. It is shown how the ongoing modernization of the UTR-2 radio telescope have allowed to acquire new qualities in astrophysical research being made with this radio telescope and to identify new scientific directions. The example of the cited references shows how the pulsar research efforts in Ukraine have been developed and how they were integrated into the world astrophysical research of these unique objects. The purpose of this work is to show the relationship between the past and the present on the example of pulsars for longer than a semi-centennial period and to show how the scientific problems that were formulated in the past, and which could not be solved under the then-existing technical conditions, were solved by the subsequent generations of researchers. Design/methodology/approach: The methods of comparison and historical parallels show how the low-frequency studies of pulsars have been developed and evolved almost from their discovery until now. Findings: It is shown how quantitative transformations and technical development, as well as non-standard scientific approaches, unhackneyed thought and international cooperation allow to solve complex radio astronomical problems related to the low-frequency studies of pulsars. Conclusions: The paper provides a historical overview of more than half a century-long radio astronomical studies of pulsars, having been and still being made at the decameter band using the UTR-2 radio telescope. The “old” and current priorities in pulsar research are given, and it is shown how qualitatively the technical parameters of back end facility and computer performance have been changed in studying the coherent pulsar radio emission nature.

Purpose: The paper discusses the possibility for increasing the planet’s surface relief retrieving accuracy with the improved photoclinometry method through the reference of the desired relief to the altimetry data. The general approach to solving the problem is proposed. The use of altimeters having both wide and narrow beam patterns are discussed, but the narrow beam pattern altimeter data is studied more in detail. The spatial resolution of the retrieved relief calculated with the improved photoclinometry method conforms to the one of the source images. Altimetry allows absolute reference to the surface heights and improves the accuracy of the relief determination. Design/metodology/approach: The work is based on the improved photoclinometry method for the planet’s surface relief retrieving from images. This method is mathematically rigorous and uses the Bayesian statistical approach, that allows calculation of the most probable relief according to available observations. Findings: An approach to determining the optimal statistical estimate of the surface heights from images in the frames of the improved photoclinometry method is proposed and an expression for the optimal filter which converts source images along with the wide beam pattern altimetry data into the most probable relief of the planet surface area is presented. The reference technique for the narrow beam pattern altimeter data is formulated. The efficiency of the method has been verified with the computer simulation. The relief of the surface area in Mare Imbrium on the Moon was retrieved using three images and laser altimeter data taken by the “Lunar Reconnaissance Orbiter” spacecraft. Conclusions: Accounting for the narrow beam pattern altimeter data increases the accuracy of the relief determination. Using the narrow beam pattern altimeter data turns out to be more preferable over the involving wide beam pattern altimeter data. Computer simulation has shown that accounting for the narrow beam pattern altimeter data significantly increases the accuracy of the calculated heights as against using images exclusively and helps to speed up the calculation procedure.

Purpose: Review of investigations of cosmic sources radioemission scintillations due to interplanetary plasma irregularities made at the Institute of Radio Astronomy of the National Academy of Sciences of Ukraine, from the first observations in the mid-70s until now. Design/methodology/approach: In the course of preparation of this paper, the authors have reviewed, analyzed and summarized the information being published in the home and foreign publications, and reported at scientific conferences. Findings: The investigations of the interplanetary scintillations carried out at the Institute of Radio Astronomy, NAS Ukraine have been reviewed. A retrospective discussion has been made on how in the course of these researches the knowledge about the basic parameters of interplanetary scintillations in the decameter wavelength range, as well as that on the important parameters of the solar wind and its structure, have been obtained. Also, various methods of processing and analysis of experimental data were offered, and new means for receiving cosmic radiation were created. The place and importance of the discussed researches for the world science are shown. Conclusions: Over the years since the beginning of the research, the think tank of the Department of Low-Frequency Radio Astronomy of the Institute of Radio Astronomy, NAS Ukraine has obtained a number of new relevant results, which bring Ukraine into the cohort of world centers of interplanetary scintillation researches. The construction of a new GURT radio telescope, among other things, creates new prospects for the development of this relevant line of investigation.

Purpose: Acoustic and atmospheric gravity waves (AAGW) are generated by many natural and anthropogenic sources. The AAGW propagation at ionospheric heights is accompanied by the generation of disturbances in the magnetic and electric fields. The plasma presence plays a crucial role. The mechanisms for generating electrical and magnetic disturbances in the near-Earth atmosphere by the AAGW have been studied much worse. Therefore, the validation of the capability to generate electromagnetic disturbances in the near-Earth atmosphere by the AAGW is an urgent problem. The purpose of this paper is to describe the mechanism for generating disturbances in the electric and magnetic fields in the near-Earth atmosphere under the action of AAGW and to estimate the amplitudes of these disturbances for various AAGW sources. Design/methodology/approach: The impact of a series of highenergy sources often results in the generation of synchronous disturbances in the acoustic and geoelectric (atmospheric) fields, when an approximate proportionality between the pressure amplitude and the amplitude of the disturbances in the atmospheric electric field is observed to occur. Based on the observational data and making use of the Maxwell equations, the theoretical estimates of the disturbances in the electric and magnetic fields have been obtained. Findings: Simplified expressions have been obtained for estimating the amplitudes of the electric and magnetic fields under the action of the AAGW generated by natural and manmade sources. The amplitudes of the electric and magnetic fields generated by the AAGW of natural and manmade origin, which travel in the near-Earth atmosphere, have been calculated. The amplitudes of the AAGW generated electric and magnetic fields are shown to be large enough to be detected with the existing electrometers and fluxmeter magnetometers. The magnitudes of the amplitudes of the electric and magnetic fields generated in the near-Earth atmosphere under the action of AAGW are large enough to trigger coupling between the subsystems in the Earth–atmosphere–ionosphere–magnetosphere system. Conclusions: The estimates and not numerous observations are in good agreement.

This paper presents an example of the application of theoretical developments on some issues of physics of space invasion. The effect of brightness oscillations and “wobbling” in the meteor trail, which we discovered, allows us to obtain estimates of some characteristics of the meteor by measuring the frequency of changes in the brightness in the trace (f_c) and meteoroid oscillations (f_m), if its velocity and altitude are known. Based on the proposed “tuning technique”, it is possible to determine the characteristics of the meteor at one-sided observations. To do this, we set the initial parameters for the model of meteoroid dynamics by the coincidence of the calculated and measured values of the frequencies f_c and f_m. Our simulation allows us to find the altitude at which the ratio of frequencies f_c/f_m coincides with the value found in the explosion of a meteoroid. Using this “tuning technique” and assuming the mineral composition for the meteor, we found estimates of the initial velocity of 21 km/s and the mass of 850 kg of the meteoroid, which reached a critical value of surface speed at an altitude of about 20.9 km in about 7.9 s with a residual mass of about 13.9 kg and a residual speed of about 10.9 km/s. At that moment, the meteoroid exploded.

Purpose: The studies of pulsars allow enriching our knowledge in determination of parameters of both the exotic electron-positron plasma in the pulsar magnetosphere with strong magnetic field and the ordinary ion-electron plasma of the interstellar medium, which exists in a weak magnetic field. To determine the parameters of the both plasma types it is reasonable to use polarization characteristics of a pulsed radio emission of pulsars. An accurate determination of these characteristics is quite a complex problem. For its solving, primarily we have to determine two parameters of the propagation medium – its dispersion and rotation measures. Their absolute values can be determined with the relative precision of 10-4, but the problem of rotation measure value sign determination arises. This sign depends on the interstellar magnetic field direction along the line of sight. Hear, a new method of rotation measure value sign determination is proposed. Design/methodology/approach: Muller polarization matrices are usually used for determination of such a propagation parameter as the rotation measure absolute value. When only one linear polarization is received, using of these matrices allows quite accurate determining the absolute value of the rotation measure, but not the sign of this parameter due to a certain symmetry of these matrices with respect to the direction of the linear polarization rotation plane. If we complement the system of equations, which determines the rotation measure value, with some new additional components, which take into account the contributions of the Earth ionosphere and magnetosphere to the rotation measure value, one can notice that this contribution is always positive in the Southern magnetic hemisphere (the majority of the Northern geographical hemisphere) and is always negative in the Northern magnetic hemisphere (the majority of the Southern geographical hemisphere). Moreover, the absolute value of this contribution is maximal at noon and minimal at midnight, when the concentration of ions in the Earth ionosphere is maximal and minimal, respectively. Accounting for these regularities allows to determine not only the absolute value of the rotation measure, but also its sign by means of two independent time-shifted estimations of the observed absolute value of this parameter for various ionization degrees of the Earth ionosphere. Findings: We show that using of additional equations, which take into account the contribution of the Earth ionosphere and magnetosphere to the value of the rotation measure parameter, allows full determination of this parameter accounting for the sign of this value even for the antennas, which can record a single linear polarization only. This approach allows to determine all polarization parameters of the pulsar radio emission as well as of the pulsed or continuum polarized radio emission of other cosmic sources. Conclusions: The paper presents the results of measurement of the rotation measure for the two closest to the Earth pulsars, namely J0814+7429 (B0809+74), J0953+0755 (B0950+08), and the comparison of the proposed technique for this parameter determination with other existing techniques.

Purpose:The main cause of geomagnetic disturbances are cosmic sources, processes acting in the solar wind and in the interplanetary medium, as well as large celestial bodies entering the terrestrial atmosphere. Earthquakes (EQs) also act to produce geomagnetic effects. In accordance with the systems paradigm, the Earth–atmosphere–ionosphere–magnetosphere system (EAIMS) constitute a unified system, where positive and negative couplings among the subsystems, as well as feedbacks and precondition among the system components take place. The mechanisms for the action of EQs and processes acting in the lithosphere on the geomagnetic field are poorly understood. It is considered that the EQ action is caused by cracking of rocks, fluctuating motion in the pore fluid, static electricity discharges, etc. In the course of EQs, the seismic, acoustic, atmospheric gravity waves (AGWs), and magnetohydrodynamic (MHD) waves are generated. The purpose of this paper is to describe the magnetic effects of the EQ, which took place in Turkey on 24 January 2020. Design/methodology/approach: The measurements are taken with the fluxmeter magnetometer delivering 0.5-500 pT sensitivity in the 1-1000 s period range, respectively, and in a wide enough studied frequency band within 0.001 to 1 Hz. The EM-II magnetometer with the embedded microcontroller digitizes the magnetometer signals and performs preliminary filtering over 0.5 s time intervals, while the external flash memory is used to store the filtered out magnetometer signals and the times of their acquisition. To investigate quasi-periodic processes in detail, the temporal variations in the level of the H and D components of the geomagnetic field were applied to the systems spectral analysis, which makes use of the short-time Fourier transform, the wavelet transform using the Morlet wavelet as a basis function, and the Fourier transform in a sliding window with a width adjusted to be equal to a fixed number of harmonic periods. Findings: The train of oscillations in the level of the D component observed 25.5 h before the EQ on 23 January 2020 is supposed to be associated with the magnetic precursor. The bidirectional pulse in the H component observed on 24 January 2020 could be due to the piston action of the EQ, which had generated an MHD pulse. The quasi-periodic variations in the level of the H and D components of the geomagnetic field, which followed 75 min after the EQ, were caused by a magnetic disturbance produced by the traveling ionospheric disturbances due to the AGWs launched by the EQ. The magnetic effect amplitude was estimated to be close to 0.3 nT, and the quasi-period to be 700-900 s. The amplitude of the disturbances in the electron density in the AGW field was estimated to be about 8 % and the period of 700-900 s. Damping oscillations in both components of the magnetic field were detected to occur with a period of approximately 120 s. This effect is supposed to be due to the shock wave generated in the atmosphere in the course of the EQ. Conclusions: The magnetic variations associated with the EQ and occurring before and during the EQ have been studied in the 1-1000 s period range.