Nonstationary Electromagnetic Fields Research Articles

The Convincing Cosmic Energy Gravitational Genesis of the Strongest Geomagnatic Anomalies of the Magnetic Field of the Earth

The author presents convincing evidence of the cosmic (planetary and solar) energy gravitational origin (related to the maximal and minimal combined planetary and solar integral energy gravitational influences on the internal rigid core of the Earth) of the maximal temporal intensifications of the global magnetic processes of the Earth. In fairly good agreement with the calculated date 2007.416666666 AD (of the local minimal planetary and solar integral energy gravitational influence on the internal rigid core), it was observed the very rapid changes of the geomagnetic field near the date March 2007 AD (corresponding approximately to 19-20 April 2007 AD). This fairly good agreement gives the additional convincing argument that the date March 2007 AD can be considered as the possible beginning of the geomagnetic reversal during the evaluated range (2007÷2216) AD. The strong magnetic anomaly occurred on 6 January 2020 AD in perfect agreement with the calculated date 2020.016666667 AD (corresponding to 6 January 2020 AD) related to the local maximal planetary and solar integral energy gravitational influence on the internal rigid core. In fairly good agreement with the calculated date 2023.26666666 AD (corresponding approximately to 7 April 2023 AD) of the local maximal planetary and solar integral energy gravitational influence on the internal rigid core, it was observed the strongest (during the last 6 years) magnetic anomaly on 23 March 2023 AD. These convincing agreements demonstrate the physical validity of the established global prediction thermohydrogravidynamic principles, which can be considered as the proven physical basis for the development of the general unified geophysical theory (describing the possible geomagnetic reversal during the evaluated range (2007 ÷ 2216) AD) combining the Special Theory of Relativity, the relativistic electrodynamics and the relativistic theory of the non-stationary gravitation, which can be developed based on the established physical analogy between the established relation for the energy flux (of the gravitational energy) and the Lorentz’s calibration condition (for the vector potential related with the scalar potential of the non-stationary electromagnetic field).

Cross-spectral purity of nonstationary vector optical fields: A similarity with stationary fields

This study establishes a reduction formula for nonstationary cross-spectrally pure vector (or electromagnetic) light fields with any spectral bandwidth. In general, for nonstationary cross-spectrally pure electromagnetic fields, the reduction formula of the two-time Stokes parameters normalized by the corresponding usual Stokes parameters is not similar to the one for stationary fields since the correlation properties for nonstationary fields depend on two-time instants t1 and t2, in addition to their time difference. Here, we derive a reduction formula by including time-integrated correlations that share a similar mathematical structure to that of reduction formulas used for stationary vector fields if the normalized spectra of the interfering fields are identical. Additionally, we examine the requirement of strict cross-spectral purity for nonstationary electromagnetic fields using a time-integrated coherence function, which exhibits a mathematical form similar to that of strict cross-spectral purity in stationary vector fields. This investigation sheds light on the cross-spectral purity of pulse-type fields, which holds potential applications in statistical optics.

Temporal factorization of a nonstationary electromagnetic cavity field

Temporal factorization of a nonstationary electromagnetic cavity field

Modeling of the Temperature Regimes in a Layered Bimetallic Plate under Short-Term Induction Heating

A mathematical model for determining the temperature field of a bimetallic plate with plane-parallel boundaries during short-term induction heating by a non-stationary electromagnetic field is proposed. Initial boundary value problems for determining the parameters of a non-stationary electromagnetic field and temperature are formulated. The temperature and the component of the magnetic field intensity vector that is tangential to the plate base were selected as defining functions. We used an approximation of the defining functions in each layer of the plate with quadratic polynomials by the thickness coordinate and Laplace transform of the integral over time. General solutions to the formulated problems under uniform non-stationary electromagnetic action were obtained. Based on them, the temperature during short-term induction heating by a non-stationary electromagnetic field was numerically analyzed depending on its amplitude-frequency parameters and duration.

Аналіз теплового режиму електропровідного трубчастого елемента з тонким зовнішнім електропровідним покриттям за дії неусталеного електромагнітного поля

An electrically conductive tubular element with a thin external electri-cally conductive coating underthe action of an unsteady electromagnetic field of the radio frequency range is considered. To analyze the thermal re-gime, the initial-boundary problem of electrodynamics for a two-layer conductive non-ferromagnetic hollow cylinder under the action of an ex-ternal non-stationary electromagnetic field is formulated. The electromag-netic field is given by the values of the axial component of the magnetic field intensity vector on the inner and outer surfaces of the cylinder. To construct the general solution of the formulated initial-boundary value problem, a quadratic approximation of the key function (the axial compo-nent of the magnetic field intensity vector) along the radial coordinate in each constituent layer (base and cover) of the hollow cylinder was used. As a result, the original initial-boundary value problem for the key function is reduced to the Cauchy problem in terms of the time variable for the charac-teristics of the key function integral over the radial coordinate. The coeffi-cients of the approximation polynomials are presented through the integral characteristics of the key function and its given values on the inner and outer surfaces of the cylinder as a function of time. The solution of the Cauchy problem is obtained using the integral Laplacetransform. Expres-sions of the key function in each component layer of the cylinder are rec-orded in the form of quadratic polynomials, the coefficients of which are convolutions of functions describing the given limit values of the key func-tion on the inner and outer surfaces of the cylinder and homogeneous solu-tions of the Cauchy problem on integral characteristics. Expressions of the key function and Joule heat in the base and coating of the considered tubu-lar element under the action of an unsteady electromagnetic field in the mode with a pulsed modulating signal were obtained on the basis of gen-eral solutions for homogeneous non-stationary electromagnetic action. A computer analysis of the change in time and thickness of the constituent layers of this tubular element of the axial component of the vector of mag-netic field intensity and Joule heat was carried out.

On the adapting ability of living organisms to stationary and non-stationary electromagnetic fields

The adapting ability of living organisms is the key to survival of the species, and its scope is defined by homeostasis, meaning the tendency of any living system to maintain its biologic parameters. Heat shock proteins are part of a homeostasis system in charge with the regulation of damaged proteins caused by the action of several types of stressors. Among all types of stressors, the electromagnetic radiation has not yet been investigated in terms of heat shock protein response. Recent investigations regarding in vivo experiments using electromagnetic exposure from laboratory sources and commercial mobile phones indicate that the biologic response is more intense when using real life sources. This paper proposes a model for heat shock proteins expression as response to electromagnetic radiation exposure, based on a Hill controller.

Determination and Analysis of Joule’s Heat and Temperature in an Electrically Conductive Plate Element Subject to Short-Term Induction Heating by a Non-Stationary Electromagnetic Field

We propose a mathematical model that allows us to determine the temperature field of a parallel-sided electrically conductive plate element subject to uniform non-stationary electromagnetic action. We formulate initial-boundary value problems to determine the parameters of the non-stationary electromagnetic field (NEMF) and the temperature. We develop a methodology to solve these initial-boundary value problems using the approximation of determining functions by cubic polynomials over thickness of the plate element. General solutions for the related Cauchy problems at uniform non-stationary electromagnetic action are obtained. Based on these solutions, the temporal variation of Joule’s heat and temperature in the plate element, subject to short-term induction heating by an NEMF in the mode of impulse modulating signal (MIMS), is analyzed. Temperature dependencies on the different values of electromagnetic field stress and on the different time duration were obtained. The choice of the carrier frequency of electromagnetic field oscillations is explained for the frequencies mostly used in industrial devices for inductive heating.

Features of high-density transient electromagnetic sounding data inversion under oil and gas prospecting in the Nepa-Botuoba anteclise area

The data of near-field transient electromagnetic sounding, which are widely used for the purposes of oil and gas exploration within the Nepa-Botuoba anteclise, are typically interpreted in terms of quasi-horizontally-layered models of media. The purpose of this study is to develop an approach to the inversion of transient electromagnetic sounding curves obtained via high-density 3D observation networks. The study was based on mathematical modeling, whose results allowed to estimate the lateral spatial parameters of a non-stationary electromagnetic field as well as to understand the differences between the results of one-dimensional inversion of the transient electromagnetic sounding data and the true parameters of the target horizon. As a result, the characteristic of the electromagnetic field described by an exponential function and used in the lateral-constraint inversion of high-density electromagnetic sounding was obtained. The proposed approach was tested on the practical data within the site under investigation located on the slope of the Nepa-Botuobа anteclise. It is shown that the use of spatial discrepancy under TEM sounding data inversion makes it possible to obtain geoelectric models characterized by lateral consistency of section geoelectric parameters. The application of the spatial stacking-based approach in the inversion process allows to increase the solution stability of the inverse problem of the near-field TEM sounding data.

Mathematical modeling and study of thermoelastic behavior of a bimetallic layer with plane-parallel boundaries under the action of electromagnetic pulses

The dynamic problem of thermomechanics for a bimetallic layer with plane-parallel boundaries under the action of a homogeneous nonstationary electromagnetic field has been formulated. The thermal stress state, the bearing capacity, and the contact properties of the considered layer under the action of electromagnetic pulses of microsecond duration are numerically analyzed.

Complete coherence of random, nonstationary electromagnetic fields

Despite a wide range of applications, the coherence theory of random, nonstationary (pulsed or otherwise) electromagnetic fields is far from complete. In this work, we show that full coherence of a nonstationary vectorial field at a pair of spatiospectral points is equivalent to the factorization of the cross-spectral density matrix, and full pointwise coherence over a spatial volume and spectral band leads to a factored cross-spectral density throughout the domain. We further show that in the latter case, the time-domain mutual coherence matrix factors in the spatiotemporal variables, and the field is temporally fully coherent throughout the volume. The results of this work justify that certain expressions of random pulsed electromagnetic beams appearing in the literature can be called coherent-mode representations.

Cross-spectral purity of nonstationary vector fields in space–time and space–frequency domains

We establish the concept of cross-spectral purity for nonstationary electromagnetic fields having any degree of coherence or polarization. The conditions of cross-spectral purity in all Stokes parameters are derived for both space-time and space-frequency domains, which demonstrate that the normalized two-point coherence properties of such fields can be expressed as products of a spatial and a time (or frequency) dependent function. We further determine the condition of strict cross-spectral purity for nonstationary fields, which establishes the equivalence of normalized two-point Stokes parameters governing the spatial factors of the space-frequency and space-time domains. This study may provide interesting aspects of statistical properties of beams obtained from practically available sources such as pulsed lasers, modulated and fluctuating light sources, etc.

Computer Model and Calculation of Magnetic Field Induction of Induction Concentrator

Computer modeling of the induction concentrator-transformer and calculation of the induction of the magnetic field in it for different variants of design are carried out. The peculiarity of the induction system that was modeled is that it is a two-stage step-down transformer. Such a system has not been considered in the literature, but it is promising for certain applications, and is of practical interest for the technology of induction heating of solids and plasma. The study of this system is also of scientific interest because it is characterized by parameters that are distributed in space, and the usual circuit approach to its analysis is inappropriate.Computer modeling for the study of induction concentrator-transformer consisted of 4 stages: the creation of a geometric model and the spatial boundary of the calculations; assignment of physical properties to the elements of the model in accordance with the electromagnetic problem; establishment of boundary and initial conditions; creation of a settlement grid. In accordance with the purpose of the study, the work examines the processes that are united by the name - electromagnetic research. This study is not only initial - it is a key study that determines the study of all processes in the induction concentrator-transformer. The adequacy of the model of magnetic field induction distribution to physical reality determines the quality of all subsequent calculations.The distribution of magnetic field induction depending on the diameter of the working inductor and its position in the concentrator is established. The calculation is performed according to Maxwell's equations in differential form, which is appropriate for non-stationary electromagnetic fields. The properties of the material were considered isotropic, as well as the hysteresis and magnetic saturation were neglected. The model took into account the distribution of current density in the elements of the induction concentrator-transformer, self- and mutual induction between the elements.The dependences of the magnetic field induction distribution on the supply current frequency (for 5.7 kHz, 60 kHz and 440 kHz) and design parameters are obtained, which prove the existence of several resonances of energy transfer from the primary inductor to the working one. Moreover, with increasing frequency, the amplitude value of the induction of the magnetic field decreases proportionally. The question of the choice of frequency in induction devices for technological purposes is always ambiguous. Criteria for optimal design and operating modes of induction concentrator-transformer depend on its purpose, but the determinants are always reliability and productivity.The obtained results reflect a good correlation with the physical properties of induction systems, which confirms the adequacy of the constructed model and calculations with it. The study does not allow to make unambiguous conclusions and proposals for the optimal design and operating modes of the concentrator-transformer, however the constructed and researched model is the first and decisive stage of physical and topological modeling of induction two-stage concentrator-transformer.

Методика побудови розв’язку двовимірної задачі електродинаміки для електропровідного тіла з плоскопаралельними межами за дії зов-нішнього нестаціонарного електромагнітного поля

A two-dimensional initial-boundary value problem of electrodynamics for an electroconductive non-ferromagnetic body with planar-parallel boundaries is formulated under the action of an external non-stationary electromagnetic field. The electromagnetic field is given by the values of the inhomogeneous longitudinal coordinate of the component of the magnetic field intensity vector at its bases. To construct a general solution of the formulated initial boundary value problem under such electromagnetic action, a cubic approximation by thickness coordinate and an integral Fourier transform along a longitudinal coordinate was used for a key function — a given component of the magnetic field intensity vector. As a result, the initial two-dimensional initial boundary value problem for the key function is reduced to the one-dimensional initial boundary value problem. This initial boundary value problem is on the integral key function. These characteristics are the functions of time variable and the thickness coordinate. The coefficients of the polynomial approximating the key function are given by the transformants of the integral characteristics of the key function and given its values on the bases of the body as corresponding functions of time and longitudinal coordinate. The general solutions of the one-dimensional initial boundary value problem are obtained as a convolution of functions. These functions describe homogeneous solutions and key function boundary values on the bases of the body. Using the inverse Fourier transforms, the solution of the original electrodynamics problem under the action of an arbitrary variable in time and by the longitudinal coordinate of a non-stationary electromagnetic field is written. On the basis of such a common solution, as a partial case, we also write the solutions of the original two-dimensional initial boundary value problem under the action of a stationary harmonic in time variable electromagnetic field. In order to improve the accuracy of the approximate solution of the problem under consideration, an independent approximation of the corresponding component of the electric field intensity vector along the thickness coordinate is proposed. Systems of equations are formulated to determine the integral characteristics of this component, both under the action of an arbitrary variable in time and for a longitudinal coordinate non-stationary and the stationary electromagnetic field.

Main features of using the shock pulse method for vibration diagnostics of turbogenerator stators

The present work is devoted to the calculation and experimental study of the vibrational state of the stator end zone elements at high-power turbogenerators. Due to the design features and operating conditions under the combined effect of temperature and non-stationary electromagnetic fields, the structural elements of the stator end zones at powerful turbo generators are subject to vibration. Excessive levels of the structure vibration lead to the appearance of fatigue cracks in the vibration-loaded elements and their subsequent failure, leading to the stop of the generator and, as a consequence, the whole power unit. In this regard, the creation of a reliable electric machine is an important and urgent scientific and technical task. To solve such problems, various computational and experimental methods are being actively used at present, which are often used independently of each other. A feature of this work is the joint use of modern design and experimental methods for solving the problem of ensuring vibrational reliability of the end zone elements of stators at powerful turbo-generators. The paper considers the use of the method of shock impulses for vibration diagnostics of turbogenerator stators, in order to increase the vibrational reliability. Numerical simulation of the impulse dynamic impact on the end winding element of a powerful turbogenerator is performed. The model comprises a bus holder rigidly fixed on the base of the pressure plate, and an output end with composite insulation. The physical and mechanical properties of insulations are assumed according to results of design and experimental studies. The results of computation studies have made it possible to determine the dependencies of the recorded responses on the location and duration of the impact, and also to select the point of pulse application, depending on the shape of the oscillations. Recommendations for conducting vibration diagnostics by shock pulses have been developed on the example of output busbars of turbo generator stators, which allow to increase the level of received signals and the probability of detecting all forms of oscillations in the required frequency range.

APPROACH TO DETERMINATION OF NO LOAD CURRENT OF THREE-PHASE POWER TRANSFORMERS WITH PLANE RODS MAGNETIC SYSTEMS

Purpose. Development a new effective approach for determining the open-circuited transformer parameters by implementing a combination of a schematic and spatial mathematical model of nonstationary electromagnetic fields in three-phase transformers, taking into account the constructive structure of the active part, the nonlinearity of the magnetic properties of electrical steels providing high accuracy and computational efficiency.Methods. The researches were carried out using the methods of the electromagnetic field theory, the theory of electrical circuits, the theory of power transformers, mathematical physics, the finite element method, regression analysis methods.Results. Theoretical researches of electromagnetic processes based on numerical realization of a three-dimensional mathematical model of a power three-phase transformer in open-circuited operation are carried out. An approach is proposed for improving the field simulation efficiency of the open-circuited operation, which consists in reducing the dimension of the computational domain and the transition to 2D models. It allow reducing the computing resources cost more than 2.8 times, time resources more than 250 times at a weighted average discrepancy of not more than 3.6%. The regularities of the distribution of flux density and the energy of the magnetic field for the active part of the transformer in open-circuited operation are determined. Their quantitative ratio value for the rods of different phases, which determining the ratio of the currents and resistances of the forward and reverse sequences of the transformer are calculated. A new approach to determine the open-circuited parameters of three-phase transformers with flat rod magnetic systems, based on the methods of circuit and 3D modeling, harmonic analysis and symmetrical components is realized. It characterized by high efficiency of numerical realization and accuracy for transient processes in switching moment of the three-phase transformer without loads. System of phase idle currents, characterized by non-sinusoidality and asymmetry, is proved. The harmonic composition of these currents is dominated by the 1st, 5th and 7th harmonics, but the first harmonic component predominates. The parameters of the forward and reverse sequence of the phases of the first harmonic for open-circuited operation, based on symmetrical components method were determinated. A corrective technique, which clarifies the traditional engineering approach, is proposed. The use of parameter correction for the researched ratios of the currents of the forward and reverse sequences will been increase the accuracy of calculation of the idle current by 12-14% and the idle losses by 9-11% in comparison with the generally known engineering design techniques.Originality. An approach is proposed for improving the efficiency of field simulation of the open-circuited operation, which consists in reducing the dimension of the computational domain and the transition to 2D models. A new approach of determination of the open-circuited parameters of three-phase transformers with flat rod magnetic systems based on the methods of circuit and 3D modeling, harmonic analysis and symmetrical components is realized. It characterized by high efficiency of numerical realization and accuracy for transient processes in switching moment of the three-phase transformer without loads.Practical value. The approaches and techniques allows to reduce the cost of computing resources by more than 2.8 times, time resources more than 250 times, with a weighted average discrepancy of not more than 3.6%, and increasing the accuracy of calculation of idle currents by 12-14% and losses of idling by 9-11% in comparison with the well-known engineering methods of designing.

Kinetic equilibria of relativistic collisionless plasmas in the presence of non-stationary electromagnetic fields

The kinetic description of relativistic plasmas in the presence of time-varying and spatially non-uniform electromagnetic (EM) fields is a fundamental theoretical issue both in astrophysics and plasma physics. This refers, in particular, to the treatment of collisionless and strongly-magnetized plasmas in the presence of intense radiation sources. In this paper, the problem is investigated in the framework of a covariant gyrokinetic treatment for Vlasov–Maxwell equilibria. The existence of a new class of kinetic equilibria is pointed out, which occur for spatially-symmetric systems. These equilibria are shown to exist in the presence of non-uniform background EM fields and curved space-time. In the non-relativistic limit, this feature permits the determination of kinetic equilibria even for plasmas in which particle energy is not conserved due to the occurrence of explicitly time-dependent EM fields. Finally, absolute stability criteria are established which apply in the case of infinitesimal symmetric perturbations that can be either externally or internally produced.

Dynamics of energetic electrons in nonstationary quasi‐perpendicular shocks

A one‐dimensional full particle‐in‐cell (PIC) code is utilized to investigate energetic electron bursts produced at a nonstationary quasi‐perpendicular shock. A number of electrons are intermittently energized by interacting with nonstationary electromagnetic fields in the shock front. Some of the energetic electrons are reflected at the shock and form an upstream non‐thermal population. The reflection process is strongly affected by the non‐coplanar magnetic field component which is temporarily rather strong in the transition region of a highly nonstationary shock. Oblique whistler waves in the transition region influence the distribution function of the reflected electrons. Waves excited by the modified two‐stream instability may pitch angle scatter the electrons and thus blur the loss cone feature of the reflected electrons. Dispersive standing whistler waves are also emitted locally in the foot even when a Mach number exceeds a critical value. These whistler waves may also scatter the electrons to blur the loss cone. Furthermore, the whistler waves produce clumps of the reflected electrons in a phase space. Some electrons are trapped by the ion holes produced downstream as a remnant of a self‐reformation process of the shock front and accelerated through a drift mechanism. It is also discussed how physical quantities associated with the reflected electrons observed upstream of the shock can give information about the shock front nonstationarity as well as about local small scale wave activities in the transition region.

704 回転機械における非定常電磁場解析(OS7-1.計算電磁気学と関連話題(1),OS・一般セッション講演)

704 回転機械における非定常電磁場解析(OS7-1.計算電磁気学と関連話題(1),OS・一般セッション講演)

The equivalence theorem for the vectors of nonstationary electromagnetic field intensities in a conducting medium

An integral representation is obtained in the time domain for the vectors of the intensities of the nonstationary electromagnetic field in a homogeneous isotropic conducting medium. It is shown that, at any instant, the field at an arbitrary point in a closed volume is expressed through an integral over the surface bounding this volume and an integral over the volume. The derived formulas for the integrand functions contain the field intensities, external currents and charges and the time derivatives of these quantities at instants preceding the observation instant.

Non-stationary electromagnetic field measurements accuracy improvement

Electromagnetic field (EMF) measurements, for labor safety and environment protection purposes, are performed in the near-field. Inaccuracy of the far-field EMF measurements oscillates around ±1 dB or bit worse; in the near-field measurements, errors at the level of ±6 dB must be sometimes accepted. In the case of non-stationary EMF measurements, their sense may be changed from quantitative to qualitative ones. In order to make it possible an estimation of the non-stationary EMF measurement accuracy, it is proposed new method of the meters calibration. The method is based upon a standard excitation with identical signal as the measured one. A set for the purpose includes a pulse generator (of frequency and pulse rating identical with the radiation source) and computer-controlled amplitude modulator that reflects the radiation pattern of an antenna (e.g. radar one) and its rotations. Contrary to calibration using monochromatic continuous wave (CW) excitation, proposed method should be repeated for any radiation source. The disadvantage is compensated by a possibility to estimate (additional) error of the method. Calculations show it at the level of 10%.