Quasi-static Electromagnetic Field Research Articles

Analytical determination of a quasi-stationary electromagnetic field created by magnetic moments and eddy currents in conducting half-space

Aim. Study of the distribution of a three-dimensional alternating quasi-stationary electromagnetic field at the surface of conducting half-space with strong skin-effect, the source of which is an arbitrarily oriented magnetic moment. Methodology. The expressions for non-uniform electromagnetic field with strong skin effect are used for the analysis, which is based on the found exact analytical solution of the general three-dimensional problem and the use of expansion into asymptotic series with respect to a small parameter that is proportional to the ratio of the field penetration depth to the distance between the sources of the external field and the surface of body. Specific expressions at the surface are completely determined by the known field of external sources. In this work, the external magnetic moment field is used. Results. For strong skin effect, expressions for the electric and magnetic field strength are obtained separately for the components of the magnetic moment oriented perpendicularly and parallel to the flat surface between the dielectric and conducting areas. The features of the electromagnetic field distribution are analyzed depending on the value of introduced small parameter. The results are presented for the module and phase shift of the field strength with respect to the phase of the external field source. Originality. The expressions found for the electromagnetic field appear to be more general than the use of closed contours with alternating current, since they extend types of external field sources and allow the use of the superposition method instead of integration over the entire contour. Practical value. The found specific analytical expressions of the electromagnetic field at the surface for the external field of magnetic moments significantly simplify the solution of the problems, since they do not require additional solution of the field equations. References 20, figures 8.

Ultra-intense femtosecond laser interactions with aligned nanostructures

The interaction of ultrafast laser pulses of relativistic intensity with high aspect ratio nanostructures can efficiently and volumetrically heat matter to an ultra-high-energy-density regime encountered in the center of stars and within the core of fusion capsules compressed by the world’s largest lasers. It also generates gigantic quasi-static electromagnetic fields that accelerate particles to very high energy. Here, we present an overview of the physics and applications of these dense relativistic plasmas that can be created with pulses of relatively modest energy from lasers that can operate at a high repetition rate. Recent nanowire array experiments produced near-solid density plasmas with an extreme degree of ionization (e.g., Au+72), converted ultrafast pulses of laser light into intense x-ray flashes with record efficiency, and accelerated ions to MeV energies, efficiently driving micro-scale fusion reactions that generate flashes of quasi-monoenergetic neutrons. These plasmas also serve as a platform for advancing the understanding of atomic processes in extreme environments and open a new pathway to laser-driven fusion energy. The irradiation of nanostructures at intensities of >1×1022Wcm−2 is predicted to lead to an extreme ultra-high energy density plasma regime characterized by terabar pressures that is virtually unexplored.

Error Estimation of the Cauer Ladder Network Method Based on Eigenfunction Expansion

The Cauer ladder network (CLN) method is a model order reduction technique used for quasi-static electromagnetic field analysis. In this study, we derive an explicit formula for the error of the truncated transfer function and its error estimators using the eigenvalues of a linear operator and the orthogonal polynomials associated with the basis functions of the CLN method. The effectiveness of the proposed method is clarified through the finite element analysis of a 2-D inductor model.

Energy Flow and Photons from Primary Coil to Secondary Coil of Transformer

The author proposed the mutual energy theorem in 1987 and the mutual energy flow theory since 2017. The theory of mutual energy has an axiom more than Maxwell’s equations, that is, the law of conservation of energy. The conservation of energy law is not Poynting’s theorem, but an extension of the mutual energy theorem. Because of this new axiom, the new axiom conflicts with Poynting’s theorem. In fact, it is also a conflict with Maxwell’s electromagnetic theory. The author believes that the law of conservation of energy should be adhered to, so Poynting’s theorem or Maxwell’s classical electromagnetic theory should be appropriately modified. These works have been completed by the author in other papers. Recently, when studying the magnetic quasi-static electromagnetic field, the author found that the electromagnetic energy conservation law proposed by the author can be strictly proved in the magnetic quasi-static electromagnetic field environment. This is a great inspiration to the author. Based on the theory of magnetic quasi-static electromagnetic field, the author strictly proves the law of conservation of energy (mutual energy theorem) and the mutual energy flow theorem proposed by the author, and applies this theory to calculate the energy flow from the primary coil to the secondary coil of transformer. In order to simplify the problem, the author only calculates the mutual energy flow between two parallel current elements. The calculation results show that the mutual energy flow is generated on the primary coil and annihilated on the secondary coil. The properties of mutual energy flow are completely consistent with those of photons. It is also close to the photon model in Cramer’s transactional interpretation of quantum mechanics. The author believes that the transmitting antenna is consistent with the primary coil of the transformer, and the receiving antenna is consistent with the secondary coil of the transformer. The author believes that for the theoretical generalization from magnetic quasi-static electromagnetic field to radiated electromagnetic field, the law of conservation of energy, the theorem of mutual energy flow should guarantee and the time average value of self energy flow should be kept at zero. In this way, a new electromagnetic field theory which is different from Maxwell’s electromagnetic theory is obtained. Maxwell’s electromagnetic field theory adds displacement current, but it makes formulas such as the energy conservation law problematic in the case of radiation field. Maxwell’s electromagnetic field theory and mutual energy theory provide the same electric field, but the far-field part of the magnetic field (i.e. radiated electromagnetic field) is different. In addition, the electromagnetic mutual energy theory proposed by the author believes that the charge of the receiver produces an advanced wave. Advanced wave violates today’s causality, but it is an objective physical existence.

Reduction in the Computational Complexity of Calculating Losses on Eddy Currents in a Hydrogen Fuel Cell Using the Finite Element Analysis

This paper considers the issues of the reduction in the computational complexity of the numerical problem and the requirements of the computer memory size when calculating the power of the eddy currents in a hydrogen fuel cell based on a proton exchange membrane. The study was performed on a model problem based on a geometric pattern of a hydrogen fuel cell of typical dimensions and characteristics operating at a nominal load in steady-state conditions. The power of the eddy currents was calculated using a numerical model based on a tetrahedral finite element mesh and a mathematical model of a quasi-stationary electromagnetic field in the classical formulation through the vector magnetic potential. The requirements for the minimum degree of the geometric model approximation by a finite element mesh to achieve mesh stability of the computational problem results were defined. The paper considers issues of finite element order selection, the method of ordering, and the solution of the systems of linear algebraic equations (SLAEs). It shows the techniques for determining the accuracy of the calculated SLAE solution obtained by the direct method, as well as the effectiveness of the low-rank approximation of the SLAE to reduce the computational complexity of the computational problem solution and reduce the requirements for the amount of computer memory needed, considering the reduced accuracy of the SLAE solutions.

Overcritical electron acceleration and betatron radiation in the bubble-like structure formed by re-injected electrons in a tailored transverse plasma

We present a novel scheme for dense electron acceleration driven by the laser irradiation of a near-critical-density plasma. The electron reflux effect in a transversely tailored plasma is particularly enhanced in the area of peak density. We observe a bubble-like distribution of re-injected electrons, which forms a strong quasistatic electromagnetic field that can accelerate electrons longitudinally while also preserving the electron transverse emittance. Simulation results demonstrate that over-dense electrons could be trapped in such an artificial bubble and accelerated to an energy of ∼500MeV. The obtained relativistic electron beam can reach a total charge of up to 0.26 nC and is well collimated with a small divergence of 17 mrad. Moreover, the wavelength of electron oscillation is noticeably reduced due to the shaking of the bubble structure in the laser field. As a result, the energy of the produced photons is substantially increased to the γ range. This new regime provides a path to generating high-charge electron beams and high-energy γ-ray sources.

Penetration of a Heating Electromagnetic Pulse into Plasma in Magnetic Field

Penetration of a heating pulse of quasistationary electromagnetic field into plasma in constant magnetic field directed along its surface was studied. Weakening of electron heat transfer across the magnetic field leads to more efficient heating of electrons near the plasma surface. As a result, the penetration of the field into the plasma decreases, which is accompanied by suppression of the “inverse” skin effect. Inhomogeneous heating of electrons across the magnetic field leads to generation of an electric field strength component orthogonal to both the magnetic field and the direction of temperature gradient. Appearance of the additional field strength component leads to a change in polarization of the reflected pulse. In a sufficiently strong magnetic field, due to suppression of the electron heat flux and less significant effect of the magnetic field on the ion heat flux, a state with large difference of electron and ion temperatures occurs.

COMPUTATION OF QUASISTATIC ELECTROMAGNETIC FIELDS OF COMPLEX ELECTRIC POWER FACILITIES

: Accurate computation of low-frequency quasistatic electromagnetic fields is important in the design of electricity transmission and conversion devices. This work presents the theoretical groundwork of a computation using integral equations. The procedures for solving these equations are defined by applying the method of moments and the point matching method. The unknown distribution of the source function density on the thin-wire elements is approximated by the third degree polynomials. On rectangular planes the approximation of an unknown source function is achieved by means of bilinear elements. A program has been developed for the parallel electromagnetic field computation based on the described method.

Моделювання та аналіз тривимірних квазистаціонарних електромагнітних полів безкон-тактних індуктометрів, розміщених над електропровідним ґрунтом сільськогосподар-ського призначення. Ч. ІІ.

The paper is devoted to solving the problem of the theory of three-dimensional quasi-stationary electromagnetic field generated by a non-contact inductometer in its interaction with the electrically conductive agricultural soil located below it at some distance and whose specific electrical conductivity is measured. The peculiarity of this study is that it is based on obtaining an accurate analytical solution to the problem of an electromagnetic field created by an arbitrary spatial circuit with a current (contactless inductometer model) located near a magnetized electrically conductive body with a flat surface (agricultural conductive soil model). Solutions made by taking into account the closed circuits are found in the form of squares for vector and scalar potentials, magnetic and electric field strengths in an electrically conductive medium without restrictions on the geometry of the circuits, environmental properties, and field frequency. Having a precise solution, in addition to the indisputable advantage associated with the validity of the results found, allows obtaining a number of consequences that are valid for an arbitrary field in the system. Another important consequence of an accurate solution is the conclusion that an inhomogeneous electromagnetic field when penetrating into an electrically conductive space with depth always attenuates faster than a homogeneous field. For pulsed fields, the calculation is limited to a certain period of time from the beginning of the current pulse, and the closer to the initial moment of time, the more accurately the electromagnetic field is calculated. Since the current pulse usually changes the fastest and reaches its highest values in a relatively short period of time, it is at this most important stage that the electromagnetic field is determined.

Моделювання та аналіз тривимірних квазістаціонарних електромагнітних полів безконта-ктних індуктометрів, розміщених над електропровідним ґрунтом сільськогосподарського призначення. Ч. І.

The paper is devoted to solving the problem of the theory of three-dimensional quasi-stationary electromagnetic field generated by a non-contact inductometer in its interaction with the electrically conductive agricultural soil located below it at some distance and whose specific electrical conductivity is measured. The peculiarity of this study is that it is based on obtaining an accurate analytical solution to the problem of an electromagnetic field created by an arbitrary spatial circuit with a current (contactless inductometer model) located near a magnetized electrically conductive body with a flat surface (agricultural conductive soil model). Solutions made by taking into account the closed circuits are found in the form of squares for vector and scalar potentials, magnetic and electric field strengths in an electrically conductive medium without restrictions on the geometry of the circuits, environmental properties, and field frequency. Having a precise solution, in addition to the indisputable advantage associated with the validity of the results found, allows obtaining a number of consequences that are valid for an arbitrary field in the system. Another important consequence of an accurate solution is the conclusion that an inhomogeneous electromagnetic field when penetrating into an electrically conductive space with depth always attenuates faster than a homogeneous field. For pulsed fields, the calculation is limited to a certain period of time from the beginning of the current pulse, and the closer to the initial moment of time, the more accurately the electromagnetic field is calculated. Since the current pulse usually changes the fastest and reaches its highest values in a relatively short period of time, it is at this most important stage that the electromagnetic field is determined.

Long time dynamics and upper semi-continuity of attractors for piezoelectric beams with nonlinear boundary feedback

A system of boundary-controlled piezoelectric beam equations, accounting for the interactions between mechanical vibrations and the fully-dynamic electromagnetic fields, is considered. Even though electrostatic and quasi-static electromagnetic field approximations of Maxwell’s equations are sufficient for most models of piezoelectric systems, where the magnetic permeability is completely discarded, the PDE model considered here retains the pronounced wave behavior of electromagnetic fields to accurately describe the dynamics for the most piezoelectric acoustic devices. It is also crucial to investigate whether the closed-loop dynamics of the fully-dynamic piezoelectric beam equations, with nonlinear state feedback and nonlinear external sources, is close to the one described by the electrostatic/quasi-static equations, when the magnetic permeability μ is small. Therefore, the asymptotic behavior is analyzed for the fully-dynamic model at first. The existence of global attractors with finite fractal dimension and the existence of exponential attractors are proved. Finally, the upper-semicontinuity of attractors with respect to magnetic permeability to the ones of the electrostatic/quasi-static beam equations is shown.

Coupling the Cell Method with the Boundary Element Method in Static and Quasi–Static Electromagnetic Problems

A unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed in literature, can be rigorously formulated within this framework. As a main outcome, a novel direct hybrid approach amenable to iterative solution is derived. Both direct and indirect hybrid approaches, applied to an axisymmetric model, are compared with a reference third-order 2D FEM solution. The effectiveness of the indirect approach, equivalent to the direct approach, is finally tested on a fully 3D benchmark with more complex topology.

EXACT ANALYTICAL AND APPROXIMATE ASYMPTOTIC CALCULATION METHODS TO DETERMINE THREE-DIMENSIONAL ELECTROMAGNETIC FIELD NEAR CONDUCTING BODY WITH FLAT SURFACE

The analytical solution of the three-dimensional quasi-stationary electromagnetic field problem for a current located near conducting body with a flat surface is considered. The exact and approximate solution of the problem is presented. The exact solution has no restrictions on the external field configuration, physical properties of the medium, and frequency. The approximate solution is based on an expansion in asymptotic series and has limitations: for sinusoidal field, the solution is limited to frequencies above the lower limit; for pulsed field, the solution is limited by the initial time interval of the current pulse. Based on comparison of the results of exact and approximate calculations for nonuniform sinusoidal field at the interface between the media, the admissible value of the introduced small parameter is determined. For pulsed field the proposed choice of the limited time interval for calculating electomagnetic field using the asymptotic method is justified. References 29, figures 7.

Unified Expression of the Quasi-Static Electromagnetic Field: Demonstration With MEG and EEG Signals.

Objective:Electromagnetic recordings are useful for non-invasive measurement of human brain activity. They typically sample electric potentials on the scalp or the magnetic field outside the head using electroencephalography (EEG) or magnetoencephalography (MEG), respectively. EEG and MEG are not, however, symmetric counterparts: EEG samples a scalar field via a line integral over the electric field between two points, while MEG samples projections of a vector-valued field by small sensors. Here we present a unified mathematical formalism for electromagnetic measurements, leading to useful interpretations and signal processing methods for EEG and MEG.Methods:We represent electric and magnetic fields as solutions of Laplace’s equation under the quasi-static approximation, each field representable as an expansion of the same vector spherical harmonics (VSH) but differently weighted by electro- and magnetostatic multipole moments, respectively.Results:We observe that the electric and the magnetic fields are mathematically symmetric but couple to the underlying electric source distribution in distinct ways via their corresponding multipole moments, which have concise mathematical forms. The VSH model also allows us to construct linear bases for MEG and EEG for signal processing and analysis, including interference suppression methods and system calibration.Conclusion:The VSH model is a powerful and simple approach for modeling quasi-static electromagnetic fields.Significance:Our formalism provides a unified framework for interpreting resolution questions, and paves the way for new processing and analysis methods.

The problem of the structure of quasi-stationary electromagnetic field of an infinite solenoid induction loaded with a metal cylinder of constant conductance

An exact solution of the problem of distribution of the magnetic and electrical field intensities in space around the metal cylinder placed inside an infinite solenoid, with alternating current flowing through it, is obtained. The solution is derived for Maxwell equations, describing the cylindrically symmetric electromagnetic field outside the metal cylinder for complex values of the magnetic and electric components of the electromagnetic field. A comparison between the derived exact solution and an approximate one is drawn. Their asymptotic convergence is shown.

Dynamic Electromagnetic Positioning System for Accurate Close-Range Navigation of Multirotor UAVs

An accurate close-range positioning and navigation system is the key to autonomous cruise and the fine operations of multi-rotor UAVs. In this paper, a dynamic electromagnetic positioning system is designed and implemented to accurately navigate a UAV to a very small landing zone. The system is composed of three quasi-static electromagnetic field generators (EGs) installed around the landing zone, and one electromagnetic field sensor (ES) mounted on the UAV. The ES adaptively controls its gain and adjusts the power of the EGs, so it can detect electromagnetic signals under a high SNR (signal-to-noise ratio) condition and has an anti-saturation ability. Consequently, the coordinate and azimuthal angle of the UAV can be measured during the process of the UAV approaching the landing zone. Hardware experiments demonstrate that the prototype system can effectively navigate a UAV to a small landing zone that is slightly larger than the size of the UAV, and the terminal positioning error is less than 2 cm.

Динамический изгиб бесконечного электромагнитоупругого стержня

The problem of non-stationary bending of an infinite electromagnetoelastic rod is considered. It is assumed that the material of the rod is a homogeneous isotropic conductor. The closed-form system of process equations is constructed under the assumption that the desired functions depend only on the longitudinal coordinate and time using the corresponding relations for shells which take into account the initial electromagnetic field, the Lorentz force, Maxwell’s equations, and the generalized Ohm’s law. The desired functions are assumed to be bounded, and the initial conditions are assumed to be null. The solution of the problem is constructed in an integral form with kernels in the form of influence functions. Images of kernel are found in the space of Laplace transformations in time and Fourier transformations in spatial coordinates. It is noted that the images are rational functions of the Laplace transform parameter, which makes it quite easy to find the originals. However, for a general model that takes into account shear deformations, the subsequent inversion of the Fourier transform can be carried out only numerically, which leads to computational problems associated with the presence of rapidly oscillating integrals. Therefore, the transition to simplified equations corresponding to the Bernoulli – Euler rod and the quasistationary electromagnetic field is carried out. The method of a small parameter is used for which a coefficient is selected that relates the mechanical and electromagnetic fields. In the linear approximation, influence functions are found for which images and originals are constructed. In this case, the zeroth approximation corresponds to a purely elastic solution. Originals are found explicitly using transform properties and tables. Examples of calculations are given for an aluminum rod with a square cross section. It is shown that for the selected material the quantitative difference from the elastic solution is insignificant. At the same time, taking into account the connectedness of the process leads to additional significant qualitative effects.

Research on the transmission efficiency of different shielding structures of wireless power transfer system for electric vehicles

Wireless Power Transfer (WPT) charging system can cause eddy loss on the steel part and the chassis of Electric Vehicle (EV). To study different shielding structures' influence on the transmission efficiency of the WPT system, boundary conditions and assumptions of WPT model in the quasi-stationary electromagnetic field were established and finite element method (FEM) was adopted. The shielding effectiveness of ferrite plate and annular aluminum plate was investigated as well as their effects on coupling coefficient of WPT. It was found that, the setting of ferrite core enhanced the transmission field strength, improved the coupling between two coils, and increased transmit power as well as the actual eddy loss. The actual necessary shielding-area was not confined into the same-size area but distributed around the edge of the ferrite. By arranging specialized size annular aluminum plate between chassis and ferrite core, the eddy loss can be effectively shielded and an optimal transmission efficiency was reached with acceptable coupling coefficient decrease. The optimized ferrite bar structure and its EMC characteristics were also studied. It was also found that with equal volume, the optimized ferrite bar structure had better performance in EMC and coupling enhancement than the full ferrite plate.

Massively Parallel Computation for 3-D Nonlinear Finite Edge Element Problem With Transmission Line Decoupling Technique

Transmission line method (TLM) has been used in 2-D scalar finite-element (FE) analysis due to its parallelism and constant admittance matrix. In this paper, the TLM is extended for the 3-D nonlinear vector FE problem that is more widely used for electromagnetic apparatus in practice. TLM is specially adapted for tetrahedron edge elements to calculate quasi-static electromagnetic field distribution for eddy current problems, and a dummy scalar gauge is applied to make the reduced magnetic vector FE formulation full-ranked and uniquely solvable by TLM. For each element, the nonlinearity is separated by transmission lines and only local small-scale Newton–Rapson iteration is needed, which is suitable for massive parallelization due to the independence between different elements. The TLM is implemented on a many-core GPU for a nonlinear FE power inductor case study, and the comparison of the results with a commercial FE software shows over 50 times speedup with a relative error of less than 2%.

Electromagnetic field growth triggering super-ponderomotive electron acceleration during multi-picosecond laser-plasma interaction

The dependence of the mean kinetic energy of laser-accelerated relativistic electrons (REs) on the laser intensity, so-called ponderomotive scaling, explains well the experimental results to date; however, this scaling is no longer applicable to multi-picosecond (multi-ps) laser experiments. Here, the production of REs was experimentally investigated via multi-ps relativistic laser–plasma-interaction (LPI). The lower slope temperature shows little dependence on the pulse duration and is close to the ponderomotive scaling value, while the higher slope temperature appears to be affected by the pulse duration. The higher slope temperature is far beyond the ponderomotive scaling value, which indicates super-ponderomotive REs (SP-REs). Simulation and experimental evidence are provided to indicate that the SP-REs are produced by LPI in an under-critical plasma, where a large quasi-static electromagnetic field grows rapidly after a threshold timing during multi-ps LPI.