Electromagnetic Field Computation Research Articles

Uniform electric-field optimal design method using machine learning

The demand for uniform electric fields (UEFs) in engineering is very high, particularly in high-voltage devices. The existing methods encounter limitations in terms of optimization region and universality. Herein, we propose a method for designing UEFs based on finite element calculations of electromagnetic fields and machine learning. First, the electric-field distribution of the plate-to-plate electrode structure determined using three electrode-shape parameters (ESPs) is calculated using finite element software and is drawn. Thereafter, a dataset of 2000 images is created with different electric-field strength distributions using various ESPs. Net, we employ image-processing techniques to extract nine statistical features from the gray-level information in the images. Models are trained through machine learning to predict ESPs based on the gray-level features (GLFs). Finally, the electric-field strength distribution image of the expected ideal uniform field is artificially selected. In addition, the ESPs from which the uniform electric-field is produced are predicted by the models. The proposed method provides an accurate solution for optimizing the design of a uniform electric-field and a new approach for solving inverse problems of electric-field. This involves drawing the required electric-field strength distribution image for high-voltage engineering and obtaining the required ESPs.

Relativistic beam loading, recoil-reduction, and residual-wake acceleration with a covariant retarded-potential integrator

An algorithm is demonstrated that performs first-principles tracking of relativistic charged-particles. A covariant approach is used which relies on retarded vector potentials for trajectory integration instead of performing electromagnetic field calculations. When accounting for retardation effects, the peak vector potential and corresponding Lorentz force in the direction of travel increase asymptotically for high-β particles. This produces a very strong field distribution at small angles from the particle’s direction of travel, which can result in considerable change in momentum when approaching a conducting or charged object. We study these dynamics using protons and electrons at relativistic energies passing through apertures in conducting surfaces, where substantial energy shifts are observed for particles passing within roughly 10μm of the aperture boundary.We also simulate breaking a test particle’s line of sight with a conductor or other charged body. After this instant, the test particle continues to accelerate due to residual fields, but no longer produces an opposing force on any charged or conducting object; thus any recoil on the enclosing structure is effectively reduced. In this test, a 1% energy gain is observed for an 85MeV electron traversing its reflected wake after having conducting plate in its path screened by a dielectric object.We then incorporate a micro-scale dielectric laser acceleration (DLA) device into our simulations. Compared with a 2 mm DLA on its own, we find a factor of two increase in energy gain when adding a series of conducting-surface choppers.

Electromagnetic Fields Calculation and Optimization of Structural Parameters for Axial and Radial Helical Air-Core Inductors

To improve the current density distribution and electromagnetic performance of air-core inductors, a structural optimization method combining back-propagation(BP) neural network and genetic algorithm(GA) is proposed for the study of axial and radial spiral multi-winding inductors. The Monte Carlo method was used to extract the structural size samples of the inductors, and the training dataset was obtained through the finite element calculation of electromagnetic fields. Based on BP neural networks, nonlinear mapping models between the inductance value, volumetric inductance density, current distribution non-uniformity coefficient, and inductor structural parameters were constructed. A sensitivity analysis of the inductor inductance value affected by the structural parameters was conducted using the Sobol index calculation. Using the current distribution non-uniformity coefficient as the fitness function and the volumetric inductance density as the constraint condition, a genetic algorithm was applied to globally optimize the structural parameters of the inductor. The optimization results were verified through a finite element comparison. The results show that, under the requirement of satisfying the volumetric inductance density, the current distribution non-uniformity coefficient of the Axial Helical Inductor (AHI)-type inductor was reduced by 4.57% compared with the best sample in the sampling, while that of the Radial Helical Inductor (RHI)-type inductor was reduced by 5.33%, demonstrating the practicality of the BP-GA joint algorithm in the structural optimization design of inductors.

Полосковый резонатор СВЧ с объемным кристаллом: экспериментальные характеристики и определение эффективной диэлектрической проницаемости

The paper presents the results of an experimental study and modeling of the frequency characteristics of a resonator in the form of two strip vibrators, separated by a large gap and covered with a bulk lithium niobate crystal. A metal electrode with a floating potential is installed on the upper surface of the crystal. The frequency dependences of the scattering matrix coefficients of a stripline resonator were measured in the frequency range up to 3 GHz. Electrodynamic analysis was carried out in the COMSOL Multiphysics numerical simulation environment. A comparison was made of experimental and numerical results, which showed good qualitative agreement between the transmission coefficients and reflection coefficients. Resonant oscillations were obtained at two or three frequencies depending on the location and orientation of the crystal. It has been established that at the first resonant frequency the electrode acts as a screen. The absence of an electrode leads to the disappearance of resonance. The simulation carried out in COMSOL made it possible to estimate the effective dielectric constant of the resonator corresponding to the values of the resonant frequencies. The calculation of electromagnetic fields made it possible to establish the types of waves corresponding to resonant frequencies. Knowing the type of waves and estimating the relative dielectric constant made it possible to construct an algorithm for a refined iterative procedure for calculating the values of the resonant frequencies and the effective dielectric constant of the resonator. The possibility of using resonators as single-link bandpass filters with a passband of about 1%, insertion loss of –1.1 dB and minimal return loss of –28 dB at the center frequency is shown.

Frequency-Dependent Grounding Impedance of a Pair of Hemispherical Electrodes: Inductive or Capacitive Behavior?

This article is the authors’ last contribution to a trilogy of research papers submitted to Energies’ Special Issue on Electromagnetic Field Computation, aimed at the theoretical analysis and numerical computation of the frequency-dependent complex impedance of hemispherical electrodes. In this work, we consider a pair of distant identical hemispherical electrodes buried in the ground, whose constitutive parameters (conductivity and permittivity) are assigned diverse values. Simulation experiments carried out using a full-wave finite element method, considering different combinations of the earth’s constitutive parameters, reveal that the grounding impedance of the electrode system can exhibit surprisingly varied frequency behavior. For frequencies close to zero, the impedance can start out inductive or capacitive, then go through a number of resonant transitions between inductive and capacitive states, finally tending towards purely resistive behavior. The results are interpreted using theoretical approximations valid for low- and high-frequency regimes.

Reply to Comment on “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation”

Abstract The recent comment on our previously published article questioned the novelty and computational efficiency of our work. Here we respond by restating the novelty and scientific value of our work as well as showing why the specific alternative methods stated in the comment are unlikely to outperform the methods we compare for metasurface applications involving high refractive index particles near high refractive index substrates.

The method of calculating the vector antenna pattern based on the algebra of quaternions

The quaternion algebra contains the algebra of real and complex numbers, as well as three-dimensional vector algebra. The algebra of quaternions finds application in describing the rotations of coordinate systems, which is also of interest in describing problems of electrodynamics, in which it is often necessary to perform a transition from the basis of sources to the basis of observation. It is shown that using the algebra of quaternions, it is possible to express Maxwell's equations and their solutions in a coordinate system invariant form. A method for calculating a vector antenna based on the algebra of quaternions is proposed. It is shown that the algebra of quaternions is applicable not only for the calculation of electromagnetic fields, radiation patterns, but also for the calculation of polarization characteristics. All transformations define products of rotation functions, for which it is enough to find trigonometric functions sinx and cosx once, and all subsequent rotation operations are performed when implementing quaternion algebra procedures. The application of the quaternion algebra also avoids errors in determining the directions of turns. The proposed methodology can be used to design antennas placed on mobile objects when solving problems of analysis and synthesis.

Creating a computer model of a synchronous motor for the implementation of the project «Creation of a series of electric motors with a modernized rotor for electric transport of low power»

RELEVANCE. The challenges of creating modern permanent magnet synchronous motors require solving technical problems in conjunction with economic realities. Due to the use of permanent magnets in the construction of synchronous motors, their cost limits their industrial application. Therefore, there is an urgent issue of optimizing the design of synchronous motors, which can be solved by changing the topology.TARGET. The goal is to create more economical permanent magnet synchronous motors (PMSMs) in low-power electric vehicles. It is planned to implement a new method for constructing PMSM. This solution will reduce weight and size parameters and increase specific power, which are important indicators for electric transport.METHODS. To modernize modern synchronous motors, a complex topological optimization method based on a genetic algorithm is proposed.RESULTS. A computer model was obtained in the form of calculation of electromagnetic fields in the stator and rotor of a synchronous motor with permanent magnets.CONCLUSION. Modeling the parameters of synchronous motors with permanent magnets has a low degree of development in the domestic mechanical engineering due to the lack of developed infrastructure in the field of low-power electric transport; the creation of domestic developments in this area is of a strategic nature.

Electromagnetic fields of lightning return stroke to wind turbines with discontinuous impedance model

This study introduces an electric field calculation model for wind turbine return strokes, incorporating impedance discontinuity within the turbine, a feature not considered in traditional tall tower models. The model introduces a reflection coefficient, ρx, at the connection between the blades and the tower. Disregarding the generation of upward leaders, this paper calculates the electric field of subsequent return strokes for different distances from the wind turbine and for different model parameters. The results demonstrate that changes in the reflection coefficient ρx affect oscillation amplitude and also slightly influence the pulse width, with a negative ρx leading to smaller and more frequent pulses. Contrasts with measured waveforms indicate that models with a constant reflection coefficient are inaccurate. Adopting variable reflection coefficient values yields a more accurate match. This approach offers a new perspective for electromagnetic field calculations in lightning-struck structures, emphasizing the significance of impedance dynamics of return stroke channel.

Effects of Multispectral Absorbing Coating on the Generated Voltage of Solar Radiation–Thermoelectric System

The effective utilization of solar energy is an important development direction to realize the exploration of clean energy. Herein, a model of solar radiation–thermoelectric generation (TEG) system is established, which is composed of solar absorbing coating and TEG component. Five different microscopic structures of coating are designed and the spectral absorption properties are numerically analyzed with the finite‐difference time‐domain method. Then, the absorbed solar energy and produced open‐circuit voltage with different coating structures are compared, with the coupling calculation of temperature field and electromagnetic field achieved. Additionally, the effects of structural size parameters on the output voltage performance are discussed. It can be observed that the absorbing coating can effectively improve the performance of TEG component, and the multilayer structure with appropriate gold particle diameter chosen is an optimization research direction for more efficient energy conversion.

Design and cooling of permanent magnet generator in MW-class space closed Brayton cycle system

The closed Brayton cycle (CBC) system is a prime energy conversion technology to convert heat from the reactor to electric power for space missions due to its light weight, compact and stable operation. The CBC system incorporates a permanent magnet generator (PMG) mounted on the CBC shaft with the turbine and compressor. To ensure safe operation of the CBC system, a small fraction of the working fluid is used to provide the required cooling. In this study, four different cooling schemes used in CBC system are concluded and the key dimensions of the PMG are obtained through mechanical design theory and electromagnetic theory. Comprehensive research on the electromagnetic field and loss calculation is then performed. Furthermore, the cooling paths of the PMG are designed and the resulting temperature profiles are calculated. Finally, different cooling schemes are compared and the appropriate cooling advice is proposed.

Comment on “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation”

Abstract The article entitled “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation (DDA)” written by W. Liu and E. McLeod presents a method for computing the Green function in presence of a substrate or multilayer in an efficient way. Unfortunately, the proposed method has been known for more than twenty years and significantly ameliorated. It can be found in its optimized version in some open-source DDA codes. In this comment, we recall the different approaches (and related papers) addressing the computation of the Green function of a multilayered system. We show that they address all the points raised by Liu and McLeod in their paper and provide more efficient solutions to their computational issues.

Electromagnetic Vibration and Noise Analysis of Linear Phase-Shifting Transformer

The advantages of adjustable angle phase-shifting and great expansibility make the linear phase-shifting transformer a novel type of power conversion device with a wide range of potential applications. However, during the procedure, there is a lot of noise. For the purposes of transformer design and vibration and noise reduction, it is crucial to investigate its electromagnetic vibration and noise. In this paper, the radial electromagnetic force wave considering the influence of the end effect as the source of the noise of the linear phase-shifting transformer was deduced and calculated. Based on this, the spectrum and space–time properties of the radial electromagnetic force waves were simulated and verified. Additionally, a finite element model was created using the Ansys Workbench 2022R1 platform to study the electromagnetic vibration and noise of the linear phase-shifting transformer. A joint simulation of the electromagnetic, structural, and sound fields was then performed. First, the transformer’s natural frequency was determined by modal analysis. After that, the transformer’s structure and the results of the transient electromagnetic field computation were combined and a harmonic response analysis was conducted to determine the vibration acceleration spectrum. Finally, in order to solve the sound pressure field, the transformer’s boundary vibration acceleration was coupled to the air domain. Furthermore, an analysis was conducted to determine the noise distribution surrounding the linear phase-shifting transformer. The joint simulation findings demonstrate that the linear phase-shifting transformer’s resonance, which produces larger electromagnetic vibration and noise, is indeed caused by the radial electromagnetic force. Simultaneously, the impact of the LPST core’s fixed components on the electromagnetic vibration and noise of the core was examined.

Influence of stator and rotor core material definition method on no‐load electromagnetic field calculation results for tubular hydrogenerator

AbstractIn this letter, the effects of various material definition approaches for stator and rotor cores on the no‐load electromagnetic field calculations of a 34 MW tubular hydrogenerator are investigated, utilizing the transient motion electromagnetic field time‐step finite element (FE) method. The findings indicate that employing a linear simplified definition for the stator core material maintains high accuracy and rationality in the calculation results of the no‐load electromagnetic field and voltage waveform while offering substantially greater computational efficiency than the non‐linear definition method. Conversely, using a linear simplified definition for the magnetic pole core material of the rotor significantly increases the error margin in the results, rendering them unacceptable.

Investigation of the influence mechanism of shield on the strong magnetic field during electromagnetic launch

The electromagnetic launch process generates low-frequency pulsed magnetic fields with peak values reaching Tesla-levels, imposing greater demands on the interference immunity of electronics within projectiles. However, during the propagation of low-frequency pulsed strong magnetic fields, their characteristics are affected by the shielding properties of the surrounding medium materials, resulting in modifications to the actual internal magnetic fields of the devices. This paper presents a theoretical analysis, numerical simulation, and experimental investigation based on the shielding mechanisms of conductive and magnetic materials to elucidate their impact on the pulsed magnetic fields. Additionally, leveraging previous work on electromagnetic railgun projectile magnetic field calculations, the shielding model is established to determine the shielding effects of different material combinations on the magnetic field during electromagnetic launch. The results reveal that both conductive and magnetic materials influence the amplitude, pulse width, and initiation time of the pulsed magnetic field, a finding validated through dynamic projectile-borne magnetic field testing.

Computer Simulation of Explosive Emission Processes in Strong Electromagnetic Fields

The paper discusses the problem of computer simulation of explosive emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell’s equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

Optimal Control for a Superconducting Hybrid MagLev Transport System with Multirate Multisensors in a Smart Factory.

Recently, magnetic levitation systems have been applied and studied in various industrial fields. In particular, in-tracktype magnetic levitation conveyor systems are actively studied since they can effectively minimize electromagnetic effects in processes that require a highly clean environment. In this type of system, diverse and multiple sensors are structurally required so that the control performance of an integrated system is primarily governed by the slowest measuring sensor. This paper proposes a multisensor fusion compensator to integrate the outputs obtained from various sensors into one output with the single fastest time rate. Since the state of the system is estimated at a fast time rate, the optimal controller also guarantees fast performance and stability. The computation of electromagnetic fields and the control performance of the considered superconducting hybrid system were analyzed using a computer simulation based on finite element methods.

Electromagnetic Field Calculation of Superconducting Magnetic Levitation Rotor under Alternating Magnetic Field

Electromagnetic Field Calculation of Superconducting Magnetic Levitation Rotor under Alternating Magnetic Field

Analysis of leakage flux, losses, and temperature in large synchronous generator end zone under the multi‐layer screen thickness based on novel iterative method

AbstractThe multi‐layer screen is the key component in the large synchronous generator end zone. The leakage flux, losses, and temperature of end components are significantly affected by the thickness of multi‐layer screen in the synchronous generator. To investigate the influence of multi‐layer screen thickness on the end leakage flux, losses, and temperature in the synchronous generator end zone, 1407MVA nuclear power synchronous generator is studied. Three‐dimensional transient electromagnetic field model of synchronous generator end zone is established. Three‐dimensional transient electromagnetic field in the end zone of 1407MVA synchronous generator with the multi‐layer screen is calculated based on the novel iterative method. The flux density of end components is compared and studied in the end zone under the variation of multi‐layer screen thickness. Influence of the different thicknesses of multi‐layer screen on the losses of the shield plate, screen, finger plate, and stator end core is researched. The losses of end components obtained from 3D end electromagnetic field calculation are applied to the end zone as the heat source in the three‐dimensional fluid and thermal coupled field. The temperature distribution of the end components is determined. The accuracy of the calculated results is validated by the experimental values.

Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation

Abstract Metasurface design tends to be tedious and time-consuming based on sweeping geometric parameters. Common numerical simulation techniques are slow for large areas, ultra-fine grids, and/or three-dimensional simulations. Simulation time can be reduced by combining the principle of the discrete dipole approximation (DDA) with analytical solutions for light scattered by a dipole near a flat surface. The DDA has rarely been used in metasurface design, and comprehensive benchmarking comparisons are lacking. Here, we compare the accuracy and speed of three DDA methods—substrate discretization, two-dimensional Cartesian Green’s functions, and one-dimensional (1D) cylindrical Green’s functions—against the finite difference time domain (FDTD) method. We find that the 1D cylindrical approach performs best. For example, the s-polarized field scattered from a silica-substrate-supported 600 × 180 × 60 nm gold elliptic nanocylinder discretized into 642 dipoles is computed with 0.78 % pattern error and 6.54 % net power error within 294 s, which is 6 times faster than FDTD. Our 1D cylindrical approach takes advantage of parallel processing and also gives transmitted field solutions, which, to the best of our knowledge, is not found in existing tools. We also examine the differences among four polarizability models: Clausius–Mossotti, radiation reaction, lattice dispersion relation, and digitized Green’s function, finding that the radiation reaction dipole model performs best in terms of pattern error, while the digitized Green’s function has the lowest power error.