Calculation Of Magnetic Field Research Articles

Magnetic Hopfions: A Review

Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge emergent vector potential and emergent magnetic field are widely used to calculate the 3D topological charge (the Hopf index) of magnetic textures. The relation of the magnetic hopfions with classical field theory is demonstrated, and a special role of the curvilinear toroidal coordinates in the description of the hopfions is underlined. The hopfion stability and dynamics in ferromagnetic films and dots are considered. A critical discussion of calculations of the magnetization emergent magnetic field and the Hopf index of the toroidal magnetic hopfions in restricted geometries is presented.

Finite-field Cholesky decomposed coupled-cluster techniques (ff-CD-CC): theory and application to pressure broadening of Mg by a He atmosphere and a strong magnetic field.

For the interpretation of spectra of magnetic stellar objects such as magnetic white dwarfs (WDs), highly accurate quantum chemical predictions for atoms and molecules in finite magnetic field are required. Especially the accurate description of electronically excited states and their properties requires established methods such as those from coupled-cluster (CC) theory. However, respective calculations are computationally challenging even for medium-sized systems. Cholesky decomposition (CD) techniques may be used to alleviate memory bottlenecks. In finite magnetic field computations, the latter are increased due to the reduction of permutational symmetry within the electron-repulsion-integrals (ERIs) as well as the need for complex-valued data types. CD enables a memory-efficient, approximate description of the ERIs with rigorous error control and thus the treatment of larger systems at the CC level becomes feasible. In order to treat molecules in a finite magnetic field, we present in this work the working equations of the left and right-hand side equations for finite field (ff)-EOM-CD-CCSD for various EOM flavours as well as for the approximate ff-EOM-CD-CC2 method. The methods are applied to the study of the modification of the spectral lines of a magnesium transition by a helium atmosphere that can be found on magnetic WD stars.

Iterative algorithm for computing magnetic field considering remanent magnetization and demagnetization

SUMMARY Efficient and high-precision methods for performing large-scale numerical calculations under high magnetic susceptibility conditions are essential for magnetic exploration applications. This paper proposes an algorithm for magnetic field modelling considering both demagnetization and remanent magnetization. The 3-D partial differential equation of magnetic potential is reduced to a 1-D ordinary differential equation in the space-wavenumber domain through a 2-D Fourier transform in the horizontal direction. Using the quadratic interpolation finite element method to obtain the pentagonal equation, the chasing method is used to solve the equation efficiently, and a contraction operator based on electromagnetic integral equation method is introduced to ensure stable iteration convergence. The validity of the algorithm was confirmed by comparing it with analytical solutions. Numerical examples demonstrate the importance of considering demagnetization under high magnetization conditions. Test results reveal that magnetic susceptibility is the sole factor affecting convergence among the factors examined. Further analysis showed that, for the same magnetic susceptibility, the algorithm converges with the same number of iterations and higher precision is achieved with an increasing number of nodes. Under the same grid configuration, higher magnetic susceptibility requires more iterations to converge and results in lower algorithm precision. The algorithm presented in this paper shows higher efficiency compared to those based on integral equations. Moreover, we demonstrate the algorithm's high accuracy when applied to models with anomalies near boundaries. Finally, the adaptability of the algorithm to complex geological models and undulating topography is verified by combining model tests with DEM data. This algorithm presents an efficient and high-precision method for magnetic field calculations under conditions of high susceptibility and strong remanent magnetization, offering promising prospects for geoscience applications.

Analytical prediction of electromagnetic performance for surface-embedded permanent magnet in-wheel machines considering iron’s nonlinearity

Accurate magnetic field calculation is the premise of electromagnetic performance prediction. Conventional subdomain (SD) techniques assume that the iron’s relative permeability is infinite, leading to falsely overestimated flux density. We propose an accurate magnetic field analytical model for permanent magnet (PM) in-wheel machines considering iron’s magnetization nonlinearity and saturation. Specifically, according to the excitation source and topology, the entire solution domain of the machine is divided into sub-regions such as stator slots/teeth, stator slot-openings/tooth-tips, air-gap, and rotor slots/teeth, etc. Poisson’s or Laplace’s magnetic vector potential (MVP) equations are solved using Maxwell’s electromagnetic theory and complex Fourier series methods in each sub-region. Specifically, in our approach, The Cauchy product theorem addresses the discontinuous magnetic permeability change at the slot and tooth interface. The machine’s magnetic saturation effect is considered by combining the actual magnetization characteristics of iron with an iterative algorithm. The general solution for the MVP is solved using the boundary conditions between adjacent subregions. Subsequently, electromagnetic properties such as air-gap flux density, back electromotive force (EMF), and electromagnetic torque are obtained. The accuracy of the analytical model is verified by finite element analysis (FEA) and prototype tests, which proved that the proposed analytical model can consider the iron’s nonlinearity and the magnetic saturation. In addition, the inaccurate overestimation of electromagnetic torque and air-gap magnetic flux density by the conventional SD techniques has also been proven.

Magnetic field calculation of a uniformly magnetized sphere using solid angles

A new method to calculate the magnetic field of a uniformly magnetized sphere or spherical shell with surface current density K=Kosinθ using the solid angle concept is presented. The field can be shown easily to be constant inside the shell and dipole-like outside with a direct integral of Biot-Savart’s law without invoking magnetic vector potential or special scalar functions typically used for this classical problem.

Magnetic Field Calculation of the U-Shaped Interior Permanent-Magnet Synchronous Machine Considering the Parallel Magnetization and Bridge Saturation

Magnetic Field Calculation of the U-Shaped Interior Permanent-Magnet Synchronous Machine Considering the Parallel Magnetization and Bridge Saturation

Magnetic Field and Force Calculation of Transverse Flux Linear Synchronous Motor With Improved Analysis Model

Magnetic Field and Force Calculation of Transverse Flux Linear Synchronous Motor With Improved Analysis Model

On-load magnetic field calculation for linear permanent-magnet actuators using hybrid 2-D finite-element method and Maxwell–Fourier analysis

PurposeThe purpose of this study is to present a novel extended hybrid analytical method (HAM) that leverages a two-dimensional (2-D) coupling between the semi-analytical Maxwell–Fourier analysis and the finite element method (FEM) in Cartesian coordinates.Design/methodology/approachThe proposed model is applied to flat permanent-magnet linear electrical machines with rotor-dual. The magnetic field solution across the entire machine is established by coupling an exact analytical model (AM), designed for regions with relative magnetic permeability equal to unity, with a FEM in ferromagnetic regions. The coupling between AM and FEM occurs bidirectionally (x, y) along the edges separating teeth regions and their adjacent regions through applied boundary conditions.FindingsThe developed HAM yields accurate results concerning the magnetic flux density distribution, cogging force and induced voltage under various operating conditions, including magnetic or geometric parameters. A comparison with hybrid finite-difference and hybrid reluctance network methods demonstrates very satisfactory agreement with 2-D FEM.Originality/valueThe original contribution of this paper lies in establishing a direct coupling between the semi-analytical Maxwell–Fourier analysis and the FEM, particularly at the interface between adjacent regions with differing magnetic parameters.

Optimal design of thick-walled circular coils for uniform magnetic field generation

Abstract Uniform magnetic field coils are widely used as electromagnetic equipment in industrial, medical, and research applications, with Helmholtz coils being a common configuration. For applications requiring a relatively high magnetic field (∼mT), Helmholtz coils typically feature a large coil cross-section. However, this characteristic makes them unsuitable for describing the magnetic field generated by a current loop model during the design process. In this work, we model the magnetic field of a large cross-section Helmholtz coil system, often referred to as a thick-walled Helmholtz coil. By employing a genetic algorithm, we transform the design problem of a Helmholtz coil into a constrained optimization problem. Subsequently, we propose a method for reverse designing a Helmholtz coil based on constraints on the target magnetic field. Finite element simulations verify the accuracy of the established magnetic field calculation model in describing the magnetic field generated by the thick-walled Helmholtz coil. Moreover, the designed Helmholtz coil effectively meets the design constraints and objectives. This method addresses the issue of significant errors in calculating the magnetic field and its uniformity resulting from the cross-sectional effect during the design of thick-walled Helmholtz coils. Furthermore, it satisfies the constraints for coil operating time and lightweight design.

Efficient magnetic forward modeling for strongly magnetized bodies: An iterative integral equation approach

Magnetic surveying encounters challenges in high-precision detection and inversion on strongly magnetized bodies. Nonuniform magnetization caused by self-demagnetization and mutual magnetization makes magnetic field calculation using analytical formulas impractical. The previous discrete numerical methods have suffered from computational inefficiency or low accuracy. To resolve this issue, we develop an algorithm to solve the magnetic field integral equation for calculating the magnetization state of high-susceptibility bodies, combining the improved spatial convolution forward approach with the adaptive relaxation iteration method. To address the excessive computational burden in the magnetization field between 3D voxel arrays of the discrete model, we construct the circular convolution kernel matrix directly when the subsurface space is divided with an equidistant grid, significantly reducing redundant computations. Then, the fast Fourier transform is used to accelerate the forward discrete circular convolution operation. In addition, we derive an iterative computation scheme that adaptively adjusts the relaxation factor based on magnetic field changes to correct the effective magnetization for algorithm convergence. From a pragmatic perspective, equating the cuboid to equal-volume sphere subdivisions is developed to enhance computational efficiency further by approximately 50% despite sacrificing slight accuracy. The sphere and spherical shell models validate the algorithm accuracy, efficiency, and convergence. Furthermore, we analyze the characteristics of the mutual magnetization effect among magnetic bodies under different magnetization conditions. Finally, the applicability of the algorithm is demonstrated with a realistic example. Our algorithm shows promise for precisely exploring highly magnetized minerals, underground pipelines, and unexploded ordnance.

Deconfinement of runaway electrons by local vertical magnetic field perturbation

Runaway electron (RE) deconfinement and subsequent suppression is of prime importance for successful long-term operation of any tokamak. In this work, to deconfine and mitigate REs, the efficacy of local vertical field (LVF) perturbation has been explored numerically. LVF perturbation-assisted RE loss studies are carried out by simulating the drift orbits of the REs in magnetostatic perturbed fields and estimating the resulting orbit losses for different initial energies and magnitudes of LVF perturbation. To this end, the pre-existing PARTICLE code has been extended to the relativistic full-orbit-following code PARTICLE-3D (P3D) integrated with the magnetic field calculation code EFFI and plasma equilibrium field calculation code IPREQ to include the required fields for studying particle dynamics in general; this is then used to numerically model LVF perturbation-assisted RE deconfinement experiments conducted in the ADITYA tokamak. Simulation results show a significant (∼90%) deconfinement of REs with the application of LVF perturbation of a suitable amplitude (∼0.1% of the total magnetic field) in a preferred direction. The existence of a threshold magnitude of the applied field is also established, which is observed to be dependent on the energy of the REs. The simulation results reproduce all the experimental observations and reveal other interesting features of RE mitigation using LVF perturbation. The temporal map of orbiting time of REs shows that REs originating from the inboard side edge region ( ψ N > 0.5) of the plasma are relatively more prone to be lost with the application of suitable LVF perturbation than those originating from the plasma core. Interestingly, the simulation results demonstrate the existence of strong correlation between the safety factor (q) profile in the plasma edge region ( ψ N > 0.7) and the level of RE deconfinement using LVF perturbation.

A New Field Line Tracer for the Study of Coronal Magnetic Topologies

We present a new code for the tracing of magnetic field lines and calculation of related quantities such as the squashing factor in the solar corona. The Universal Fieldline Tracer (UFiT) is an open-source package that can currently take inputs directly from four well-established coronal models, with additional models planned to be made directly accessible in the future. This package contains tools to make use of large-scale three-dimensional field line maps to calculate volumetric quantities, such as the total volume of the open corona, or the fraction that maps to regions on the solar surface within some distance of a coronal hole boundary, which may be relevant to phenomenological models of solar wind speed such as the Wang–Sheeley–Arge model. Synthetic coronagraphs can also be produced rapidly by this package. We have postprocessed long-term magnetofrictional simulations to demonstrate that the separatrix web occupies a larger fraction of the corona during solar maximum than solar minimum.

New Features of the Traps Code for Accurate 3D Magnetic Field Calculations

New Features of the Traps Code for Accurate 3D Magnetic Field Calculations

Analytical Calculation of Magnetic Field and Analysis of Rotor Permeability Effects on Permanent Magnet Synchronous Motor with Fractional Slot Concentrated Winding

Accurate calculation of the flux and the magnetic field distribution of fractional slot concentrated winding permanent magnet synchronous motor (FSCW PMSM) is the basis for motor performance analysis, and rapid calculation is key. In this paper, to solve the problem of difficult modeling and accuracy guarantee of the flux linkage differential method, a method is proposed to calculate the flux and the no-load back EMF by the slotless subdomain model. By introducing the leakage flux calculation link, the calculation accuracy is improved, the analytical method results are compared with the finite element method results, and the effectiveness of the proposed method is verified. On this basis, the nonlinear variations of the magnetic field and the no-load back EMF with rotor permeability are determined, and the influence mechanism of rotor length and rotor permeability on the main magnetic circuit is revealed. Finally, an experiment of the prototype is carried out, and the correctness and accuracy of the analytical method and the finite element method is verified by comparing with the experimental results.

Noise suppression for an aeromagnetic measurement system on an unmanned helicopter.

An unmanned helicopter is one of the main platforms for conducting unmanned aerial vehicle aeromagnetic measurements and combines the advantages of rotary-wing and fixed-wing unmanned aerial vehicles. However, unmanned helicopter-based aeromagnetic measurement systems face complex static magnetic noise and maneuvering magnetic interference, which limit their practical performance. To address this issue, an improved multi-channel frequency measurement algorithm for the optically pumped magnetic sensor is proposed to suppress the static magnetic noise proportional to the frequency noise generated by the random quantization error and the airborne electromagnetic interference. A novel aeromagnetic compensation method for the maneuvering magnetic interference is then proposed to weaken the negative effects of the strong multicollinearity of the attitude parameters of the unmanned helicopter on the compensation accuracy and stability by introducing a regularization term and weight matrix. In addition, dedicated software is developed for the real-time calculation and compensation of magnetic interference fields. A dedicated unmanned-helicopter-based aeromagnetic measurement system is developed, and ground and flight experiments are carried out. The ground test results indicate that the static noise of the proposed system is only 0.000 82 nT. In the flight experiments, the system achieves an improvement ratio of 8.33, which is higher than the improvement ratio of 4.37 for a state-of-the-art commercial compensator. Furthermore, the dynamic noise after compensation decreases by 37.6% from 0.0157 to 0.0098 nT.

Analytical Calculation of the No-Load Magnetic Field of a Hybrid Excitation Generator

Hybrid excitation generators combine the advantages of electric excitation motors and permanent magnet generators. Focusing on a permanent magnet generator as the object of study, an auxiliary excitation winding is introduced for voltage regulation. The main magnetic field is established by the permanent magnet, and the auxiliary excitation winding provides the magnetic potential required to regulate the air-gap magnetic field. While improving the voltage regulation performance of permanent magnet generators, it also reduces the loss of excitation windings in electrically excited generators. Based on a hybrid excitation generator with dual excitation windings, in the following article, we present a hybrid excitation generator equivalent to a full permanent magnet motor with the minimum output voltage, and an accurate subdomain model of the full permanent magnet motor is established considering the influence of slot opening. By establishing a matrix, the distribution curve of air-gap magnetic density was solved and ultimately verified using finite element analysis. The results of the present study lay a solid foundation for solving the air-gap magnetic density distribution of various parts of the hybrid excitation generator and studying its performance in the future.

Magnetically controlled self-sealing pressure-preserved coring technology

Pressure-preserved coring is an effective means to develop deep resources. However, due to the complexity of existing pressure-preserved technology, the average success rate of pressure-preserved coring is low. In response, a novel in situ magnetically controlled self-sealing pressure-preserved coring technology for deep reserves has been proposed and validated. This innovative technology distinguishes itself from conventional methods by employing noncontact forces to replace traditional pre-tensioning mechanisms, thereby enhancing the mechanical design of pressure-preserved coring equipment and significantly boosting the fault tolerance of the technology. Here, we report on the design, theoretical calculations, experimental validation, and industrial testing of this technology. Through theoretical and simulation calculations, the self-sealing composite magnetic field of the pressure controller was optimized. The initial pre-tensioning force of the optimal magnetic field was 13.05 N. The reliability of the magnetically controlled self-sealing pressure-preserved coring technology was verified using a self-developed self-sealing pressure performance testing platform, confirming the accuracy of the composite magnetic field calculation theory. Subsequently, a magnetically controlled self-triggering pressure-preserved coring device was designed. Field pressure-preserved coring was then conducted, preliminarily verifying the technology's effective self-sealing performance in industrial applications. Furthermore, the technology was analyzed and verified to be adaptable to complex reservoir environments with pressures up to 30 MPa, temperatures up to 80 °C, and pH values ranging from 1 to 14. These research results provide technical support for multidirectional pressure-preserved coring, thus paving a new technical route for deep energy exploration through coring.

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Semiconductors have a valence band consisting of multi-subbands. Inter-subband interaction causes multiple degenerate points near the Brillouin zone center Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma$$\\end{document} even when the system exhibits space-reversal asymmetry. In the present study, we analyzed the effect of the existence of multiple degenerate points on topological features using Berry parameter investigation. For reasonable generalization, we propose a model Hamiltonian that represents multiple degeneracies in a two-dimensional quantum-well system. We also explored “topological” modifications through numerical calculations of the effective magnetic field and Berry’s connection and curvature. We found that the energy dependence of the Berry phase is affected by the interaction between degenerate points.Graphical abstract

Direct, simple and efficient computation of all components of the virtual-casing magnetic field in axisymmetric geometries with Kapur–Rokhlin quadrature

Direct, simple and efficient computation of all components of the virtual-casing magnetic field in axisymmetric geometries with Kapur–Rokhlin quadrature

Analytical computation of magnetic field in coil-dominated superconducting quadrupole magnets based on racetrack coils

Analytical computation of magnetic field in coil-dominated superconducting quadrupole magnets based on racetrack coils