Calculation Of Magnetic Field Research Articles

Quantitative assessment of finite-element models for magnetostatic field calculations

We present quantitative means for assessing the numerical accuracy of static magnetic field calculations in finite-element models. Our calculations use the three-dimensional Opera simulation software suite of Dassault Systèmes. Our need to assess the effects of fringe fields requires such a 3D algorithm. While we do discuss and compare our approach to a method of accuracy estimation used in the Opera post-processor, our methods are generally applicable to any model using relaxation techniques in finite-element systems. For purposes of illustration, we present modeling and analysis of two types of quadrupole electromagnets presently in operation in the south arc of the Cornell Electron Storage Ring (CESR). Calculations of field multipole expansion coefficients and numerical deviations from Maxwell’s equations in source-free regions are discussed, with emphasis on the dependence of their accuracy on changes to the finite-element model. Successive refinement steps in the finite-element model for the non-extraction type of CESR south arc quadrupole achieve a reduction in the RMS value of the longitudinal component of the curl vector on the magnet axis by a factor of nearly 70 from 4.38×10−2 T/m to 6.36×10−4 T/m, which is 0.0021% of the field gradient. An accuracy of 2.9% is achieved for a dodecapole coefficient of 2.4×10−4 of that of the quadrupole in the longitudinal integral of the vertical field gradient at a radius of 1 cm.

Ion-optical design and multiparticle tracking in 3D magnetic field of the gas-filled recoil separator SHANS2 at CAFE2

The CAFE2 (China Accelerator Facility for superheavy Elements) is a new facility constructed at IMP-CAS (Institute of Modern Physics, Chinese Academy of Sciences). It is based on the upgrade of a superconducting linear accelerator. A new gas-filled recoil separator SHANS2 (Spectrometer for Heavy Atoms and Nuclear Structure-2) with a total flight length path of 5.85 m at the CAFE2 is designed to synthesize and study the superheavy elements, including their physical and chemical properties. The maximum acceptable divergence angles of the SHANS2 are ±70 mrad and ±113 mrad in horizontal and vertical directions, respectively, and the maximum magnetic rigidity is 2.5 Tm. The ion-optical design and simulation are investigated in detail, including the first and the fifth order beam optics. The magnets design and magnetic field calculation are presented. Using the 3D field maps, a multiparticle tracking study is carried out for the design validation, trajectory analysis, and performance evaluation.

Calculation and Simulation of Eddy Current Magnetic Field of Ellipsoid in Changing Magnetic Field

The eddy current magnetic field generated by the ellipsoid in the changing magnetic field is theoretically deduced and calculated and simulated. The theoretical calculation and the value obtained by the simulation are compared and verified and the error is analyzed. It can be seen from the fitting results that the theoretical calculation method used in this paper and the simulation result have reached a 93% degree of fit, indicating that this method has a certain reference value for the study of the spatial distribution of the eddy current magnetic field.

Микроволновый индикатор потенциальной геоэффективности и жгутовая магнитная структура солнечной активной области

We analyze the presence of a microwave neutral-line-associated source (NLS) in a super-active region NOAA 12673, which produced a number of geo-effective events in September 2017. To estimate the NLS position, we use data from the Siberian Radioheliograph in a range 4–8 GHz and from the Nobeyama Radioheliograph at 17 GHz. Calculation of the coronal magnetic field in a non-linear force-free approximation has revealed an extended structure consisting of interconnected magnetic flux ropes, located practically along the entire length of the main polarity separation line of the photospheric magnetic field. NLS is projected into the region of the strongest horizontal magnetic field, where the main energy of this structure is concentrated. During each X-class flare, the active region lost magnetic helicity and became a CME source.

Microwave indicator of potential geoeffectiveness and magnetic flux-rope structure of a solar active region

We analyze the presence of a microwave neutral-line-associated source (NLS) in a super-active region NOAA 12673, which produced a number of geo-effective events in September 2017. To estimate the NLS position, we use data from the Siberian Radioheliograph in a range 4–8 GHz and from the Nobeyama Radioheliograph at 17 GHz. Calculation of the coronal magnetic field in a non-linear force-free approximation has revealed an extended structure consisting of interconnected magnetic flux ropes, located practically along the entire length of the main polarity separation line of the photospheric magnetic field. NLS is projected into the region of the strongest horizontal magnetic field, where the main energy of this structure is concentrated. During each X-class flare, the active region lost magnetic helicity and became a CME source.

Heat capacities and thermodynamic functions of neodymia and samaria doped ceria

Doped ceria materials are ionic conductors currently under investigation for use in solid oxide fuel cells, catalysts, and other applications. We measured the heat capacity of several doped ceria samples from 1.8 K to 300 K to better understand their physical properties. The samples used in this study were either singly doped with Nd or Sm, or co-doped with both Nd and Sm. This work complements an earlier detailed study of their heats of formation and ionic conductivity. Here we provide the thermodynamic functions based on theoretical fits of our heat capacity measurements including Cp,m°, Δ0TSm°, Δ0THm°, and Φm°. We also detected splitting of nuclear magnetic states, which appeared as an upturn in the heat capacity below 10 K. We observed this phenomenon in all samples and provide calculations of the local magnetic field causing the splitting.

Hybrid Analytical Modeling of Air-Gap Magnetic Field in Asymmetric-Stator-Pole Flux Reversal Permanent Magnet Machine Considering Slotting Effect

This article proposes an accurate and computationally efficient hybrid analytical (HA) model for the air-gap magnetic field computation of asymmetric-stator-pole flux reversal permanent magnet machine, which can provide a thorough insight into the working mechanism by taking the slotting effects into account. The proposed HA model combines the subdomain method and Schwarz–Christoffel (SC) transformation, which can account for the stator and rotor slotting effects, respectively. The subdomain method is first employed to predict the air-gap magnetic field considering the rotor slotting effect by converting the machine geometry to a slotless stator model. Afterward, a complex relative permeance function is obtained by the SC transformation, in which the stator slotting effect is taken into account. Finally, the complete air-gap magnetic field distribution of the machine can be efficiently predicted by the proposed HA analytical model. The effectiveness of the proposed HA model is verified by both finite-element analyses and experimental results.

3-D FEM–BEM Coupling for the Magnetic Field Computation in Thin Shells: Application to the Evaluation of Ship Magnetic Signature

In this article, a model based on finite element-boundary element methods (FEM-BEM) coupling is developed for the magnetic field computation in thin magnetic shells submitted to external magnetic fields. The model is formulated in terms of the reduced magnetic vector potential. Surface fictitious currents are used for the FEM-BEM coupling. Only the active arts are discretized by using edge elements. The model is validated by comparing with analytical results for a magnetic hollow sphere in a homogeneous magnetic field. An application to the evaluation of ship magnetization is then considered.

Measurements of self-field and voltage for the REBCO stacked tapes assembled in rigid structure (STARS) conductor at 77 K

The measurements of self-fields and voltages for the stacked tapes assembled in rigid structure (STARS) conductor were carried out when the conductor immersed in liquid nitrogen was energized. In the measurements, a 3 m straight line shaped STARS conductor, which is composed of 45 REBCO tapes (15 tapes × 3 rows) embedded in a copper stabilizer, was used as a conductor sample. The measurement results indicate that the ramp rate at the conductor excitation and the one-time thermal cycle of the conductor do not affect the self-fields but the voltages.The current center position in the conductor cross-section during the conductor excitation was analyzed from the measurement results of the self-fields. The current center position always maintains the same position in the middle of the cross-section during the excitation. The analysis indicates that the current distribution of the STARS conductor is stable during the excitation. In addition, two-dimensional magnetic field calculations were conducted using the various models for the cross-sectional configuration of the STARS conductor. As a result, the calculation results agree with the measurement results regarding the self-fields.

The Mechanical Performance evaluation of Vertical Stability Coil under Electromagnetic-structure Coupling Analyses

The vertical stability coil is a set of active feedback control coil that is used to deal with the vertical instability of plasma. To improve the response performance, the coil is mounted in the vacuum vessel, which denotes the coil-body will suffer from large electromagnetic force from the plasma current and poloidal field coils. Besides the current flowing in the feeder is nearly perpendicular with magnetic field originated from toroidal coil. It implies large electromagnetic force will be generated on the feeder. In order to withstand the impact from the electromagnetic force, a series of reinforce compo-nents are designed and installed on the coil. It is necessary to verify whether or not the coil conductor and auxiliary components could successfully bear the shock of large electromagnetic force. A three-dimensional magnetic field model is built to accurately calculate the magnetic field and electromag-netic force. Corresponding to the magnetic field calculation model, a more detailed me-chanical anal-ysis model is created to launch the electromagnetic-structural coupling analysis. Based on the stress analysis results, the local structure of the coil is optimized to decrease the peak stress. The updated model is reanalyzed and stress linearization is exerted to extract the different kinds of stress on the coil components. Finally, the stress is evaluated based on ASME analytical design. The evaluation result is helpful to guide the further design optimization.

A two-phase-five-phase transformer calculating features

The paper describes a new approach to constructing a transformer with a rotating magnetic field. Such a transformer mathematical description with a rotating magnetic field is given. A transformer calculating method for a primary and secondary windings phases different number is considered. A two-phase-five-phase transformer with a rotating magnetic field calculation is shown as an example. Based on a transformer with a rotating magnetic field calculation, its simulation model is built. The output currents oscillograms at the sinusoidal and rectangular shape input voltage were obtained.

2-D and 3-D Analytical Calculation of the Magnetic Field and Levitation Force Between Two Halbach Permanent Magnet Arrays

As we know, the analytical calculation of magnetic field and magnetic force has important guiding significance for the optimal design of the size and structure of a magnet. At present, the magnetic field and magnetic force between two permanent magnet (PM) monomers have been described by effective analytical models. However, the magnetic field strength and magnetic force generated by two PM monomers are limited and cannot meet the requirements of a PM levitation system with high magnetic field strength and large levitation force. To this end, this article establishes analytical calculation models of magnetic field and levitation force between two Halbach PM arrays. First, on the basis of Ampere molecular circulation hypothesis, the 2-D analytical model of magnetic field was established based on the surface current method; on the basis of magnetic charge theory, the 3-D analytical model of magnetic field was established based on the magnetic charge method. Second, based on the analytical models of magnetic field, the 2-D and 3-D analytic models of levitation force were derived by virtual work method, respectively. Numerically, the results of two analytical models of magnetic field and two analytical models of levitation force have been compared to verify the accuracy of the models. At the same time, the 2-D and 3-D finite element simulation models of magnetic field and levitation force were established, respectively, and the accuracy of the analytical models were verified again. The results show that the analytical models established in this article is effective and can be used to guide the design and optimization of the magnet composed of two Halbach arrays.

Biot–Savart Approach to Analytical Computation of Magnetic Fields and Forces of CCT Magnets

The current distribution in a canted cosine theta (CCT) multipole magnet can be written starting from the equation of an azimuthal modulated helix. In the ideal case of coaxial layers of infinitely long and infinitely thin windings, both the magnetic field and Lorentz forces are analytically obtained by applying the Biot-Savart law. The calculations are extended to multiwire magnets, where the conductors are modeled as sets of infinitely thin filaments. In order to evaluate the impact of the infinitesimal conductor thickness assumption, a comparison with finite element model results was performed. A very good agreement was found, demonstrating that the analytical model can be used as a powerful tool to support CCT magnet design as well as a useful and simple approach for didactic purpose.

Особливості розрахунку параметрів магнітного поля відкритих осесиметричних магнітних систем

У статті розглянуті дослідження розподілу магнітного поляв міжполюсному проміжку відкритих вісесиметричних магнітних систем. Отримано рівняння з граничними умовами, рішення якого дозволяє скоротити обсяг подальших чисельних методів розрахунків.Для ряду нестійких завдань математичної фізики Р.Латтесом і Ж.Лионсом розроблений метод квазізвернення, який може бути застосований як для еволюційних завдань, так і стаціонарних. Основна ідея методу квазізвернення полягає в належній зміні диференціальних операторів, що входять в завдання. Ця зміна робиться введенням додаткових диференціальних членів. Застосування цього методу дозволяє ефективно використати чисельні методи розрахунку крайового завдання для відкритих осесиметричних систем.

Modeling of PV Module and DC/DC Converter Assembly for the Analysis of Induced Transient Response Due to Nearby Lightning Strike

Photovoltaic (PV) systems are subject to nearby lightning strikes that can contribute to extremely high induced overvoltage transients. Recently, the authors introduced a 3D semi-analytical method to study the electromagnetic transients caused by these strikes in a PV module. In the present paper we develop an improved model of the PV module that: (a) takes into account high-frequency effects by modelling capacitive and inductive couplings; (b) considers the electrical insulation characteristics of the module; (c) includes the connection to a DC/DC converter. The whole process involves three major steps, i.e., the magnetic-field computation, the evaluation of both common-mode- and differential-mode-induced voltages across the PV module, and the use of the calculated voltages as input to a lumped equivalent circuit of the PV module connected to the DC/DC converter. In such a framework, the influence of the PV operating condition on the resulting electrical stresses is assessed; moreover, the relevance or insignificance of some parameters, such as the module insulation or the frame material, is demonstrated. Finally, results show that the induced overvoltage are highly dependent both on the grounding of the conducting parts and on the external conditions such as lightning current waveforms and lightning channel (LC) geometry.

The magnetic field calculation in electromechanical systems with saturated ferromagnetic structural elements

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Analytical Calculation of Magnetic Field in Fractional-Slot Windings Linear Phase-Shifting Transformer Based on Exact Subdomain Model

Fractional-slot windings linear phase-shifting transformers (FW-LPSTs) are a new type of transformer that can be used as an important component of multi-rectifier and multi-inverter systems. The FW-LPSTs are proposed for the first time, and few scholars have studied their magnetic field. However, accurate calculation of magnetic field distribution of the FW-LPSTs is the premise of the optimal design of the ontology, and the establishment of an accurate analytical model which remains a challenging task is the key to solving the magnetic field distribution. In view of the limitation of traditional analytical theory in solving the magnetic field, the FW-LPST model based on the exact subdomain method is proposed to obtain the exact magnetic field distribution. Considering the influences of the permeability and the structural parameters of the slot subdomain and the interaction of all slots on the distribution of the magnetic field, the governing equations of the air gap and slot subdomains are established using magnetic vector potential as the variable. According to the boundary conditions of each subdomain, all equations of the boundary condition are listed based on the Fourier series method. Finally, the vector magnetic potential and open-circuit magnetic flux density distribution of each subdomain are solved. The model accurately analyzes the influence of the cogging effect on the magnetic field distribution. The inductances of the primary side and the induced potentials of the secondary side are solved using the magnetic flux linkage method. The accuracy of the proposed analytical model is verified by comparison of the results obtained with those obtained by the finite element method.

Numerical Calculation of Low-frequency Magnetic Field on Three-dimensional Orthogonal Equidistant Grid by Barnes-Hut Tree Method Executed in Reverse Order

Numerical Calculation of Low-frequency Magnetic Field on Three-dimensional Orthogonal Equidistant Grid by Barnes-Hut Tree Method Executed in Reverse Order

Field Reconstruction for Modeling Multiple Faults in Permanent Magnet Synchronous Motors in Transient States

Conventional field reconstruction model (FRM) for electrical machines has proved its main strength in efficient computations of magnetic fields and forces in healthy permanent magnet synchronous machines (PMSM) or faulty machines in steady states. This study aims to develop a magnet library of different magnet defects and include inter-turn short-circuit (ITSC) in the FRM for PMSM. The developed FRM can model a combination fault between ITSC, and magnet defect in a PMSM in transient states. Within the framework, an 8-turn ITSC was modelled in both finite element analysis (FEA) and FRM, and then identified by the extended Park’s vector approach. The air-gap magnetic field reproduced by the FRM shows a good agreement with the result from time-stepping FEA. The computation speed is over 1000 times faster than an equivalent time-stepping FEA. The suggested FRM allows for quickly understanding effect of faults in the rotor and stator on the air-gap magnetic flux density and identifying unique signatures for such defects.

Аналитическое и численное моделирование магнитоэлектрических вентильных двигателей

An analytical method for calculating the magnetic field of a magnetoelectric valve motor is proposed, based on the tearing of its active region into a set of geometrically homogeneous bands, at the boundaries of which the conditions for the conjugation of their magnetic fields are met: scalar magnetic potentials and normal components of magnetic induction do not undergo a jump (break). If the magnetic sheets of the windings, for calculation convenience, are located at the boundaries of the specified bands, then the magnetic potentials at the boundaries will have a jump by the value of the total current of the magnetic sheet. To increase the accuracy of the calculation, you should increase the number of bands (sampling) of the active region. When using the computational technology of Fourier variables separation, the conjugation conditions will be reduced to solving a system of linear equations to find the corresponding Fourier constants. As sources of the magnetic field of the motor, in addition to permanent magnets and stator winding currents, the magnetization of the ferromagnetic sections of its magnetic circuit is proposed. The results of magnetic field calculation by this analytical method are compared with the data of the numerical simulation of the considered machine based on the mathematical program ELCUT 6.3.