Eddy Current Effects Research Articles

Generating a Cauer Ladder Network Representation of Eddy Current Fields Using Scalar Potentials

Formulations in terms of scalar potentials are proposed to solve the static field problems occurring when computing the parameters of a Cauer ladder network representation of two-pole devices involving eddy-current effects. The curl equations are satisfied by efficiently generating vector potentials describing the known flux density and current density and introducing unknown scalar potentials to represent the electric and magnetic field intensities. The scalar potentials are approximated using nodal basis functions in the finite-element realization, thus leading to Poisson equations to be easily solved. A simple numerical example illustrates the method.

B-Spline Parameterized Joint Optimization of Reconstruction and K-Space Trajectories (BJORK) for Accelerated 2D MRI.

Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image reconstruction quality in a supervised learning manner. We parameterize trajectories with quadratic B-spline kernels to reduce the number of parameters and apply multi-scale optimization, which may help to avoid sub-optimal local minima. The algorithm includes an efficient non-Cartesian unrolled neural network-based reconstruction and an accurate approximation for backpropagation through the non-uniform fast Fourier transform (NUFFT) operator to accurately reconstruct and back-propagate multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude enforce hardware constraints. Sampling and reconstruction are trained jointly using large public datasets. To correct for possible eddy-current effects introduced by the curved trajectory, we use a pencil-beam trajectory mapping technique. In both simulations and in- vivo experiments, the learned trajectory demonstrates significantly improved image quality compared to previous model-based and learning-based trajectory optimization methods for 10× acceleration factors. Though trained with neural network-based reconstruction, the proposed trajectory also leads to improved image quality with compressed sensing-based reconstruction.

Hierarchical CoNi alloys toward microwave absorption application: Chain-like versus particle-like

CoNi alloys are well known as excellent magnetic microwave absorption materials, but their various structures greatly influence electromagnetic properties, especially chains versus particles. Hierarchical CoNi chains were prepared using the solvothermal method in conjunction with an external magnetic field, and hierarchical CoNi particles were obtained in the absence of the magnetic field. Changing the reaction time from 6 to 12 h can change the surface structures of hierarchical CoNi alloys, as seen in the SEM images. The lattice parameters of samples are determined by XRD results, which include crystalline structures, lattice constants, mean crystallite sizes, and internal strain. The investigation of magnetic properties indicates that CoNi chains possess a stronger saturation magnetization and higher coercivity than CoNi particles as a result of their higher aspect ratios and larger crystalline sizes. Furthermore, CoNi chains have a higher microwave absorption capacity than CoNi particles, with a minimum reflection loss value of −42.113 dB (16.5 GHz) and an effective absorption bandwidth of 3.5 GHz (13–16.5 GHz). Conductive loss, defect-induced polarization relaxation, eddy current effect, exchange resonance, N é el relaxations, multiple reflections, and scatterings all contribute to the excellent microwave absorption performance of the CoNi chains. This research establishes that a chain-like structure outperforms a particle-like structure for hierarchical CoNi alloys as microwave absorbers, and it will provide clear guidance for designing high-performance magnetic microwave absorption materials.

Decoupling gaseous hydrogen production from liquid water using a magnetic‐photo‐thermal coupling reactor

AbstractTaking monolithic TiO2/nickel foam as a model photocatalytic material, we hereby report the application of magnetic‐photo‐thermal coupling field toward enhanced solar photocatalytic hydrogen production. This enhancement is attributed to the increased temperature induced by eddy current effect and effective charge separation caused by the electric field force under the alternating magnetic field condition. Particularly, we demonstrate that a proper set of the position of the monolithic catalyst relative to the reaction solution, that is, at the water‐air interface, will lead to a further enhancement of the photocatalytic activity because of the improved mass transfer property of the reactants, with a hydrogen evolution rate of 104.3 μmol h−1. Specifically, the increased temperature of the catalyst leads to the rapid evaporation of water. Hydrogen generation is thus decoupled from liquid water, avoiding kinetically disfavored bubble formation. This work provides a novel strategy to facilitate photocatalytic performance with the application of external field.

Characterization and correction of diffusion gradient-induced eddy currents in second-order motion-compensated echo-planar and spiral cardiac DTI.

Very high gradient amplitudes played out over extended time intervals as required for second-order motion-compensated cardiac DTI may violate the assumption of a linear time-invariant gradient system model. The aim of this work was to characterize diffusion gradient-related system nonlinearity and propose a correction approach for echo-planar and spiral spin-echo motion-compensated cardiac DTI. Diffusion gradient-induced eddy currents of 9 diffusion directions were characterized at b values of 150 s/mm2 and 450 s/mm2 for a 1.5Tesla system and used to correct phantom, ex vivo, and in vivo motion-compensated cardiac DTI data acquired with echo-planar and spiral trajectories. Predicted trajectories were calculated using gradient impulse response function and diffusion gradient strength- and direction-dependent zeroth- and first-order eddy current responses. A reconstruction method was implemented using the predicted -space trajectories to additionally include off-resonances and concomitant fields. Resulting images were compared to a reference reconstruction omitting diffusion gradient-induced eddy current correction. Diffusion gradient-induced eddy currents exhibited nonlinear effects when scaling up the gradient amplitude and could not be described by a 3D basis alone. This indicates that a gradient impulse response function does not suffice to describe diffusion gradient-induced eddy currents. Zeroth- and first-order diffusion gradient-induced eddy current effects of up to -1.7rad and -16 to +12 rad/m, respectively, were identified. Zeroth- and first-order diffusion gradient-induced eddy current correction yielded improved image quality upon image reconstruction. The proposed approach offers correction of diffusion gradient-induced zeroth- and first-order eddy currents, reducing image distortions to promote improvements of second-order motion-compensated spin-echo cardiac DTI.

Multiobjective optimization of 3-DOF magnetic bearing considering eddy current effects and saturation

The multiobjective optimization method of three-degrees-of-freedom hybrid magnetic bearings (3-DOF HMBs) is crucial compared to time-consuming finite element calculation due to their three dimensional magnetic field. Solid rotors are the first choice for high-speed applications because the yield strength of laminated rotors is lower. However, solid materials may induce eddy current effects and saturation problems. In addition, a 3-DOF HMB has solid and laminated materials and permanent magnet materials, and the material price presents a risk for the structure. In view of the above mentioned problems, a dynamic magnetic circuit model of the 3-DOF HMB with eddy current and saturation effects is initial given. Subsequently, a multiobjective optimization design method for maximum axial and radial bearing capacity and the lowest cost is proposed. Finally, the optimized parameters are given, and a prototype is manufactured. The range of all optimal solutions considering saturation is less than that without saturation, and the maximum reduction is 99%. The experimental results demonstrate the effectiveness of the optimized design results.

Axial scalable add-on PET/MRI prototype based on four-layer DOI detectors integrated with a RF coil

We developed an add-on PET which was a PET insert based on 4-layered depth-of-interaction (DOI) detectors integrated with a birdcage RF-coil. The PET detectors were placed close to subjects to achieve high sensitivity. The DOI capability suppress degradation of spatial resolution at the edge of the field of view (FOV). Previously, we developed an first prototype which had a short axial FOV. In order to extend the axial FOV, we developed new scalable add-on PET prototype. The constructed RF-coil of the new prototype was combined with 24 DOI-PET detector units Each detector unit with two PET detectors was shielded with a carbon fiber shielding box. Each PET detector consisted of a 14 × 14 × 4-layer array of lutetium fine silicate crystals (1.9 mm × 1.9 mm × 4.0 mm), an 8 × 8 multi-pixel photon counter (MPPC, S12641PA-050) array and a readout circuit board with an ASIC. The RF coil was tuned for a 3T clinical MRI (MAGNETOM Verio, Siemens). We evaluated performance the scalable add-on PET prototype in simultaneous PET/MRI measurements. We obtained spatial resolutions of 2.0 mm at the center of the FOV and better than 3.3 mm in the whole FOV. The energy resolution of 12.4 % was obtained at 511 keV. In addition, we observed no degradation of PET performance caused by the MRI measurement. The signal-to-noise ratio (SNR) of the MRI image was 186.2 in simultaneous measurements with the PET. The maximum ΔB0 and maximum difference of the secondary magnetic field due to the eddy current effect were smaller than 0.2 ppm and ±1.0μT, respectively. It meant that the influence of the PET detectors on the static magnetic field and secondary magnetic field did not cause problems.

Coil induced eddy current analysis of a fast kicker magnet

The eddy current effect is an important issue in pulsed magnet design. The eddy currents in the iron cores and the metal supports are proven to be the major causes of the eddy current effects in accelerator magnets. In our previous study, we focused on the eddy current effects in yoke and metal supports of a fast kicker magnet in Huazhong University of Science and Technology (HUST). Simulations using OPERA 3D revealed that eddy currents in yoke and metal supports have no significant influence on the magnetic field quality. However, the measured magnetic field distortion is approximately ± 0.4% during the fast change of magnetic field, and it takes several hundreds of microseconds to disappear. In addition, it is difficult to achieve a fast transient from the rising process to a steady state. Herein, we investigate the coil induced eddy current effect of a fast kicker magnet and reveal the main reason for the field distortion and the difficulty in the pulsed power supply commissioning. With design considerations of the coil induced eddy current, the simulation results can be in good agreement with the measurement results. Based on the dynamic performance of the load inductance, a fast transient from the rising process to a steady state can be achieved. The research findings can provide a good reference in the design and optimization of such pulsed magnet and associated power supply, especially for the fast kicker/bump magnet with windows frame yoke.

In silico evaluation of adverse eddy current effects in preclinical tests of magnetic hyperthermia

Background and ObjectiveMagnetic hyperthermia is an oncological therapy that employs magnetic nanoparticles activated by alternating current (AC) magnetic fields with frequencies between 50 kHz and 1 MHz, to release heat in a diseased tissue and produce a local temperature increase of about 5 °C. To assess the treatment efficacy, in vivo tests on murine models (mice and rats) are typically performed. However, these are often carried out without satisfying the biophysical constraints on the electromagnetic (EM) field exposure, with consequent generation of hot spots and undesirable heating of healthy tissues. Here, we investigate possible adverse eddy current effects, to estimate AC magnetic field parameters (frequency and amplitude) that can potentially guarantee safe animal tests of magnetic hyperthermia. MethodsThe analysis is performed through in silico modelling by means of finite element simulation tools, specifically developed to study eddy current effects in computational animal models, during magnetic hyperthermia treatments. The numerical tools enable us to locally evaluate the specific absorption rate (SAR) and the produced temperature increase, under different field exposure conditions. ResultsThe simulation outcomes demonstrate that in mice with weight lower than 30 g the thermal effects induced by AC magnetic fields are very weak, also when slightly overcoming the Hergt-Dutz limit, that is the product of the magnetic field amplitude and frequency should be lower than 5·109 A/(m·s). Conversely, we observe significant temperature increases in 500 g rats, amplified when the field is applied transversally to the body longitudinal axis. A strong mitigation of side-effects can be achieved by introducing water boluses or by applying focused fields. ConclusionsThe developed physics-based modelling approach has proved to be a useful predictive tool for the optimization of preclinical tests of magnetic hyperthermia, allowing the identification of proper EM field conditions and the design of setups that guarantee safe levels of field exposure during animal treatments. In such contest, the obtained results can be considered as valid indicators to assess reference levels for animal testing of biomedical techniques that involve EM fields, like magnetic hyperthermia, thus complying with the Directive 2010/63/EU on the protection of animals used for scientific purposes.

Influence and Suppression Method of the Eddy Current Effect on the Suspension System of the EMS Maglev Train

The suspension system of the EMS (Electro-Magnetic Suspension) medium-and-low-speed maglev train is affected by the eddy current effect when the train is in motion. This is a crucial problem related to the improvement of train operation speed. In this article, this phenomenon is analyzed and the method of suppressing the eddy current effect is put forward. Firstly, theoretical analysis and experimental verification are carried out. It is worth mentioning that the experimental data, which thoroughly show how the suspension current changes with the maglev train speed under the influence of the eddy current effect, are collected and published for the first time, which strongly confirms the accuracy of the theoretical analysis. Secondly, an improved scheme to suppress the influence of the eddy current effect is proposed from the perspective of the rail structure for the first time and simulation results verify the effectiveness of the improved scheme. This research makes important progress on the improvement of the rail used in the maglev train.

Dynamic modeling of stack giant magnetostrictive actuator with magnetic equivalent network considering eddy current effect

Stack giant magnetostrictive actuators (SGMAs) are widely used in various fields for its merits such as saving the space and improving the evenness of the bias magnetic field provided for the giant magnetostrictive material (GMM). In this paper, based on the flow path of the magnetic flux in SGMA, a magnetic equivalent network corresponding to quasistatic conditions is proposed taking flux leakage and fringing effect into account. Meanwhile, complex reluctances of the GMM rods are introduced to describe the decrease and phase shift of magnetic field intensities caused by eddy current under high-frequency excitation signals. Furthermore, the magnetic equivalent network, determining the relationship between excitation signals and magnetic field intensities, is combined with the Jiles–Atherton model, nonlinear constitutive theory of GMM concerning multi-field coupling, and structural dynamics of SGMA so as to derive a multi-field coupling model predicting the tracking behaviors of SGMA to the excitation signals. Moreover, a finite element method is conducted, an SGMA prototype is fabricated, and an experimental platform is set up to verify the proposed model. Comparison between results derived from the magnetic equivalent network and those calculated by the finite element method indicates that the proposed network is able to predict the magnetic field distribution inside the SGMA prototype in quasistatic conditions; further comparison between results obtained from the proposed multi-field coupling model and those from experiments indicates that the model can accurately predict tracking behaviors of the SGMA prototype to the excitation signals.

Photo- and magneto-responsive highly graphitized carbon based phase change composites for energy conversion and storage

Phase change material (PCM) as latent heat storage unit shows great potential in various scenes, including solar energy storage system and magnetically induced energy conversion and storage. But insufficient optical activity and electromagnetic response capability seriously hinder its wider applications. Herein, we reported an advanced high-performance photo- and magneto-driven composite phase change material (CPCM), where metal-organic framework (MOF) derived magnetic highly graphitized carbon (MGC) served as a fast-charging photo- and magneto-responsive supporting skeleton, and octadecanol (ODA) acted as a latent heat storage unit. In graphitic structure, there were numerous sp2 carbon atoms and π electrons. Under solar irradiation, heat is quickly discharged by lattice vibration resulting from π-π∗ transition and subsequent electron-phonon coupling in highly graphitized carbon. Moreover, in situ anchored magnetic cobalt nanoparticles contribute to another exothermic effect triggered by light and alternative magnetic field owing to its surface plasmon resonance (SPR) and eddy current effect, respectively. Additionally, cobalt nanoparticles can also serve as the heterogenous nucleation sites to promote the crystallinity of ODA molecules, thus profiting the increase of phase change enthalpy. Therefore, our developed cobalt-decorated highly graphitized carbon based photo- and magneto-responsive CPCM synergistically reached an enhanced photothermal efficiency of 88.1%, thermal energy storage capacity of 131.14 J/g, and excellent thermal cycling stability and reliability after undergoing multiple charging-discharging cycles, showing great potential in latent heat storage, solar and magnetic energy harvesting.

Structure of a permanent magnet motor used for electric vehicles to suppress the eddy current effect

Structure of a permanent magnet motor used for electric vehicles to suppress the eddy current effect

Integrated hybrid sensing and microenergy for compact active microsystems

Wearable electronics, as essential components of the Internet of Things (IoT), have attracted widespread attention, and the trend is to configure attractive wearable smart microsystems by integrating sensing, powering, and other functions. Herein, we developed an elastic hybrid triboelectric–electromagnetic microenergy harvester (named EHTE) to realize hybrid sensing and microenergy simultaneously. This EHTE is a highly integrated triboelectric nanogenerator (TENG) and electromagnetic nanogenerator (EMG). Based on the triboelectric–electromagnetic hybrid mechanism, an enhanced electrical output of the EHTE was achieved successfully, which demonstrates the feasibility of the EHTE for microelectronics powering. Moreover, with the merits of the EMG, the developed hybrid microenergy harvester integrated both active frequency sensing and passive inductive sensing capabilities. Specifically, the almost linear correlation of the electromagnetic outputs to the frequencies of the external stimulus endowed the proposed EHTE with an outstanding active frequency sensing ability. In addition, due to the unique structural configuration of the EMG (i.e., a conductive permanent magnet (PM), hybrid deformation layer, and flexible printed circuit board (FPCB) coil), an opportunity was provided for the developed EHTE to serve as a passive inductive sensor based on the eddy current effect (i.e., a form of electromagnetic induction). Therefore, the developed EHTE successfully achieved the integration of hybrid sensing (i.e., active frequency sensing and passive inductive sensing) and microenergy (i.e., the combination of electromagnetic effect and triboelectric effect) within a single device, which demonstrates the potential of this newly developed EHTE for wearable electronic applications, especially in applications of compact active microsystems.

Eddy Current Magnetic Localization of Nonmagnetic Metal Targets Based on Metal Shell Model

Target detection technology based on magnetic anomalies, due to its wide detection range, high localization accuracy, all weather conditions and other characteristics, plays an important role in geological prospecting, medical monitoring, disaster rescue and other fields. Some nonmagnetic or weakly magnetic metal targets are difficult to observe with passive magnetic anomaly detection (MAD) methods. The active MAD method based on the eddy current magnetic effect can locate nonmagnetic metal targets. However, traditional detection methods based on magnetic dipoles require knowledge of the target magnetic moment in advance and are not suitable for near-field detection. To solve these problems, this paper establishes a detection model based on a nonmagnetic metal shell target and derives the eddy current magnetic field (ECMF) expression of the nonmagnetic metal shell target. An ECMF extraction method that separates the ECMF from the excitation magnetic field and background interference from the perspective of the signal phase is further proposed. Then, the particle swarm optimization (PSO) algorithm is used to locate the nonmagnetic metal target. When the metal target is located within the range of 1.2 m*1.2 m, the localization error is approximately 2.5%. This method is important and valuable in the fields of medical pill tracking, drug dose conversion monitoring, trapped miner locating, indoor autonomous robot navigation, unexploded object detection and other fields.

Data-driven modeling of nonlinear materials in normal-conducting magnets

Accurate numerical modeling of normal-conducting accelerator magnets requires a reliable characterization of the iron saturation and hysteresis as well as a precise knowledge of the magnet geometry as built. Computations of the field quality are not easily achieving the accuracy required by the accelerator operation, particularly for eddy-current effects in fast-ramping magnets. This paper proposes a (measurement) data-driven model for the nonlinear magnetization of normal-conducting magnets. The model adopts a volume integral formulation compatible with eddy-current simulations. A two-step updating procedure is applied. The first step is the fitting of material parameters directly in the magnet model. The second step is the updating of the magnetization by measurements of the integral field harmonics. The result is a full-order updated model that can be employed in static or dynamic simulations. Finally, the procedure is validated on an iron-dominated, normal-conducting magnet.

Eddy current thermal effect based on magnesium microrods for combined tumor therapy

Magnetic hyperthermia therapy (MHT) is a minimally invasive cancer treatment to ablate tumors under an alternating magnetic field (AMF), possessing advantages including excellent tissue penetration, tumor-targeted selectivity, and negligible damage to the normal tissues. However, the low magnetothermal conversion efficiency (MTCE) of the magnetocaloric nanoagents limits its application. Herein, magnesium @ doxorubicin (Mg@DOX) microrods were prepared by electrospinning technology for the combined MHT and chemotherapy under AMF. The constructed Mg@DOX rods exhibited apparent magnetic field intensity-dependent temperature rise under AMF, stemming from the eddy thermal effect with good thermal stability, outstanding MTCE, and excellent penetration depth. Meanwhile, the DOX release increased with the prolonged magnetothermal time and the decreased pH value, thus realizing combined therapy. In vitro experiments showed that Mg@DOX microrods had an obviously cell-killing ability on account of the MHT and accelerated DOX release. In vivo experiments were further performed by implanting Mg@DOX microrods into 4T1 mouse breast tumors and the deep-seated rat liver tumors, showing excellent combined therapeutic effects. Moreover, Mg@DOX microrods showed excellent biocompatibility and displayed insignificant toxicity to the implanted animals. Our work highlighted the effective combined therapy of the unique eddy thermal effect of Mg@DOX microrods.

Structure regulation in N-doping biconical carbon frame decorated with CoFe2O4 and (Fe,Ni) for broadband microwave absorption

The typical environment pollution of superfluous microwave radiation has become an urgent problem to be solved at current stage. Herein, a new-style composite of unique biconical carbon framework decorated with CoFe2O4 and (Fe,Ni) nanoparticles was obtained by the co-hydrothermal and pyrolysis route. With the temperature-depended adjustability in microstructure, the composite calcined under 600℃ possesses the largest length–width ratio of amorphous carbon skeleton and the smallest median diameter of decorated NPs among all the samples. This could promote the interface polarization ability and geometrical anisotropy for conductivity, together with N-doping induced dipole polarization, the composite represents excellent dielectric loss capacity for microwave absorption. Moreover, the eddy current effect of magnetic alloy and natural resonance associated with ferrite also assist to this wastage. Under the optimal impedance matching, this composite owns maximal RL of −34.3 dB at 12.92 GHz for 2.0 mm with its broadest effective absorption bandwidth of 6.55 GHz at only 1.87 mm, covering the whole Ku and partial X bands. This work offers a novel microwave absorber with appropriate absorbing intensity and excellent bandwidth for practical usage.

Impedance Modeling of Self-Inductive Displacement Sensor Considering Iron Core Reluctance and Flux Leakage

The inductive displacement sensor has been widely used in active magnetic bearings (AMBs). The excitation frequency of this kind of sensor is usually as high as tens of kHz, so it is significant and cannot be ignored the influence of eddy current effect, hysteresis effect, flux leakage, and excitation frequency on the sensor performance. However, the above influence cannot be studied through the traditional ideal model considering only air gap reluctance. This paper introduced complex permeability to account for the influence of eddy current and hysteresis effects, introduced the flux leakage coefficient to account for the influence of flux leakage, and then established an improved core coil impedance model of self-inductive displacement sensor, and presented a method to calculate the model parameters through experimental results. For the designed self-inductive displacement sensor with a nominal air gap of 1.2 mm, the inductance and AC resistance of sensor core coils under different excitation frequencies and rotor displacements were measured, and then the model parameters were calculated. The improved model predicted the core coil impedance of the same sensor under three different excitation frequencies, and the relative error with the experimental value is no more than 3%. For a self-inductive displacement sensor with a nominal air gap of 1.0 mm, the predicted output voltage and sensitivity have relatively small errors with the experimental results, which verifies the correctness and accuracy of the improved impedance model.

Effective magnetic path length in Epstein frame test of electrical steels.

The effective magnetic path length lm for a 25cm Epstein frame test is studied on the basis of a relevant demagnetizing model and determined by a comparative measurement of dc and ac hysteresis loops at each value of peak flux density Bp, with the field recorded by H-coils placed above the mid-section of the limbs or calculated from the magnetizing current. The obtained Bp and frequency dependences of lm for testing core loss Ps and peak field Hp of an electrical steel are explained in terms of differential susceptibility along the measured loops and demagnetizing and eddy-current effects on local magnetization processes.