United States

Recent trends in the distribution of electrical energy through medium- and low-voltage grids, involving a variety of sources and smart infrastructures, call for extensive use of medium frequency transformers, as required for conversion steps and bidirectional power transfers. The employed grain-oriented (GO) cores are subjected to kHz frequencies and harmonics-rich voltages. These are scarcely assessed working regimes, regarding both loss behavior and dynamics of the domain structure. We perform in this work a thorough investigation on the energy loss dependence on frequency f (DC – 10 kHz) and peak polarization Jp (0.25 T – 1.7 T) of high-permeability 0.29 mm thick GO steel sheets, combined with the magneto-optical Kerr analysis of the dynamics of the domain walls and the evolution of the domain structure in well-oriented grains. The predicting model starts with the determination of the induction profile across the sheet thickness at any instant of time, according to the Maxwell’s diffusion equation, which is applied using the experimental normal/anhysteretic curves as magnetic constitutive equations. The classical energy loss component Wcl is calculated versus f and Jp, together with the evolution of the hysteresis loss Wh. This, although increasing with f, is observed to provide negligible contribution in the kHz range. The Kerr images show that the regular antiparallel domain wall (dw) structure is initially preserved under increasing f, at the cost of bowing and dw densification, while the excess loss Wexc follows a regular power law. However, at sufficiently high f and Jp values, the dws meet and annihilate at the surface, while remaining stuck as cylindrical domains at the sheet midplane. It turns out that in the high (f, Jp) corner the magnetization process occurs by penetration towards the midplane of extended dws parallel to the sheet surface, with Wexc and Wh dwarfed by the classical loss component.

MMM 2020

Domain Structure and Energy Losses up to 10 kHz in Grain-Oriented Fe-Si Sheets

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

Transcranial magnetic stimulation (TMS) is a non-invasive technique used to regulate the synaptic activity of neurons in the brain, improving the functionality of connecting regions and bringing effective treatment to different neurological and psychiatric disorders. Treatment of many of these conditions requires application of external time-varying magnetic fields on a small cortical region to precisely alter connecting pathological sub-networks. The TMS induced field needs to be focused enough to avoid unwanted side effects caused by stimulation of the adjacent regions. Attempts at TMS in small animals[1] like rodents are highly constrained[2,3,4], since most of these studies use commercial equipment intended for humans, with power and coil geometries not intended for small animals. The present work shows the design and evaluation of customized arrays of two and four double-winding coils with a silicon steel core to restrict the stimulation to areas as small as 1 mm2, using finite element analysis with ANSYS Maxwell software. The coil is made with 50 turns of a wire with thickness = 1 mm, I.D. = 0.7 mm, O.D. = 4.5 mm and height = 25.4 mm. The cylindrical cores were designed with V-shape tip sharpening. The core material is silicon steel of 1.75 T of saturation flux density at 800 A/m and initial relative permeability of 500. The B-field was calculated 4.25 mm below the coil (vertical distance from the top of the scalp to the cortical layer 5/6 in adult rats) with currents of 1,000 A in short single (non-repetitive) pulses (≤ 4 msec) and showed values of up to 270 mT in 1 mm2. The very small area achieved supports the utility of the coil to perform in-vivo experimentation on rodents. Future works will seek to improve the duration of pulses for repetitive TMS (rTMS) with refrigeration and pulse conformation techniques and to validate the novel TMS device with in-vivo experiments in rat models. This study was partially funded by the Dept. of VA Biomedical Lab Research and Development 2I01BX001147-05A2 merit review award (M. Baron, PI).References: [1] J. Boonzaier, P. I. Petrov, W. M. Otte, N. Smirnov, S. F. W. Neggers, and R. M. Dijkhuizen, “Design and Evaluation of a Rodent Specific Transcranial Magnetic Stimulation Coil: An In Silico and In Vivo Validation Study,” Neuromodulation Technol. Neural Interface, p. ner.13025, Jul. 2019, doi: 10.1111/ner.13025. [2] J. Selvaraj, P. Rastogi, N. P. Gaunkar, R. L. Hadimani, and M. Mina, “Transcranial Magnetic Stimulation: Design of a Stimulator and a Focused Coil for the Application of Small Animals,” IEEE Trans. Magn., vol. 54, no. 11, Nov. 2018, doi: 10.1109/TMAG.2018.2846521. [3] M. T. Wilson, A. D. Tang, K. Iyer, H. McKee, J. Waas, and J. Rodger, “The challenges of producing effective small coils for transcranial magnetic stimulation of mice,” Biomed. Phys. Eng. Express, vol. 4, no. 3, Apr. 2018, doi: 10.1088/2057-1976/aab525. [4] I. P. de Sousa, C. R. H. Barbosa, and E. C. Monteiro, “Safe exposure distances for transcranial magnetic stimulation based on computer simulations,” PeerJ, vol. 2018, no. 6, 2018.

Quadruple Silicon Steel Core Coil for Highly Focused Transcranial Magnetic Stimulation in Small Animals

I Introduction In order to obtain the deformation characteristic of silicon steel with yoke clamping applied under alternating magnetic field, a stress-dependent magnetostriction model of silicon steel must be construct. Due to the rotation of magnetic domain and the movement of magnetic domain wall with stress applied, the magnetostrictive deformation of the material will reverse and saturate in both magnitude and direction [1-3]. Therefore, the saturated magnetic domain wall movement effect must be considered in stress-dependent magnetostriction model. II The hysteresis stress-dependent magnetostriction model of silicon steel Based on the comparison of the measured magnetostrictive strain curves and hysteresis loops, the hysteresis effect of magnetostrictive curve is obvious even the area of hysteresis loop is small [2]. Therefore, this paper constructs the magnetization model based on the J-A hysteresis model. Then, based on the macroscopic thermodynamics and Gibbs free energy expansion, the stress-dependent magnetostriction model in the excitation state is constructed. Meanwhile, due to the pinning effect, the magnetostrictive curve of silicon steel in demagnetization process cannot return along the original path and reach the initial state. Therefore, the magnetostrictive parameter λws which express the magnetic domain wall movement under varying stress in saturated magnetization was introduced into the magnetostriction model in the demagnetization case. The parameters of the model which control the saturated magnetic domain wall movement are extracted from the measured magnetic curves of non-oriented silicon steel sheet, which are shown in Fig. 1. III Results and discussion The simulated results are shown in Fig. 2. As shown, the time when magnetostriction reaches the maximum in the simulation is consistent with the experimental results, which shows that influence of saturated magnetic domain wall movement on magnetostrictive deformation is accurately simulated in the model.References: [1] Zhu L, Li J, Yang Q, et al. An Improved Magnetostriction Model for Electrical Steel sheet Based on Jiles-Atherton Model[J]. IEEE Transactions on Magneics, 2020, 56(3):7514604. [2] Zhang Y, Zhou H, Zhou Y. Vibration suppression of cantilever laminated composite plate with nonlinear giant magnetostrictive material layers[J]. Acta Mechanica Solida Sinica, 2015, 28(1):50-61. [3] Wang Z, Zhang Y, Ren Z, et al. Modeling of Anisotropic Magnetostriction Under DC Bias Based on an Optimized BP Neural Network[J]. IEEE Transactions on Magnetics, 2020, 56(3): 7512204

An Improved Magnetostriction Model of Silicon Steel Considering the Saturated Magnetic domain Wall Movement

Patients with schizophrenia often receive rTMS treatment, in which the dorsolateral prefrontal cortex or the primary auditory cortex and the Temporo-Parietal Junction are stimulated in order to treat negative symptoms and cognitive deficits or auditory hallucinations, respectively [1], [2]. Finite element (FE) simulations of TMS on heterogeneous head models have been conducted to mimic what might be happening electromagnetically within the brain, a comparison between clinical resting motor threshold (RMT) data and simulation data has not been published [3]. In this study, we used individualized finite element models derived from patients’ MRIs to investigate the correlation between RMT and brain anatomy. We first developed anatomically accurate head and brain models of 20 schizophrenia patient MRIs using SimNIBS pipeline. We then utilized FE analysis software to compute induced electric fields using patient’s clinical parameters during their investigational procedure as shown in Fig. 1. In this way, the simulations were based on real patient data and completely customized to each subject. The electric field induced in the brain was recorded and compared with variables such as cortex-coil distance (CCD), age, and RMT as shown in Fig 2 (a) and (b) respectively. Our results show that there is little to no correlation between the measured CCD at M1 and the clinically-reported RMT or the maximum electric field recorded in the brain after TMS was simulated using Sim4Life. Thus, we hypothesize that the lack of clear correlation between the CCD at M1 and the measured RMT suggests that there are many other variables which may be influencing an individual’s RMT, beyond the CCD. We hope the results of this study highlight key considerations that may be useful to future researchers designing methodology for studying RMT in TMS FE simulations. This project was partially funded by NSF (#1357565) and Wellcome Trust / DBT India Alliance Early Career Fellowship to U. M. Mehta (IA/E/12/1/500755)References: [1] E. Poulet, J. Brunelin, B. Bediou, R. Bation, L. Forgeard, and J. Dalery, “Slow Transcranial Magnetic Stimulation Can Rapidly Schizophrenia,” Soc. Biol. Psychiatry, pp. 95–98, 2005, doi: 10.1016/j.biopsych.2004.10.007. [2] H. He, J. Lu, L. Yang, J. Zheng, F. Gao, Y. Zhai, J. Feng, Y. Fan, and X. Ma, “Repetitive transcranial magnetic stimulation for treating the symptoms of schizophrenia: A PRISMA compliant meta-analysis,” Clin. Neurophysiol., vol. 128, no. 5, pp. 716–724, 2017, doi: 10.1016/j.clinph.2017.02.007. [3] E. G. Lee, P. Rastogi, R. L. Hadimani, D. C. Jiles, and J. A. Camprodon, “Impact of non-brain anatomy and coil orientation on inter- and intra-subject variability in TMS at midline,” Clin. Neurophysiol., vol. 0, no. 0, doi: 10.1016/J.CLINPH.2018.04.749.

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Effect of cortex-coil distance on resting motor threshold in Schizophrenia patients during transcranial magnetic stimulation INVITED

Solid walls become increasingly important when miniaturizing fluidic circuitry. They limit flow-rates achievable for a given pressure drop, and are plagued by fouling1. Approaches to reduce the wall interactions include hydrophobic coatings2, liquid-infused porous surfaces3, changing the surface electronic structure4, electrowetting5, and surface tension pinning6. A better solution may be to avoid the solid walls altogether7. Droplet microfluidics or sheath flow achieves this, but require continuous flow of both the liquid transported and the outer carrier liquid. Here we present a new approach8, where wall-less aqueous liquid channels are surrounded by an immiscible magnetic liquid, both being stabilised by a quadrupolar magnetic field. This creates self-healing, uncloggable, anti-fouling, and near-frictionless liquid-in-liquid fluidic channels with millimetre effective slip lengths, with diameters of order 10 cm, or as small as 10 µm. Pumping is achieved by moving permanent magnets that have no physical contact with the liquid channel. We show that this magnetostaltic pumping method can be used to transport whole human blood with very little damage due to shear forces; haemolysis is reduced by an order of magnitude compared to traditional peristaltic pumping. Our liquid-in-liquid approach provides new avenues to transport delicate liquids, particularly when scaling channels down to the micron scale with no need for high pressures, while retaining basic microfluidic circuitry functionalities.References: 1. R. Mukhopadhyay, Anal. Chem. 77, 429 A-432 A (2005). 2. B. Zhao, et al., Science 291, 1023–1026 (2001). 3. W. Wang, et al., Nature 559, 77 (2018). 4. E. Secchi, et al., Nature 537, 210–213 (2016). 5. K. Choi, et al., Annu. Rev. Anal. Chem. 5, 413–440 (2012). 6. E. J. Walsh, et al., Microfluidics with fluid walls. Nat. Commun. 8, 816 (2017). 7. J. M. D. Coey, et al., Proc. Natl. Acad. Sci. U.S.A. 106, 8811 (2009) 8. P. Dunne et al., Nature, 581, 58 (2020)

Liquid Flow and Control without Solid Walls INVITED

In-tissue embedded magnetic nanoparticle (MNPs) detection is one of the most requested cases for biomedical applications. We propose to use synthetic hydrogel with certain amount of MNPs. Natural tissue requires tight protocol of storage and testing but synthetic hydrogels mimic many functional properties being less demanding to test conditions. In order to make functional ferrogels (FG) widely available there is a need in the development of synthesis techniques with enhanced size of a batch: electrophysical techniques of electric explosion of the wire or laser target evaporation (LTE) ). We have developed magnetic biosensor prototype for the detection of mesoscopic distributions of nanoparticles using magnetimpedance (MI). Prototype with FeNi-based multilayered structures was designed and tested. MI responses were measured with and without polyacrylamide FG layer in order to evaluate stray fields of embedded MNPs. A model for MI response based on a solution of Maxwell equations with Landau-Lifshitz equation was developed. LTE MNPs were used for synthesis of polyacrylamide ferrogels. Their adhesive and proliferative potentials were studied. We discussed the possibility of creation of a new generation of drug delivery systems for multifunctional devices. We discussed the possibility of creation of a new generation of drug delivery systems for magnetic field assisted delivery and biosensing. This research was funded by the Russian Science Foundation, grant number 18-19-00090.References: 1. Beketov I.V. et al. AIP Adv., 2 (2012) 022154. 2. Safronov A.P. et al. AIP Adv. 3(5) (2013) 052135. 3. Kurlyandskaya G.V. et al. Appl. Phys. Lett., 106 (19) (2015) 193702. 4. Buznikov N.A. et al. Bios. Bioelectr. 117 (2018) 366. 5. Blyakhman F.A. et al. Nanomater. 9 (2019) 232.

Functional magnetic ferrogels: from biosensors to regenerative medicine INVITED

Abstract – Cutting is a necessary manufacturing technique when using silicon steel to produce electrical devices. Different cutting methods have different effects on the internal structure and magnetic properties of electrical steel sheets[1]. Laser cutting will produce thermal stress during processing, while mechanical cutting will produce plastic deformation near the cutting edge, which both lead to deterioration in the magnetic properties of the material. Therefore, studying the effect of different cutting techniques on magnetic properties is of great significance to accurately simulate and predict the iron losses of electrical equipment. The existing research methods cut the same sample into the different number of strips along the rolling direction, and these methods conclude that the cutting has a certain influence on the magnetic properties of the electrical steel sheet. But they cannot systematically compare the differences in magnetic properties and degraded range of the three cutting methods[2]. In this paper, the influence of cutting methods, such as wire cutting, laser cutting, and shear cutting on the local magnetic properties of the silicon steel sheet is studied and analyzed. The magnetic properties measurement system is shown in Fig. 1. A mobile B-H composite sensor is designed to sense the distribution of local magnetic properties near the cutting edges. The results show that different cutting methods have different effects on the spatial distribution of magnetic flux and the corresponding B-H curves. With the increase of the distance from the cutting edge, the degree of magnetic degradation decreases gradually. Two mathematical models used to simulate the cutting edge effect by the finite element simulation can also better describe the magnetization curve of the electrical steel sheet damage trend, thus providing a model basis for the application of electrical equipment under actual working conditions.References: [1] G. Loisos, A. J,Moses,Journal of Materials Processing Tech., vol. 161, p. 151-155(2005) [2] A. Saleem, N. Alatawneh, R. R. Chromik and D. A. Lowther, IEEE Transactions on Magnetics., vol. 52, no. 5, p. 1-4(2016)

Magnetic Properties Measurement and Simulation of Electrical Steel Sheet under Cutting Influence

Some recent nondestructive testing methods have been developed to detect very small variations in the magnetic field surrounding a massive ferromagnetic structure, such as a tank or pipe [1]. In particular, the detection of sinking in buried pipelines becomes possible [2]. The sinking is characterized by local plastic deformation and the creation of long range residual stresses. These two elements are known to have a considerable influence on the magnetic behavior [3,4,5]. One of the keys to detection is the substantial modification of the remanent magnetization of the material. The study material is a two-phase ferrito-pearlitic steel. Strips are subjected to an incremental tensile plastic deformation interspersed with elastic unloading. The magnetic behavior is carried out along the tensile direction at different levels of applied stress after deformation. The figure below shows the typical evolution of the remanent magnetization. The figure highlights: (i) that the remanent magnetization increases with the applied stress to a maximum value then decreases; (ii) that the plastic strain at zero stress considerably reduces the remanent magnetization in a highly non-linear manner; (iii) that the behavior of the deformed material seems to be able to be obtained by a simple translation in the stress space of the behavior at the undeformed state. These results join some former results [6] and the interpretation of the effect of plastic deformations by Hubert & Lazreg [7]. Following this work, a magneto-elastic two-phase modeling of the magnetization is proposed. Plasticity is introduced as an internal stress state inherent with the plastic deformation of the two-phase material (so-called kinematic hardening). The associated mechanical state being multiaxial, an equivalent uniaxial state can be calculated, requiring the use of a new material coefficient making it possible to consider the effect of the pearlitic phase on the average behavior of the medium. It is shown that the translation in the stress space predicted by the model is consistent with the experimental values.References: [1] international patent CA2998095A1 [2] E. A. Fnaiech, M.Munschy, S. Corbineau, M. Marzin, P. Rohart, S. Takillah, “Large stand-off magnetometry (LSM) for buried pipeline inspection: Influence of dent depth on residual magnetic signal “, Pipeline Technology Conference, Berlin (2020) [3] R.M. Bozorth, Ferromagnetism, Wiley-IEEE press, (1993) [4] J.M. Makar, B.K. Tanner, J. Magn. Magn. Mater. 184, p.193 (1998) [5] O. Hubert, M. Clavel, I. Guillot, E. Hug, Jal Phys. IV, 9, p.207 (1999) [6] V.E. Iordache, E. Hug, N. Buiron, Mater. Sci. Eng. A 359, p.62 (2003) [7] O. Hubert, S. Lazreg, Journal of Magnetism and Magnetic Materials, 424 2, p.421 (2017)

Effect of plastic straining on the remanent magnetization of ferrite-pearlitic steel: experimental and modeling aspects

Magnetic flux leakage (MFL) is a widely used non-destructive method for the detection of defects and abnormalities in magnetic structures such as oil and gas steel tubes for health and condition monitoring [1]. MFL involves the application of a magnetizing field in close proximity to the inspected magnetic medium and measuring the resulting leakage magnetic fields from defects, which are key for the detection and characterization of defects. To understand the correlation between the measured fields and physical defects dimensions, leakage fields are conventionally modeled for simple defect shapes (such as rectangles [2] or cylinders [3,4]) using magnetic charge sheets representing the inner surfaces of the defect. This approach assumes uniform magnetic charges through the defect and ignores nonlinear saturation effects in the corners which makes characterization and sizing of defects from measured field distributions difficult and inaccurate. Frequency domain analysis of leakage fields in MFL provide an alternative and less explored method for characterization of defects. The spectrum of the leakage magnetic fields in MFL was recently derived for rectangular defects based on magnetic charge sheets [5,6]. This approach revealed spectral features that potentially enable more accurate sizing of defects from measured MFL signals compared to direct analysis of spatial field distributions. In this work the Fourier transforms of the leakage magnetic fields from rectangular and tilted two-dimensional defects are analytically derived using scalar magnetic potential theory and superposition [7,8]. This approach does not assume uniform magnetic charges through the defect surfaces. The scalar magnetic potential approach yielded closer agreement to more detailed finite-element calculations and published measurements, and used to assess the sensitivity and feasibility of the spectral sizing method for different defect geometries.References: [1] D. E. Bray and R. K. Stanley, Nondestructive Evaluation, Part IV: Magnetic Flux Leakage Techniques in Nondestructive Evaluation, Florida: CRC Press (1997). [2] N. Zatsepin and V. Shcherbinin, Defektoskopiya 5, 50 (1966). [3] C. Mandache and L. Clapham, J. Phys. D: Appl. Phys. 36, 2427 (2003). [4] S. M. Dutta, F. H. Ghorbel, and R. K. Stanley, IEEE Trans. Magn. 45, 1959 (2009). [5] Li E, Kang Y, Tang J, Wu J, and Yan X, IEEE Trans. Magn. 54, 1 (2018). [6] M. M. Aziz, R. Abdulla, and M. Al-Dujaili, IEEE Mag. Lett. 10, 2102404 (2019). [7] M. M. Aziz, A. Edress, and C. D. Wright, IEEE Trans. Magn. 52, 3300712 (2016). [8] D. A. Lindholm, IEEE Trans. Magn. 12, 710 (1976). 

Magnetic Field Spectra and Sizing of Defects in Magnetic Flux Leakage Inspection

The noise produced by power transformers and electrical machines is harmful and its reduction is the hot subject in continuous research. Such systems are likely to be in resonance and become more vociferous, and the resonance may be mechanical or magnetic forces. The interaction between deformation due to magnetostriction and mechanical resonance of a structure made up of laminated steel sheets is investigated in this paper. The resonance phenomena are generally studied and analyzed by considering that frequency and spatial distribution of electromagnetic forces coincide with natural frequency and modes shapes of the corresponding structure. It is observed that magnetostriction may induce a resonance without the need to combine these two conditions. Two closed sheets structures of frame shape and ring shape consisting of cold-rolled grain-oriented (GO) and non-grain oriented (NO) electrical steels are used to confirm this assumption. Finite element (FE) calculations and measurements are made and compared with vibration displacements. Results of mechanical resonance induced by the magnetostrictive strain from ferromagnetic materials are shown, as well as the corresponding vibration spectrums. CONTENT: This paper presents a complete study on magnetostriction induced resonance from mechanical study to resonance detection. In Section II, the studied structure is described. In Section III, a comparison between Maxwell stresses and magnetostrictive strains is introduced and results of simulation are discussed. In Section IV, a complete study of mechanical properties of structure is presented and comparison between experimental and modeling results is described. In Section V, the summary of mechanical resonance due to magnetostriction is detailed. CONCLUSION: This paper has demonstrated that magnetostriction deformation can be implicated in mechanical resonance of a laminated structure and should be considered at the design stage for cold-rolled GO and NO electrical materials or any magnetostrictive materials grade.References: [1] K. Fonteyn, A. Belahcen, R. Kouhia, et al, “FEM for directly coupled magneto-mechanical phenomena in electrical machines,” IEEE Trans. Magn., vol. 46, no. 8, pp. 2923-2926, Aug. 2010. [2] U. Aydin, et al., “Magneto-mechanical modeling of electrical steel sheets,” J. Magn. Magn. Mater., vol. 439, pp. 82-90, Oct. 2017. [3] M. Liu, et al., “Reduction of power transformer core noise generation due to magnetostriction-induced deformations using fully coupled finite element modeling optimization procedures,” IEEE Trans. Magn., vol. 53, no. 8, Aug. 2017, Art. no. 8400511. [4] S. Somkun, A. J. Moses, and P. I. Anderson, “Mechanical resonance in nonoriented electrical steels induced by magnetostriction under PWM voltage excitation,” IEEE Trans. Magn., vol. 44, no. 11, pp. 4062-4065, Nov. 2008.

Study of Mechanical Resonance Induced by Magnetostriction in Closed Structures Based on Fe-Si

In the eddy current testing (ECT), a coil carrying alternating current is used to induce eddy current in the test object and/or collect signals. The resistance and reactance of the coil change with frequency because of skin and proximity effects in the winding. There is also stray capacitance between the wires. The coil resonates at a particular frequency. For conventional ECT, the coil normally operates far below its self-resonant frequency, the capacitance is negligible; the resistance and reactance are considered to be frequency-invariant. An ECT coil is practically modelled by a serially connected resistance and reactance without taking into account the eddy current effect in the coil itself. In last decades, the range of ECT application is expanded, together with widening of operating frequency. Probes working at extremely high and low frequencies have been developed. On the other hand, the conventional ECT coil is explored anew in ‘unconventional’ frequency range. Nevertheless, in-depth understanding of a coil’s frequency characteristic is essential. As the first trial, we studied a simple air-cored coil’s frequency characteristics and apply it to exam conductivity change. The signals were attained from sweep frequency eddy current testing [1], analyzed based on lumped element circuit model, together with simplified analytical and numerical analysis. Fig. 1 shows the impedances of the coil itself, the coil on test pieces of conductivity AISC 100.98%, 57.71% and 19.70%, respectively. Different resonant frequency and impedance-at-resonant correspond to different conductivity. For signals taken far below the resonant frequency, the local minimum of normalized resistance [1] (enclosed by ellipse in Fig. 2) also indicates conductivity change. All the indicators appear at frequencies that the effect of the test piece’s thickness is cut to minimum. Acknowledgement: This work was partially supported by JSPS KAKENHI Grant Number JP20k05000.References: Weiying Cheng, Thickness Measurement of Metal Plates Using Swept-Frequency Eddy Current Testing and Impedance Normalization, IEEE Sensors Journal, July 15, 2017, Vol.17, No.14, pp.4558-4569, DOI: 10.1109/JSEN.2017.2710356

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Domain Structure and Energy Losses up to 10 kHz in Grain-Oriented Fe-Si Sheets

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