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15 pages, 5995 KiB  
Article
Conformational Analysis of Uniformly 13C-Labeled Peptides by Rotationally Selected 13Cα-13CH3 Double-Quantum Solid-State NMR
by David Middleton
Molecules 2025, 30(3), 739; https://doi.org/10.3390/molecules30030739 - 6 Feb 2025
Viewed by 422
Abstract
Peptides are an important class of biomolecules that perform many physiological functions and which occupy a significant and increasing share of the pharmaceutical market. Methods to determine the solid-state structures of peptides in different environments are important to help understand their biological functions [...] Read more.
Peptides are an important class of biomolecules that perform many physiological functions and which occupy a significant and increasing share of the pharmaceutical market. Methods to determine the solid-state structures of peptides in different environments are important to help understand their biological functions and to aid the development of drug formulations. Here, a new magic-angle spinning (MAS) solid-state nuclear magnetic resonance (SSNMR) approach is described for the structural analysis of uniformly 13C-labeled solid peptides. Double-quantum (DQ) coherence between selective pairs of 13C nuclei in peptide backbone and side-chain CH3 groups is excited to provide restraints on (i) 13C–13C internuclear distances and (ii) the relative orientations of C–H bonds. DQ coherence is selected by adjusting the MAS frequency to the difference in the resonance frequencies of selected nuclear pairs (the rotational resonance condition), which reintroduces the dipolar coupling between the nuclei. Interatomic distances are then measured using a constant time SSNMR experiment to eliminate uncertainties arising from relaxation effects. Further, the relative orientations of C–H bond vectors are determined using a DQ heteronuclear local field SSNMR experiment, employing 13C–1H coupling amplification to increase sensitivity. These methods are applied to determine the molecular conformation of a uniformly 13C-labeled peptide, N-formyl-l-methionyl-l-leucyl-l-phenylalanine (fMLF). From just six distance and six angular restraints, two possible molecular conformations are determined, one of which is in excellent agreement with the crystal structure of a closely related peptide. The method is envisaged to a useful addition to the SSNMR repertoire for the solid-state structure determination of peptides in a variety of forms, including amyloid fibrils and pharmaceutical formulations. Full article
(This article belongs to the Section Chemical Biology)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>(<b>a</b>) Chemical structure of the fMLF peptide. Filled circles denote Cα (blue) and CH<sub>3</sub> (orange) sites that were <sup>13</sup>C–<sup>13</sup>C dipolar recoupled at rotational resonance. (<b>b</b>) Pulse sequence of the 2D <sup>13</sup>C–<sup>13</sup>C DQSQRR experiment. All filled rectangles represent π/2 pulses. Signal is acquired over an 8-step phase cycle, with pulse phases ϕ<sub>1</sub> = −y; ϕ<sub>2</sub> = +x; ϕ<sub>3</sub> = +x; ϕ<sub>4</sub> = +x; ϕ<sub>5</sub> = +x; ϕ<sub>6</sub> = +y; ϕ<sub>7</sub> = +x +y − x − y; ϕ<sub>8</sub> = +y − x − y + x; ϕ<sub>9</sub> = +x +x +x +x − x − x − x − x. The receiver phase ϕ<sub>rec</sub> = +x +y − x − x − x − y +x + y. (<b>c</b>) One-dimensional <sup>13</sup>C CP-MAS NMR spectrum of [U-<sup>13</sup>C,<sup>15</sup>N]fMLF showing Cα and aliphatic side-chain resonances only. (<b>d</b>) Two-dimensional <sup>13</sup>C–<sup>13</sup>C DQSQRR spectra obtained using the pulse sequence in <a href="#molecules-30-00739-f001" class="html-fig">Figure 1</a>b at MAS frequencies corresponding to the exact <span class="html-italic">n</span> = 1 rotational resonance condition with respect to Met Cα–Leu Cδ’ (5562 Hz), Met Cα–Met Cε (6642 Hz), Phe Cα–Met Cε (7078 Hz) and Leu Cα–Met Cα (7551 Hz). Note the shorthand: Lα, etc., refers to Leu Cα, etc. At ν<sub>R</sub> = 6642 Hz, the chemical shift difference for Lα and Lδ’ is only 91 Hz away from <span class="html-italic">n</span> = 1 rotational resonance and therefore dipolar recoupling of these nuclear sites is observed. Arrows denote the carrier frequency. The ZQ excitation time, <span class="html-italic">t</span><sub>ex</sub>, is 4 ms for each spectrum. Green and blue contours represent positive and negative intensities, respectively.</p>
Full article ">Figure 2
<p>The basis of the 1D DQRR experiments for selective measurement of <sup>13</sup>C–<sup>13</sup>C distances and <sup>13</sup>C–<sup>1</sup>H bond orientations. (<b>a</b>) Basic pulse sequence. Phase cycling (ϕ<sub>1</sub>–ϕ<sub>9</sub>, ϕ<sub>rec</sub>) is as described in <a href="#molecules-30-00739-f001" class="html-fig">Figure 1</a>b. FSLG = frequency-switched Lee–Goldburg sequence for <sup>1</sup>H–<sup>1</sup>H decoupling. (<b>b</b>) How the difference intensity is measured from the observed NMR spectrum. (<b>c</b>) At <span class="html-italic">n</span> = 1 RR, dipolar interactions are recoupled between pairs of <sup>13</sup>C nuclei if the separation is less than ~7 Å. In the DQRR-CC experiment, the difference intensity is modulated by varying <span class="html-italic">t</span><sub>ex</sub> and <span class="html-italic">t</span><sub>rec</sub>. (<b>d</b>) In the DQRR-HLF experiment, t<sub>ev</sub> is varied and the difference intensities are modulated according to the relative orientations of pairs of <sup>13</sup>C–<sup>1</sup>H bonds (defined by angles θ<sub>1</sub>, θ<sub>2</sub> and θ<sub>3</sub>).</p>
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<p>Determination of the Leu Cα–Met CεH<sub>3</sub> relative orientations and <sup>13</sup>Cα–<sup>13</sup>Cε distance in solid [U-<sup>13</sup>C,<sup>15</sup>N]fMLF. The MAS frequency was set to the <span class="html-italic">n</span> = 1 RR condition for Leu Cα and Met Cε (ν<sub>R</sub> = 7551 Hz). (<b>a</b>) Series of spectra obtained in the CT-DQRR-CC experiment by varying <span class="html-italic">t</span><sub>ex</sub> and <span class="html-italic">t</span><sub>rec</sub>. (<b>b</b>) Difference intensities (filled circles) measured from the spectra in (<b>a</b>) and simulated curves for different internuclear distances, <span class="html-italic">r</span><sub>CC</sub>. Error bars represent the level of the noise. (<b>c</b>) Series of spectra obtained using the DQRR-HLF experiment, by varying <span class="html-italic">t</span><sub>ev</sub> up to the duration of one rotor cycle, <span class="html-italic">t</span><sub>R</sub>, and maintaining <span class="html-italic">t</span><sub>ex</sub> and <span class="html-italic">t</span><sub>rec</sub> at 4 ms. The top spectra were obtained without dipolar amplification using the pulse sequence in <a href="#molecules-30-00739-f002" class="html-fig">Figure 2</a>a, and the bottom spectra were obtained with dipolar amplification using the pulse sequence in <a href="#app1-molecules-30-00739" class="html-app">Figure S5</a>. (<b>d</b>) DQ evolution over one rotor cycle. Filled circles denote the DQ-filtered difference intensities measured from the amplified and unamplified experiments. The line of best fit (dotted line) is shown on the amplified data set. The red shaded areas bounded by the solid lines represent the range of variability of the difference intensities to all possible C–H and CH<sub>3</sub> orientations.</p>
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<p>Conformational analysis of fMLF from the DQRR distance and angle restraints. (<b>a</b>) An unrestrained random structure of fMLF, highlighting the 6 selective <sup>13</sup>C–<sup>13</sup>C DQ coherences forming the basis for the structural restraints. (<b>b</b>) Combinations of peptide side-chain and main-chain torsional angles 1–8 that are consistent with the 6 distance restraints only. Connecting lines represent individual peptide conformations. The torsional angle numbers are defined in <a href="#app1-molecules-30-00739" class="html-app">Figure S9</a> and explained in <a href="#app1-molecules-30-00739" class="html-app">Table S3</a>. Angles 9 and 10 are omitted for clarity. (<b>c</b>) Combinations of peptide torsional angles that are consistent with all restraints (see also <a href="#molecules-30-00739-t002" class="html-table">Table 2</a>). Two conformations are represented by triangles (conformer 1) and circles (conformer 2). (<b>d</b>) Peptide molecular conformations (conformer 1 and conformer 2) corresponding to the restrained torsional angles in (<b>c</b>) and <a href="#molecules-30-00739-t002" class="html-table">Table 2</a>. (<b>e</b>) Molecular conformations of fMLF determined previously from SSNMR restraints (PDB 1Q7O). (<b>f</b>) Molecular conformation of C-terminal methoxy fMLF [<a href="#B28-molecules-30-00739" class="html-bibr">28</a>].</p>
Full article ">Figure 5
<p>Preliminary SSNMR analysis of the peptide [U-<sup>13</sup>C-FVA]Med43-50. (<b>a</b>) Negative-stain TEM image of the peptide fibrils. (<b>b</b>) Two-dimensional DQSQRR SSNMR spectrum of the peptide fibrils at a MAS frequency of 7250 Hz, which is close to, but does not correspond exactly to, the <span class="html-italic">n</span> = 1 RR condition for any pair of observed nuclei. The red arrow signifies the spectrometer carrier frequency. The doubling of resonances (Aα, A’α, Aβ, A’β, etc.) is attributed to the polymorphism of the fibrils.</p>
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22 pages, 8086 KiB  
Article
Research on Structural Optimization and Excitation Control Method Using a Two-Dimensional OWPT System for Capsule Robots Based on Non-Equivalent Coils
by Wenwei Li, Pingping Jiang, Zhiwu Wang and Guozheng Yan
Micromachines 2024, 15(12), 1510; https://doi.org/10.3390/mi15121510 - 19 Dec 2024
Viewed by 630
Abstract
The rapid development of wireless power transfer (WPT) technology has provided new avenues for supplying continuous and stable power to capsule robots. In this article, we propose a two-dimensional omnidirectional wireless power transfer (OWPT) system, which enables power to be transmitted effectively in [...] Read more.
The rapid development of wireless power transfer (WPT) technology has provided new avenues for supplying continuous and stable power to capsule robots. In this article, we propose a two-dimensional omnidirectional wireless power transfer (OWPT) system, which enables power to be transmitted effectively in multiple spatial directions. This system features a three-dimensional transmitting structure with a Helmholtz coil and saddle coil pairs, combined with a one-dimensional receiving structure. This design provides sufficient internal space, accommodating patients of various body types. Based on the magnetic field calculation and finite element analysis, the saddle coil structure is optimized to enhance magnetic field uniformity; to achieve a two-dimensional rotating magnetic field, a phase difference control method for the excitation signal is developed through the analysis of circuit topology and quantitative synthesis of non-equivalent magnetic field vectors. Finally, an experimental prototype is built, and the experimental results show that the one-dimensional transmitting coil achieves a minimum received voltage stability of 94.5% across different positions. When the three-dimensional transmitting coils operate together, a two-dimensional rotating magnetic field in the plane is achieved at the origin, providing a minimum received power of 550 mW with a voltage fluctuation rate of 7.68%. Full article
(This article belongs to the Section B:Biology and Biomedicine)
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Figure 1

Figure 1
<p>Framework of the proposed OWPT system.</p>
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<p>3D model (<b>a</b>,<b>b</b>) and simplified wireframe (<b>c</b>) of the coils.</p>
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<p>Excitation current definitions of (<b>a</b>) the Helmholtz coil and (<b>b</b>) the saddle coil.</p>
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<p><math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>S</mi> <mi>C</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mi>γ</mi> </semantics></math> at different <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> </mrow> </semantics></math>.</p>
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<p>Quality factor of saddle coil pair versus frequency and number of turns.</p>
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<p>Self-inductance and internal resistance versus frequency.</p>
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<p>Three-phase S-S topology.</p>
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<p>Timing diagram of excitation signal.</p>
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<p>Equivalent decoupled circuit.</p>
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<p>Prototype of the proposed OWPT system.</p>
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<p>Magnetic field trajectory at the origin.</p>
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<p>Magnetic field distribution of HC1 (<b>left</b>) and SC3 (<b>right</b>) at a different time instant. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>5</mn> <mi>π</mi> </mrow> <mn>6</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mi>π</mi> </mrow> </semantics></math>. (<b>g</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>7</mn> <mi>π</mi> </mrow> <mn>6</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>i</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>3</mn> <mi>π</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>j</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>5</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>k</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>11</mn> <mi>π</mi> </mrow> <mn>6</mn> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>l</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mi>t</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> </mrow> </semantics></math>.</p>
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<p>Spatial distribution of the received voltage and power of (<b>a</b>) HC1; (<b>b</b>) SC2; and (<b>c</b>) SC3.</p>
Full article ">Figure 13 Cont.
<p>Spatial distribution of the received voltage and power of (<b>a</b>) HC1; (<b>b</b>) SC2; and (<b>c</b>) SC3.</p>
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<p>Distribution of power transfer efficiency at different locations of (<b>a</b>) HC1; (<b>b</b>) SC2; and (<b>c</b>) SC3.</p>
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<p>Received voltage (<b>a</b>) and power transfer efficiency (<b>b</b>) at different attitudes.</p>
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<p>Schematic diagram of PRC rotation.</p>
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<p><math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>R</mi> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>P</mi> <mi>R</mi> </msub> </mrow> </semantics></math> (<b>a</b>) and <math display="inline"><semantics> <mi>η</mi> </semantics></math> (<b>b</b>) at different <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mover accent="true"> <mi>n</mi> <mo>→</mo> </mover> </msub> </mrow> </semantics></math>.</p>
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18 pages, 15800 KiB  
Article
Research on Precise Attitude Measurement Technology for Satellite Extension Booms Based on the Star Tracker
by Peng Sang, Wenbo Liu, Yang Cao, Hongbo Xue and Baoquan Li
Sensors 2024, 24(20), 6671; https://doi.org/10.3390/s24206671 - 16 Oct 2024
Viewed by 1086
Abstract
This paper reports the successful application of a self-developed, miniaturized, low-power nano-star tracker for precise attitude measurement of a 5-m-long satellite extension boom. Such extension booms are widely used in space science missions to extend and support payloads like magnetometers. The nano-star tracker, [...] Read more.
This paper reports the successful application of a self-developed, miniaturized, low-power nano-star tracker for precise attitude measurement of a 5-m-long satellite extension boom. Such extension booms are widely used in space science missions to extend and support payloads like magnetometers. The nano-star tracker, based on a CMOS image sensor, weighs 150 g (including the baffle), has a total power consumption of approximately 0.85 W, and achieves a pointing accuracy of about 5 arcseconds. It is paired with a low-cost, commercial lens and utilizes automated calibration techniques for measurement correction of the collected data. This system has been successfully applied to the precise attitude measurement of the 5-m magnetometer boom on the Chinese Advanced Space Technology Demonstration Satellite (SATech-01). Analysis of the in-orbit measurement data shows that within shadowed regions, the extension boom remains stable relative to the satellite, with a standard deviation of 30′′ (1σ). The average Euler angles for the “X-Y-Z” rotation sequence from the extension boom to the satellite are [−89.49°, 0.08°, 90.11°]. In the transition zone from shadow to sunlight, influenced by vibrations and thermal factors during satellite attitude adjustments, the maximum angular fluctuation of the extension boom relative to the satellite is approximately ±2°. These data and the accuracy of the measurements can effectively correct magnetic field vector measurements. Full article
(This article belongs to the Section Remote Sensors)
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Figure 1
<p>Self-developed nano-star tracker.</p>
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<p>Electronic functional block diagram of the star tracker.</p>
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<p>Photograph of a star tracker circuit board.</p>
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<p>Schematic diagram of the multi-tasking pipeline of the star tracker.</p>
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<p>Application layer software thread of the star tracker.</p>
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<p>Composition of automatic calibration system for star tracker.</p>
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<p>Actual picture of the star tracker calibration device: (<b>a</b>) overall view; (<b>b</b>) working state.</p>
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<p>The process diagram of residual calibration: (<b>a</b>) image of the marked star points; (<b>b</b>) calibration residual diagram.</p>
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<p>Static multi-satellite simulator experimental test diagram: (<b>a</b>) the static multi-satellite simulation test device; (<b>b</b>) the test results.</p>
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<p>Ground test diagram: (<b>a</b>) the joint field stargazing experiment device of the probe assembly; (<b>b</b>) measurement results of the star tracker, where Q1, Q2, Q3, and Q4 represent the tracker’s output attitude quaternions.</p>
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<p>Measured star point image data of 100 ms exposure of star tracker—“Casiopeia”: (<b>a</b>) image collected by the star sensor; (<b>b</b>) the star point data analyzed in the software, which corresponds one-to-one with the identified stars; (<b>c</b>) starry sky image of the “Cassiopeia” position in the Stellarium software (v1.28).</p>
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<p>Remanence test experiment.</p>
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<p>Assembly diagram of the star tracker on the Chinese Advanced Space Technology Demonstration Satellite: (<b>a</b>) the probe assembly on the extension boom, with the red light shield covering the precise attitude measurement component of the nanosatellite star tracker developed in this study; (<b>b</b>) assembly diagram of the star tracker and extension rod structure on the entire satellite; (<b>c</b>) the coordinate system relationships of the satellite’s extension boom, where the satellite platform’s boom base is defined as the <span class="html-italic">XY</span> plane and the boom’s extension direction is defined as the <span class="html-italic">Z</span>-axis.</p>
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<p>Conversion Euler angles from NST system by the star tracker to satellite system, the time range of the data in the figure is UTC: 13 February 2023 9:09:10 to 12:05:50.</p>
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<p>Quaternions collected by the star tracker: (<b>a</b>) data sourced from the star tracker mounted on the satellite body; (<b>b</b>) data sourced from the star tracker on the extension boom. The time range of the data in the figure is UTC: 13 February 2023 9:09:10 to 12:05:50.</p>
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8 pages, 534 KiB  
Review
IXPE Observations of Magnetar Sources
by Roberto Turolla, Roberto Taverna, Silvia Zane and Jeremy Heyl
Galaxies 2024, 12(5), 53; https://doi.org/10.3390/galaxies12050053 - 18 Sep 2024
Cited by 1 | Viewed by 938
Abstract
Among the more than 60 sources observed in the first two years of operations, IXPE addressed four magnetars, neutron stars believed to host ultra-strong magnetic fields. We report here the main implication coming from IXPE measurements for the physics of magnetars. Polarimetric observations [...] Read more.
Among the more than 60 sources observed in the first two years of operations, IXPE addressed four magnetars, neutron stars believed to host ultra-strong magnetic fields. We report here the main implication coming from IXPE measurements for the physics of magnetars. Polarimetric observations confirmed the expectations of high polarization degrees, up to ≈80%, values which have not been detected in any other source so far, providing further proof (independent from the P-P˙ estimate) that magnetars host indeed ultra-magnetized neutron stars. Polarization measurements also indicate that softer X-rays likely come from surface regions where the overlying atmosphere underwent magnetic condensation. The agreement of the phase-dependent polarization angle with a simple rotating vector model strongly supports the presence of vacuum birefringence around the star. Full article
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Figure 1

Figure 1
<p>(<b>Left</b>) PD and PA (crosses with <math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> confidence contours) observed by <span class="html-italic">IXPE</span> for the AXP 4U 0142+61, as a function of photon energy and integrated over the rotational phase. Stars mark the simulated values of PD and PA obtained assuming thermal emission from an equatorial belt on the magnetar condensed surface reprocessed by RCS. Figure taken from [<a href="#B27-galaxies-12-00053" class="html-bibr">27</a>]. (<b>Right</b>) same for the AXP 1RXS J1708. Orange stars and green crosses report the simulated PD and PA for model A and model B, respectively (see text for details). Figure taken from [<a href="#B31-galaxies-12-00053" class="html-bibr">31</a>].</p>
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<p>(<b>Left</b>) PD and PA (crosses with <math display="inline"><semantics> <mrow> <mn>68.3</mn> <mo>%</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>99</mn> <mo>%</mo> </mrow> </semantics></math> confidence contours, respectively) measured by <span class="html-italic">IXPE</span> for SGR 1806−20 as a function of the photon energy, by averaging on the rotational phase. Figure taken from [<a href="#B41-galaxies-12-00053" class="html-bibr">41</a>]. (<b>Right</b>) count rate (panel <b>A</b>) and phase-resolved PD (panel <b>B</b>), and PA (panel <b>C</b>), energy-integrated over the <span class="html-italic">IXPE</span> band (filled circles) for AXP 1E 2259+586. In Panel <b>A</b>, the solid curve marks the <math display="inline"><semantics> <mrow> <mn>0.3</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mn>12</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>-integrated pulse profile as resulted from a 2014 observation by <span class="html-italic">XMM-Newton</span> [<a href="#B43-galaxies-12-00053" class="html-bibr">43</a>]. In Panel <b>B</b>, the solid curve marks, instead, the <math display="inline"><semantics> <msub> <mi>MDP</mi> <mn>99</mn> </msub> </semantics></math>. Finally, in Panel <b>C</b>, the curves show the best RVM fits with (dashed) and without (solid), considering a <math display="inline"><semantics> <msup> <mn>90</mn> <mo>∘</mo> </msup> </semantics></math> swing of PA during rotation; the green vertical lines mark the different phase intervals used in the analysis. Figure taken from [<a href="#B44-galaxies-12-00053" class="html-bibr">44</a>].</p>
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10 pages, 1034 KiB  
Review
X-ray Polarization of Blazars and Radio Galaxies Measured by the Imaging X-ray Polarimetry Explorer
by Alan P. Marscher, Laura Di Gesu, Svetlana G. Jorstad, Dawoon E. Kim, Ioannis Liodakis, Riccardo Middei and Fabrizio Tavecchio
Galaxies 2024, 12(4), 50; https://doi.org/10.3390/galaxies12040050 - 22 Aug 2024
Cited by 3 | Viewed by 1257
Abstract
X-ray polarization, which now can be measured by the Imaging X-ray Polarimetry Explorer (IXPE), is a new probe of jets in the supermassive black hole systems of active galactic nuclei (AGNs). Here, we summarize IXPE observations of radio-loud AGNs that have been published [...] Read more.
X-ray polarization, which now can be measured by the Imaging X-ray Polarimetry Explorer (IXPE), is a new probe of jets in the supermassive black hole systems of active galactic nuclei (AGNs). Here, we summarize IXPE observations of radio-loud AGNs that have been published thus far. Blazars with synchrotron spectral energy distributions (SEDs) that peak at X-ray energies are routinely detected. The degree of X-ray polarization is considerably higher than at longer wavelengths. This is readily explained by energy stratification of the emission regions when electrons lose energy via radiation as they propagate away from the sites of particle acceleration as predicted in shock models. However, the 2–8 keV polarization electric vector is not always aligned with the jet direction as one would expect unless the shock is oblique. Magnetic reconnection may provide an alternative explanation. The rotation of the polarization vector in Mrk421 suggests the presence of a helical magnetic field in the jet. In blazars with lower-frequency peaks and the radio galaxy Centaurus A, the non-detection of X-ray polarization by IXPE constrains the X-ray emission mechanism. Full article
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<p>Sketch of the spectral energy distribution of a blazar for three different values of the peak frequency of the synchrotron emission.</p>
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<p>Sketch (not drawn to scale) of the structure of the magnetic field lines and frequency structure of turbulent plasma flowing across a shock front. The shock could be either stationary or moving down the jet.</p>
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18 pages, 7635 KiB  
Article
A Novel Approach for Evaluating the Influence of Texture Intensities on the First Magnetization Curve and Hysteresis Loss in Fe–Si Alloys
by Daniele Carosi, Alessandro Morri, Lorella Ceschini and Alessandro Ferraiuolo
Materials 2024, 17(16), 3969; https://doi.org/10.3390/ma17163969 - 9 Aug 2024
Viewed by 1459
Abstract
This paper examines the relationship between the magnetization behavior and crystal lattice orientations of Fe–Si alloys intended for magnetic applications. A novel approach is introduced to assess anisotropy of the magnetic losses and first magnetization curves. This method links the magnetocrystalline anisotropy energy [...] Read more.
This paper examines the relationship between the magnetization behavior and crystal lattice orientations of Fe–Si alloys intended for magnetic applications. A novel approach is introduced to assess anisotropy of the magnetic losses and first magnetization curves. This method links the magnetocrystalline anisotropy energy of single crystal structures to the textures of polycrystalline materials through a vectorial space description of the crystal unit cell, incorporating vectors for external applied field and saturation magnetization. This study provides a preliminary understanding of how texture influences magnetic loss rates and the first magnetization curves. Experimental results from Electron Back-Scattered Diffraction (EBSD) and Single-Sheet Tests (SSTs), combined with energy considerations and mathematical modeling, reveal the following key findings: (i) a higher density of cubic texture components, whether aligned or rotated relative to the rolling direction, decreases magnetic anisotropy, suggesting that optimizing cubic texture can enhance material performance; (ii) at high magnetic fields, there is no straightforward correlation between energy losses and polarization; and (iii) magnetization rates significantly impact magnetization loss rates, highlighting the importance of considering these rates in optimizing Fe–Si sheet manufacturing processes. These findings offer valuable insights for improving the manufacturing and performance of Fe–Si sheets, emphasizing the need for further exploration of texture effects on magnetic behavior. Full article
(This article belongs to the Special Issue Feature Papers in Materials Physics (2nd Edition))
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<p>Conceptual map of the paper’s work.</p>
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<p>Magnetic polarization J vs. external applied magnetic field H and “knee region” highlighted.</p>
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<p>Magnetic characterization experimental energy loss <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> vs. external applied magnetic field H: energy losses along RD (<b>a</b>) and TD (<b>b</b>). The colors are related to the behavior of: L1—blue; L2—orange; and L3—yellow.</p>
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<p>Magnetic characterization experimental energy loss <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> vs. external applied magnetic field H: energy losses along RD (blue) and TD (orange). The figures are related to: (<b>a</b>) L1; (<b>b</b>) L2; and (<b>c</b>) L3.</p>
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<p>Magnetic characterization polarization J vs. external applied magnetic field H: first magnetization curves along RD (<b>a</b>) and TD (<b>b</b>). The colors are related to the behavior of: L1—blue; L2—orange; and L3—yellow.</p>
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<p>Magnetic characterization polarization J vs. external applied magnetic field H: first magnetization curves of L1 (<b>a</b>); L2 (<b>b</b>); and L3 (<b>c</b>) along RD (blue) and TD (orange).</p>
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<p>Orientations reconstruction of sheets, micrometric notch of 25 μm: (<b>a</b>) L1; (<b>b</b>) L2; (<b>c</b>) L3; (<b>d1</b>) the coordinate system of the orientation map; (<b>d2</b>) the sheet reference frame; (<b>d3</b>) the fixed specimen reference frame for the orientation analyses; and (<b>d4</b>) the IPF colorkey map.</p>
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<p>Fitted curves of experimental data of magnetic energy loss <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>f</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> vs. external applied magnetic field H along RD (<b>a</b>) and TD (<b>b</b>). The colors are related to the behavior of: L1—blue; L2—orange; and L3—yellow.</p>
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<p>Fitted curves of experimental data of magnetic energy loss <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>f</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> vs. external applied magnetic field H along RD (blue) and TD (orange). The figures are related to: (<b>a</b>) L1; (<b>b</b>) L2; and (<b>c</b>) L3.</p>
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14 pages, 1795 KiB  
Review
X-ray Polarimetry of X-ray Pulsars
by Juri Poutanen, Sergey S. Tsygankov and Sofia V. Forsblom
Galaxies 2024, 12(4), 46; https://doi.org/10.3390/galaxies12040046 - 7 Aug 2024
Cited by 5 | Viewed by 1140
Abstract
Radiation from X-ray pulsars (XRPs) was expected to be strongly linearly polarized owing to a large difference in their ordinary and extraordinary mode opacities. The launch of IXPE allowed us to check this prediction. IXPE observed a dozen X-ray pulsars, discovering pulse-phase dependent [...] Read more.
Radiation from X-ray pulsars (XRPs) was expected to be strongly linearly polarized owing to a large difference in their ordinary and extraordinary mode opacities. The launch of IXPE allowed us to check this prediction. IXPE observed a dozen X-ray pulsars, discovering pulse-phase dependent variation of the polarization degree (PD) and polarization angle (PA). Although the PD showed rather erratic profiles resembling flux pulse dependence, the PA in most cases showed smooth variations consistent with the rotating vector model (RVM), which can be interpreted as a combined effect of vacuum birefringence and dipole magnetic field structure at a polarization-limiting (adiabatic) radius. Application of the RVM allowed us to determine XRP geometry and to confirm the free precession of the NS in Her X-1. Deviations from RVM in two bright transients led to the discovery of an unpulsed polarized emission likely produced by scattering off the accretion disk wind. Full article
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<p>Possible sources of polarized emission in XRPs: (i) intrinsic polarization from the hotspot, (ii) reflection from the NS surface, (iii) reflection from the accretion curtain, (iv) reflection from the accretion disk (and accretion disk wind), (v) scattering off the stellar wind, and (vi) reflection off the optical companion. From [<a href="#B20-galaxies-12-00046" class="html-bibr">20</a>].</p>
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<p>Geometry of the pulsar and main parameters of the RVM. The pulsar angular momentum <math display="inline"><semantics> <msub> <mo mathvariant="bold">Ω</mo> <mi mathvariant="normal">p</mi> </msub> </semantics></math> makes an angle <math display="inline"><semantics> <msub> <mi>i</mi> <mi mathvariant="normal">p</mi> </msub> </semantics></math> with respect to the observer direction <b><span class="html-italic">o</span></b>. The angle <math display="inline"><semantics> <msub> <mi>θ</mi> <mi mathvariant="normal">p</mi> </msub> </semantics></math> is the magnetic obliquity, i.e., the angle between magnetic dipole <b><span class="html-italic">B</span></b> and the rotation axis. Pulsar phase <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> is the azimuthal angle of vector <b><span class="html-italic">B</span></b> in the plane <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </semantics></math> perpendicular to <math display="inline"><semantics> <msub> <mo mathvariant="bold">Ω</mo> <mi mathvariant="normal">p</mi> </msub> </semantics></math> measured from the projection of <b><span class="html-italic">o</span></b>. The pulsar position angle <math display="inline"><semantics> <msub> <mi>χ</mi> <mi mathvariant="normal">p</mi> </msub> </semantics></math> is the angle measured counterclockwise between the direction to the north (N) and the projection of <math display="inline"><semantics> <msub> <mo mathvariant="bold">Ω</mo> <mi mathvariant="normal">p</mi> </msub> </semantics></math> on the plane of the sky (N-E).</p>
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<p>Examples of the RVM with the emission pattern and polarization given by Equation (<a href="#FD3-galaxies-12-00046" class="html-disp-formula">3</a>). (<b>a</b>) Normalized flux, (<b>b</b>) PD, and (<b>c</b>) PA as functions of pulse phase for various pairs of parameters <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>i</mi> <mi mathvariant="normal">p</mi> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mi mathvariant="normal">p</mi> </msub> <mo>)</mo> </mrow> </semantics></math>. The case of (60°, 30°) is shown with black solid lines, (30°, 70°) with red dotted lines, and (70°, 85°) with blue dashed lines. (<b>d</b>) Evolution of normalized Stokes parameters <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> </semantics></math> for the same three sets of pairs. The numbers mark the pulse phase. We use here the following parameters: the NS mass <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.4</mn> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math> and radius of 12 km, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mi>max</mi> </msub> <mo>=</mo> <mn>30</mn> <mo>%</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>χ</mi> <mi mathvariant="normal">p</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
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<p>Examples of the phase-resolved spectropolarimetric analysis for two XRPs: Cen X-3 (<b>left</b>) and X Persei (<b>right</b>). The evolutions of the normalized flux (pulse profile), PD, and PA are shown in the corresponding panels (<b>a</b>–<b>c</b>). The lower panels demonstrate the phase-resolved behavior of the normalized Stokes parameters <span class="html-italic">q</span> and <span class="html-italic">u</span>.</p>
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<p>Evolution of the pulse-phase average PD (blue circles, left axis) and the PA (red circles, right axis) of Her X-1 with time (lower axis) and the super-orbital phase (upper axis). The pink rectangles show the minimum detectable polarization at 99% CL. The gray symbols show the flux evolution. From [<a href="#B47-galaxies-12-00046" class="html-bibr">47</a>].</p>
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<p>Pulse phase dependence of polarimetric characteristics of XRP LS V +44 17. (<b>a</b>) Normalized flux, (<b>b</b>) PD, (<b>c</b>) PA, and (<b>d</b>) intrinsic PA after subtraction of the constant component. Red circles and blue triangles correspond to two observations separated by two weeks. Adapted from [<a href="#B44-galaxies-12-00046" class="html-bibr">44</a>]. Panel (<b>e</b>) shows the observed phase-resolved <span class="html-italic">absolute</span> Stokes parameters <span class="html-italic">Q</span> and <span class="html-italic">U</span> (scaled to the mean flux) rebinned to the same phase intervals. The numbers mark the bins from 1 to 16, and the arrows connect the data points. The black cross is the origin. Panel (<b>f</b>) is the same diagram with the constant component subtracted. The arrows now connect the origin to a few selected points, illustrating that the arrows corresponding to the same phase bin in the two observations are nearly parallel, implying similar PA.</p>
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16 pages, 15750 KiB  
Article
Iron Loss and Temperature Rise Analysis of a Transformer Core Considering Vector Magnetic Hysteresis Characteristics under Direct Current Bias
by Minxia Shi, Teng Li, Shuai Yuan, Leran Zhang, Yuzheng Ma and Yi Gao
Materials 2024, 17(15), 3767; https://doi.org/10.3390/ma17153767 - 31 Jul 2024
Viewed by 1334
Abstract
Direct current (DC) bias induced by the DC transmission and geomagnetically induced current is a critical factor in the abnormal operation of electrical equipment and is widely used in the field of power transmission and distribution system state evaluation. As the main affected [...] Read more.
Direct current (DC) bias induced by the DC transmission and geomagnetically induced current is a critical factor in the abnormal operation of electrical equipment and is widely used in the field of power transmission and distribution system state evaluation. As the main affected component, the vector magnetization state of a transformer core under DC bias has rarely been studied, resulting in inaccurate transformer operation state estimations. In this paper, a dynamic vector hysteresis model that considers the impact of rotating and DC-biased fields is introduced into the numerical analysis to simulate the distribution of magnetic properties, iron loss and temperature of the transformer core model and a physical 110 kV single-phase autotransformer core. The maximum values of B, H and iron loss exist at the corners and T-joint of the core under rotating and DC-biased fields. The corresponding maximum value of the temperature increase is found in the main core limb area. The temperature rise of the 110 kV transformer core under various DC-biased conditions is measured and compared with the FEM (Finite Element Method) results of the proposed model and the model solely based on the magnetization curve B||H. The calculation error of the temperature rise obtained by the improved model is approximately 3.76–15.73% and is much less than the model solely based on magnetization curve B||H (approximately 50.71–66.92%). Full article
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<p>The desired field and the feedback measurement system: (<b>a</b>) Desired field. (<b>b</b>) Schematic of the experimental measurement system. (<b>c</b>) The physical single sheet tester (SST). (<b>d</b>) The physical measurement system.</p>
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<p>Loci of <b><span class="html-italic">B</span></b> and <b><span class="html-italic">H</span></b> under different <b><span class="html-italic">B<sub>max</sub></span></b> without DC bias and the corresponding magnetization curve and permeability of 30ZH120: (<b>a</b>) <b><span class="html-italic">B</span></b> locus. (<b>b</b>) <b><span class="html-italic">H</span></b> locus. (<b>c</b>) Magnetization curve and permeability of 30ZH120 at the frequency 50 Hz in easy magnetization direction.</p>
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<p>Waveforms and harmonic component amplitudes of <b><span class="html-italic">B</span></b> and <b><span class="html-italic">H</span></b> under different <b><span class="html-italic">B<sub>dc</sub></span></b>: (<b>a</b>) <span class="html-italic">B<sub>x</sub></span> and <span class="html-italic">H<sub>x</sub></span> waveforms. (<b>b</b>) <span class="html-italic">B<sub>y</sub></span> and <span class="html-italic">H<sub>y</sub></span> waveforms. (<b>c</b>) <span class="html-italic">B<sub>x</sub></span> harmonic component amplitudes. (<b>d</b>) <span class="html-italic">H<sub>x</sub></span> harmonic component amplitudes.</p>
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<p>The iron loss under different magnetization conditions: (<b>a</b>) The loss of different <span class="html-italic">B<sub>max</sub></span> and <span class="html-italic">θ</span>. (<b>b</b>) The loss of different <span class="html-italic">B<sub>max</sub></span> and <span class="html-italic">α</span>. (<b>c</b>) The loss of different <span class="html-italic">B<sub>dc</sub></span>.</p>
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<p>The movement process of magnetic domain: (<b>a</b>) The movement process of magnetic domain under the rotating magnetic field increasing for <span class="html-italic">B<sub>max</sub></span> ranging from 0.2 to 1.0 T. (<b>b</b>) The movement process of magnetic domain under the rotating magnetic field and DC-biased field for increasing <span class="html-italic">B<sub>dc</sub></span> ranging from 0.2 to 1.0 T and increasing <span class="html-italic">θ<sub>dc</sub></span> from 0 to 90°.</p>
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<p>The movement process of magnetic domain: (<b>a</b>) The movement process of magnetic domain under the rotating magnetic field increasing for <span class="html-italic">B<sub>max</sub></span> ranging from 0.2 to 1.0 T. (<b>b</b>) The movement process of magnetic domain under the rotating magnetic field and DC-biased field for increasing <span class="html-italic">B<sub>dc</sub></span> ranging from 0.2 to 1.0 T and increasing <span class="html-italic">θ<sub>dc</sub></span> from 0 to 90°.</p>
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<p>Transform core model and the mesh: (<b>a</b>) The transform core model. (<b>b</b>) The mesh.</p>
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<p>Distribution of the maximum value of <b><span class="html-italic">B</span></b> and <b><span class="html-italic">H</span></b> of the transformer core model: (<b>a</b>) Maximum value of <b><span class="html-italic">B</span></b> calculated using the magnetization curve. (<b>b</b>) Maximum value of <b><span class="html-italic">B</span></b> calculated using the improved model. (<b>c</b>) Maximum value of <b><span class="html-italic">H</span></b> calculated using the magnetization curve. (<b>d</b>) Maximum value of <b><span class="html-italic">H</span></b> calculated using the improved model.</p>
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<p>Distribution of iron loss of the transformer core model: (<b>a</b>) Iron loss calculated using the magnetization curve. (<b>b</b>) Iron loss calculated using the improved model.</p>
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<p>Distribution of temperature of the transformer core model: (<b>a</b>) Temperature calculated using the magnetization curve. (<b>b</b>) Temperature calculated using the improved model.</p>
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<p>Schematic diagram of DC bias test: (<b>a</b>) Wiring schematic diagram for DC bias test. (<b>b</b>) Temperature rise measurement point for DC bias magnetic test.</p>
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<p>Exciting current and magnetization curve of the tested transformer core: (<b>a</b>) Exciting current for different DC bias conditions. (<b>b</b>) Magnetization curve and the corresponding permeability of 27RK090 (50 Hz) of the tested transformer core in easy magnetization direction.</p>
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<p>The 2D automatic mesh with triangular elements of the physical transformer core.</p>
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<p>Distribution of <b><span class="html-italic">B</span></b> and <b><span class="html-italic">H</span></b> of the physical 110 kV transformer core: (<b>a</b>) Distribution of <b><span class="html-italic">B</span></b> and <b><span class="html-italic">H</span></b> calculated using the basic magnetization curve. (<b>b</b>) Distribution of <b><span class="html-italic">B</span></b> and <b><span class="html-italic">H</span></b> calculated using proposed model.</p>
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<p>Distribution of temperature of the physical 110 kV transformer core: (<b>a</b>) Temperature calculated using the magnetization curve. (<b>b</b>) Temperature calculated using the improved model.</p>
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<p>Comparison between calculated and measured values of local temperature of iron core: (<b>a</b>) Point A. (<b>b</b>) Point B. (<b>c</b>) Point C. (<b>d</b>) Point D.</p>
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23 pages, 9346 KiB  
Article
PMSM Sensorless Control Based on Moving Horizon Estimation and Parameter Self-Adaptation
by Aoran Chen, Wenbo Chen and Heng Wan
Electronics 2024, 13(13), 2444; https://doi.org/10.3390/electronics13132444 - 21 Jun 2024
Viewed by 1381
Abstract
The field of sensorless control of permanent magnet synchronous motor (PMSM) systems has been the subject of extensive research. The accuracy of sensorless controllers depends on the precise estimation of PMSM state quantities, including rotational speed and rotor position. In order to enhance [...] Read more.
The field of sensorless control of permanent magnet synchronous motor (PMSM) systems has been the subject of extensive research. The accuracy of sensorless controllers depends on the precise estimation of PMSM state quantities, including rotational speed and rotor position. In order to enhance state estimation accuracy, this paper proposes a moving horizon estimator that can be utilized in the sensorless control system of PMSM. Considering the parameter variations observed in PMSM, a nonlinear mathematical model of PMSM is established. A model reference adaptive system (MRAS) is employed to identify parameters such as resistance, inductance, and magnetic chain in real time. This approach can mitigate the impact of parameter fluctuations. Moving horizon estimation (MHE) is an estimation method based on optimization that can directly handle nonlinear system models. In order to eliminate the influence of external interference and improve the robustness of state estimation, a method based on MHE has been designed for PMSM, and a sensorless observer has been established. Considering the traditional MHE with large computation and high memory occupation, the calculation of MHE is optimized by utilizing a Hessian matrix and gradient vector. The speed and position of the PMSM are estimated within constraints during a single-step iteration. The results of the simulation demonstrate that in comparison to the traditional control structure, the estimation error of rotational speed and rotor position can be reduced by utilizing the proposed method. A more accurate estimation can be achieved with good adaptability and computational speed, which can enhance the robustness of the control system of PMSM. Full article
(This article belongs to the Special Issue Advances in Control for Permanent Magnet Synchronous Motor (PMSM))
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<p>Block diagram of parameter identification of MRAS.</p>
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<p>Schematic diagram of MHE method.</p>
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<p>SPMSM sensorless control scheme.</p>
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<p>Measurement of speed (SPMSM operates under Condition I with PI controller, EKF, and MHE use the same parameter initialization settings).</p>
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<p>Measurement of <span class="html-italic">i<sub>d</sub></span> and <span class="html-italic">i<sub>q</sub></span>, under condition I.</p>
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<p>Error of speed estimation, under condition I.</p>
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<p>Measurement of rotor position (under Condition I, in case of sudden torque change at 1.2 s).</p>
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<p>Error of rotor position estimation, under condition I.</p>
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<p>Measurement of speed under Condition II.</p>
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<p>Error of speed estimation, under Condition II.</p>
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<p>Measurement of <span class="html-italic">i<sub>d</sub></span> and <span class="html-italic">i<sub>q</sub></span>.</p>
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<p>Measurement of rotor position under Condition II.</p>
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<p>Error of rotor position estimation, under Condition II.</p>
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<p>Errors of speed estimation. (horizon chooses <span class="html-italic">N</span> = 3, 5, 10).</p>
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<p>Error of position estimation (horizon chooses <span class="html-italic">N</span> = 3, 5, 10).</p>
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<p>Error values of speed and rotor position with different <span class="html-italic">N</span>.</p>
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<p>The speed estimation and error of estimation of two approaches demonstrate the impact of MRAS on the accuracy of estimate findings.</p>
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<p>Position estimation of two MHE strategies.</p>
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<p>The impact of MRAS on the accuracy of estimation as demonstrated by the value of RMSE.</p>
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<p>Identification of flux, rotor resistance, and inductance by MRAS.</p>
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<p>Error of speed estimation, where red represents the general MHE and blue represents the optimized MHE calculated by the Hessian matrix and gradient vector.</p>
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<p>Error of rotor position estimation of the two schemes, in which blue represents the general MHE and red represents the optimized MHE calculated by the Hessian matrix and gradient vector.</p>
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14 pages, 2696 KiB  
Article
Analysis of Characteristics of the Electric Field Induced by an Angularly Rotating and Oscillating Magnetic Object
by Jiawei Zhang, Dawei Xiao, Taotao Xie and Qing Ji
Appl. Sci. 2024, 14(3), 1321; https://doi.org/10.3390/app14031321 - 5 Feb 2024
Viewed by 1201
Abstract
A mathematical model for an electric field induced by an angularly oscillating magnetic dipole was proposed with magnetic vector potential to analyze the characteristics of the electric field induced by a rotating and angularly oscillating magnetic object. This mathematical model was constructed for [...] Read more.
A mathematical model for an electric field induced by an angularly oscillating magnetic dipole was proposed with magnetic vector potential to analyze the characteristics of the electric field induced by a rotating and angularly oscillating magnetic object. This mathematical model was constructed for the electric field induced by a magnetic object oscillating at a certain angle. On this basis, the phase relationship among the three components of the induced electric field was analyzed (defining the right-hand Cartesian coordinate system). Evidently, a phase difference of π/2 always existed between the horizontal components of the electric field induced by a magnetic dipole rotating around the z-axis. The phase difference between the vertical and transverse components in the xz plane was also π/2. A phase difference of π was observed in the y–z plane. The above theoretical analysis was verified through simulation and experiment. The results showed that the frequency of the induced electric field was related to the angular velocity and angle of rotation. The amplitude was associated with the magnetic moment and the angular velocity and angle of oscillation. The maximum amplitude did not exceed the amplitude of the electric field induced by a magnetic object angularly oscillating at the same velocity. With regard to the amplitude and phase relationship, the three components of the induced electric field measured in the experiment were consistent with the results of the theoretical analysis. Full article
(This article belongs to the Special Issue Electromagnetic Detection Instruments and Signal Processing)
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<p>Rotating magnetic dipole.</p>
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<p>Induced electric field of rotating magnetic dipole at <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math> for (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>x</mi> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>y</mi> </msub> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>z</mi> </msub> </mrow> </semantics></math>. All data are listed as: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>x</mi> </msub> </mrow> </semantics></math> component of an induced electric field, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>y</mi> </msub> </mrow> </semantics></math> component of an induced electric field, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>z</mi> </msub> </mrow> </semantics></math> component of an induced electric field.</p>
Full article ">Figure 3
<p>Induced electric field of rotating magnetic dipole at <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math> for (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>x</mi> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>y</mi> </msub> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>z</mi> </msub> </mrow> </semantics></math>. All data are listed as: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>x</mi> </msub> </mrow> </semantics></math> component of an induced electric field, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>y</mi> </msub> </mrow> </semantics></math> component of an induced electric field, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">E</mi> <mi>z</mi> </msub> </mrow> </semantics></math> component of an induced electric field.</p>
Full article ">Figure 4
<p>Electric field induced by a sloshing magnetic dipole at <span class="html-italic">π</span>/6 for (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span>, (<b>b</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>y</sub></span>, and (<b>c</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>z</sub></span>. (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span> component of an induced electric field, (<b>b</b>) <span class="html-italic"><b>E</b><sub>y</sub></span> component of an induced electric field, and (<b>c</b>)<span class="html-italic"> <b>E</b><sub>z</sub></span> component of an induced electric field.</p>
Full article ">Figure 5
<p>Electric field induced by a sloshing magnetic dipole at <span class="html-italic">π</span>/3 for (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span>, (<b>b</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>y</sub></span>, and (<b>c</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>z</sub></span>. (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span> component of an induced electric field, (<b>b</b>) <span class="html-italic"><b>E</b><sub>y</sub></span> component of an induced electric field, and (<b>c</b>) <span class="html-italic"><b>E</b><sub>z</sub></span> component of an induced electric field.</p>
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<p>Experimental schematic diagram.</p>
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<p>Comparison of measured and theoretical values of (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span>, (<b>b</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>y</sub></span>, and (<b>c</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>z</sub></span>. (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span> component of an induced electric field, (<b>b</b>) <span class="html-italic"><b>E</b><sub>y</sub></span> component of an induced electric field, and (<b>c</b>) <span class="html-italic"><b>E</b><sub>z</sub></span> component of an induced electric field.</p>
Full article ">Figure 7 Cont.
<p>Comparison of measured and theoretical values of (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span>, (<b>b</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>y</sub></span>, and (<b>c</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>z</sub></span>. (<b>a</b>) <b><span class="html-italic">E</span></b><span class="html-italic"><sub>x</sub></span> component of an induced electric field, (<b>b</b>) <span class="html-italic"><b>E</b><sub>y</sub></span> component of an induced electric field, and (<b>c</b>) <span class="html-italic"><b>E</b><sub>z</sub></span> component of an induced electric field.</p>
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13 pages, 6315 KiB  
Article
Estimating the Inertia Tensor Components of an Asymmetrical Spacecraft When Removing It from the Operational Orbit at the End of Its Active Life
by A. V. Sedelnikov, D. I. Orlov, M. E. Bratkova and E. S. Khnyryova
Sensors 2023, 23(23), 9615; https://doi.org/10.3390/s23239615 - 4 Dec 2023
Cited by 5 | Viewed by 1339
Abstract
The paper presents a method for estimating the inertia tensor components of a spacecraft that has expired its active life using measurement data of the Earth’s magnetic field induction vector components. The implementation of this estimation method is supposed to be carried out [...] Read more.
The paper presents a method for estimating the inertia tensor components of a spacecraft that has expired its active life using measurement data of the Earth’s magnetic field induction vector components. The implementation of this estimation method is supposed to be carried out when cleaning up space debris in the form of a clapped-out spacecraft with the help of a space tug. It is assumed that a three-component magnetometer and a transmitting device are attached on space debris. The parameters for the rotational motion of space debris are estimated using this measuring system. Then, the known controlled action from the space tug is transferred to the space debris. Next, measurements for the rotational motion parameters are carried out once again. Based on the available measurement data and parameters of the controlled action, the space debris inertia tensor components are estimated. It is assumed that the measurements of the Earth’s magnetic field induction vector components are made in a coordinate system whose axes are parallel to the corresponding axes of the main body axis system. Such an estimation makes it possible to effectively solve the problem of cleaning up space debris by calculating the costs of the space tug working body and the parameters of the space debris removal orbit. Examples of numerical simulation using the measurement data of the Earth’s magnetic field induction vector components on the Aist-2D small spacecraft are given. Thus, the purpose of this work is to evaluate the components of the space debris inertia tensor through measurements of the Earth’s magnetic field taken using magnetometer sensors. The results of the work can be used in the development and implementation of missions to clean up space debris in the form of clapped-out spacecraft. Full article
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Figure 1

Figure 1
<p>A method for removing space debris using a space tug and a tether system.</p>
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<p>Scheme of attaching the magnetometer on the space debris object in an arbitrary case: Oxyz is the main body axis system of the space debris object; O<sub>b</sub>x<sub>b</sub>y<sub>b</sub>z<sub>b</sub> is the structural coordinate system of the magnetometer.</p>
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<p>Scheme of attaching the magnetometer on the space debris object in the special case.</p>
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<p>Appearance of the Aist-2D small spacecraft for remote sensing of the Earth [<a href="#B25-sensors-23-09615" class="html-bibr">25</a>].</p>
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<p>Components of the Earth’s magnetic field induction vector in the magnetometer’s structural coordinate system in stabilization mode: 1 is <span class="html-italic">B<sub>x</sub></span>; 2 is <span class="html-italic">B<sub>y</sub></span>; 3 is <span class="html-italic">B<sub>z</sub>.</span></p>
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<p>Components of the Earth’s magnetic field induction vector in the magnetometer’s structural coordinate system in reorientation mode: 1 is <span class="html-italic">B<sub>x</sub></span>; 2 is <span class="html-italic">B<sub>y</sub></span>; 3 is <span class="html-italic">B<sub>z</sub>.</span></p>
Full article ">Figure 7
<p>Continuous dependencies of the Earth’s magnetic field induction vector components in the magnetometer’s structural coordinate system, restored using the Kotelnikov series (9): (<b>a</b>) in stabilization mode (<a href="#sensors-23-09615-f005" class="html-fig">Figure 5</a>); (<b>b</b>) in reorientation mode (<a href="#sensors-23-09615-f006" class="html-fig">Figure 6</a>) 1 is <span class="html-italic">B<sub>x</sub></span>; 2 is <span class="html-italic">B<sub>y</sub></span>; 3 is <span class="html-italic">B<sub>z</sub></span>.</p>
Full article ">Figure 8
<p>Derivatives of continuous dependencies of the Earth’s magnetic field induction vector components in the magnetometer’s structural coordinate system (<a href="#sensors-23-09615-f007" class="html-fig">Figure 7</a>): (<b>a</b>) in stabilization mode; (<b>b</b>) in reorientation mode <span class="html-italic">dB<sub>x</sub></span>/<span class="html-italic">dt</span> (black); <span class="html-italic">dB<sub>y</sub></span>/<span class="html-italic">dt</span> (blue); <span class="html-italic">dB<sub>z</sub></span>/<span class="html-italic">dt</span> (red).</p>
Full article ">Figure 9
<p>Dependences for the components of the angular velocity vector in the magnetometer’s structural coordinate system, estimated by Equation (2): (<b>a</b>) in stabilization mode; (<b>b</b>) in reorientation mode <span class="html-italic">ω<sub>x</sub></span> (black); <span class="html-italic">ω<sub>y</sub></span> (blue); <span class="html-italic">ω<sub>z</sub></span> (red).</p>
Full article ">Figure 10
<p>Dependences for the components of the angular acceleration vector in the magnetometer’s structural coordinate system: (<b>a</b>) in stabilization mode; (<b>b</b>) in reorientation mode <span class="html-italic">ε<sub>x</sub></span> (black); <span class="html-italic">ε<sub>y</sub></span> (blue); <span class="html-italic">ε<sub>z</sub></span> (red).</p>
Full article ">Figure 11
<p>Dependences for the diagonal components of the inertia tensor in the magnetometer’s structural coordinate system in stabilization mode: (<b>a</b>) <span class="html-italic">I<sub>xx</sub></span>; (<b>b</b>) <span class="html-italic">I<sub>yy</sub></span>; (<b>c</b>) <span class="html-italic">I<sub>zz</sub></span>.</p>
Full article ">Figure 12
<p>Dependences for the diagonal components of the inertia tensor in the magnetometer’s structural coordinate system in reorientation mode: (<b>a</b>) <span class="html-italic">I<sub>xx</sub></span>; (<b>b</b>) <span class="html-italic">I<sub>yy</sub></span>; (<b>c</b>) <span class="html-italic">I<sub>zz</sub></span>.</p>
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19 pages, 1226 KiB  
Article
Modal Projection for Quasi-Homogeneous Anisotropic Turbulence
by Ying Zhu and Claude Cambon
Atmosphere 2023, 14(8), 1215; https://doi.org/10.3390/atmos14081215 - 28 Jul 2023
Viewed by 1295
Abstract
This article, or essay, addresses the anisotropic structure and the dynamics of quasi-homogeneous, incompressible turbulence. Modal projection and expansions in terms of spherical harmonics in three-dimensional Fourier space are in line with a seminal study by Jack Herring, around the so-called Craya–Herring frame [...] Read more.
This article, or essay, addresses the anisotropic structure and the dynamics of quasi-homogeneous, incompressible turbulence. Modal projection and expansions in terms of spherical harmonics in three-dimensional Fourier space are in line with a seminal study by Jack Herring, around the so-called Craya–Herring frame of reference, with a large review of the related approaches to date. The research part is focused on structure and dynamics of rotating sheared turbulence, including a description of both directional and polarization anisotropy with a minimal number of modes. Effort is made to generalize expansions in terms of scalar spherical harmonics (SSHs) to vector spherical harmonics (VSHs). Looking at stochastic fields, for possibly intermittent vector fields, some directions are explored to reconcile modal projection, firstly used for smooth vector fields, and multifractal approaches for internal intermittency but far beyond scalar correlations, such as structure functions. In order to illustrate turbulence from Earth to planets, stars, and galaxies, applications to geophysics and astrophysics are touched upon, with generalization to coupled vector fields (for kinetic, magnetic, and potential energies), possibly dominated by waves (Coriolis, gravity, and Alfvén). Full article
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Figure 1
<p>Craya–Herring frame of reference.</p>
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<p>Time evolution of turbulent kinetic energy. Comparisons of results from the cases with typical values of <span class="html-italic">R</span>: (<b>a</b>) in the inviscid linear limit; (<b>b</b>) in the viscous linear limit; and (<b>c</b>) with fully nonlinear ZCG.</p>
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<p>Time evolution of the deviatoric part of the Reynolds stress tensor <math display="inline"><semantics><msub><mi>b</mi><mn>12</mn></msub></semantics></math>. Comparisons of results from the cases with typical values of <span class="html-italic">R</span>: (<b>a</b>) in inviscid linear limit; (<b>b</b>) in viscous linear limit; and (<b>c</b>) with fully nonlinear ZCG.</p>
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<p>Spherical distributions of <math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="script">E</mi></mrow><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="bold-italic">k</mi><mo>)</mo></mrow></mrow></semantics></math> and <math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="script">E</mi></mrow><mn>4</mn></msup><mrow><mo>(</mo><mi mathvariant="bold-italic">k</mi><mo>)</mo></mrow></mrow></semantics></math> in viscous linear limit with <math display="inline"><semantics><mrow><mi>R</mi><mo>=</mo><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math> at <math display="inline"><semantics><mrow><mi>S</mi><mi>t</mi><mo>=</mo><mn>5</mn></mrow></semantics></math> at the wavenumber <math display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><msub><mi>k</mi><mi>λ</mi></msub></mrow></semantics></math>. Comparison of results obtained by the SO(3)-type expansion and SSH decomposition, respectively.</p>
Full article ">Figure 5
<p>Spherically averaged anisotropy spectra <math display="inline"><semantics><mrow><msup><mi>a</mi><mrow><mn>2</mn><mi>n</mi><mo>(</mo><mi mathvariant="script">E</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math> for <math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></semantics></math> in degree <math display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>=</mo><mn>2</mn></mrow></semantics></math> and <math display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>=</mo><mn>4</mn></mrow></semantics></math> at <math display="inline"><semantics><mrow><mi>S</mi><mi>t</mi><mo>=</mo><mn>5</mn></mrow></semantics></math>. Comparisons of the results obtained respectively by tensorial expansion (SO(3) type) and SSH decomposition: (<b>a</b>) in the inviscid linear limit; (<b>b</b>) in the viscous linear limit; and (<b>c</b>) with fully nonlinear ZCG.</p>
Full article ">Figure 6
<p>Spherically integral anisotropy <math display="inline"><semantics><mrow><msup><mi>a</mi><mrow><mn>2</mn><mi>n</mi><mo>(</mo><mi mathvariant="script">E</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math> for <math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>(</mo><mi mathvariant="bold-italic">k</mi><mo>)</mo></mrow></semantics></math> (top) and <math display="inline"><semantics><mrow><msup><mi>a</mi><mrow><mn>2</mn><mi>n</mi><mo>(</mo><mi>Z</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math> for <span class="html-italic">Z</span> (bottom) in degree <math display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>=</mo><mn>2</mn><mspace width="0.166667em"/><mo>,</mo><mn>4</mn><mspace width="0.166667em"/><mo>,</mo><mn>6</mn><mspace width="0.166667em"/><mo>,</mo><mn>8</mn></mrow></semantics></math>, in inviscid linear limit at <math display="inline"><semantics><mrow><mi>S</mi><mi>t</mi><mo>=</mo><mn>5</mn></mrow></semantics></math> for various values of <span class="html-italic">R</span>.</p>
Full article ">Figure 7
<p>Spherically integral anisotropy <math display="inline"><semantics><mrow><msup><mi>a</mi><mrow><mn>2</mn><mi>n</mi><mo>(</mo><mi mathvariant="script">E</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math> for <math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>(</mo><mi mathvariant="bold-italic">k</mi><mo>)</mo></mrow></semantics></math> (top) and <math display="inline"><semantics><mrow><msup><mi>a</mi><mrow><mn>2</mn><mi>n</mi><mo>(</mo><mi>Z</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math> for <span class="html-italic">Z</span> (bottom) in degree <math display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>=</mo><mn>2</mn><mspace width="0.166667em"/><mo>,</mo><mn>4</mn><mspace width="0.166667em"/><mo>,</mo><mn>6</mn><mspace width="0.166667em"/><mo>,</mo><mn>8</mn></mrow></semantics></math>, in viscous linear limit at <math display="inline"><semantics><mrow><mi>S</mi><mi>t</mi><mo>=</mo><mn>5</mn></mrow></semantics></math> for various values of <span class="html-italic">R</span>.</p>
Full article ">Figure 8
<p>Spherically integral anisotropy <math display="inline"><semantics><mrow><msup><mi>a</mi><mrow><mn>2</mn><mi>n</mi><mo>(</mo><mi mathvariant="script">E</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math> for <math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>(</mo><mi mathvariant="bold">k</mi><mo>)</mo></mrow></semantics></math> (top) and <math display="inline"><semantics><mrow><msup><mi>a</mi><mrow><mn>2</mn><mi>n</mi><mo>(</mo><mi>Z</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math> for <span class="html-italic">Z</span> (bottom) in degree <math display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>=</mo><mn>2</mn><mspace width="0.166667em"/><mo>,</mo><mn>4</mn><mspace width="0.166667em"/><mo>,</mo><mn>6</mn><mspace width="0.166667em"/><mo>,</mo><mn>8</mn></mrow></semantics></math>, with fully nonlinear ZCG, at <math display="inline"><semantics><mrow><mi>S</mi><mi>t</mi><mo>=</mo><mn>5</mn></mrow></semantics></math> for various values of <span class="html-italic">R</span>.</p>
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29 pages, 10330 KiB  
Article
Enhanced Integrator with Drift Elimination for Accurate Flux Estimation in Sensorless Controlled Interior PMSM for High-Performance Full Speed Range Hybrid Electric Vehicles Applications
by Sadiq Ur Rahman and Chaoying Xia
Machines 2023, 11(7), 769; https://doi.org/10.3390/machines11070769 - 24 Jul 2023
Viewed by 2044
Abstract
Interior Permanent Magnet Synchronous Motor (IPMSM) motion-sensorless speed control necessitates precise knowledge of rotor flux, speed, and position. Due to numerous non-ideal aspects, such as converter nonlinearities, detection errors, integral initial value, and parameter mismatches, the conventional first-order integrator’s estimated rotor flux experiences [...] Read more.
Interior Permanent Magnet Synchronous Motor (IPMSM) motion-sensorless speed control necessitates precise knowledge of rotor flux, speed, and position. Due to numerous non-ideal aspects, such as converter nonlinearities, detection errors, integral initial value, and parameter mismatches, the conventional first-order integrator’s estimated rotor flux experiences a DC offset (Doff). Low-pass filters (LPF) with a constant cut-off frequency yield accurate estimates only in the medium- and high-speed range; however, at the low-speed area, both magnitude and phase estimates are inaccurate. The presented technique resolves the aforementioned issue for a broad speed range. In order to achieve precise flux estimation, this article presents an improved technique of flux estimator with two distinct drift mitigation strategies for the motion-sensorless field-oriented control (FOC) system of IPMSM. Using the orthogonality of the α- and β-axes, the proposed drift elimination system can estimate drift in different situations while maintaining a high level of dynamic performance. The stator flux linkage (SFL) computation in the synchronous coordinate is established from the estimation of the rotating shaft’s permanent magnetic flux linkage orientation and the statistical equations model of the SFL. By comparing the calculated SFL vector to the SFL vector derived from the stator winding voltage and currents integral model with a drift PI compensation loop, a feedback loop is formed to neutralize integral drift, and the rotational speed and position of an IPMSM is estimated utilizing the vector product of the two flux linkages in a phase-locked loop. Theoretical interpretation is presented, and Matlab Simulink simulations, as well as experimental outcomes, consistently demonstrate that the suggested estimation techniques can eliminate the phenomenon of flux drift. Full article
(This article belongs to the Special Issue Advanced Data Analytics in Intelligent Industry: Theory and Practice)
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Figure 1
<p>IPMSM sensorless control using rotor flux estimation.</p>
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<p>Diagram of IPMSM voltage model for rotor speed and position estimation.</p>
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<p>Design of flux estimator combined with PLL for the motion-sensorless system of IPMSM: (<b>a</b>) drift elimination strategy 1; (<b>b</b>) drift elimination strategy 2.</p>
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<p>Schematic diagram of the PI controller’s estimation error for <math display="inline"><semantics><mrow><mover><mi>e</mi><mo stretchy="false">^</mo></mover><msub><mrow/><mrow><mi>d</mi><mi>c</mi></mrow></msub></mrow></semantics></math>.</p>
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<p>Schematic diagram of the PI controller’s estimation for <math display="inline"><semantics><mrow><mover><mi>e</mi><mo stretchy="false">^</mo></mover><msub><mrow/><mrow><mi>d</mi><mi>c</mi></mrow></msub></mrow></semantics></math>.</p>
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<p>Schematic representation of overall motion-sensorless control system.</p>
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<p>Matlab Simulation results with constant speed (300 r/min) under the <math display="inline"><semantics><mrow><mi mathvariant="normal">α</mi></mrow></semantics></math>-axis voltage disturbance (0 V and 0.6 V). (<b>a</b>) Artificially injected Doff and DC-drift estimation error, DM1, and DM2. (<b>b</b>) Speed and position estimation error, DM1, and DM2. (<b>c</b>) Observed speed estimation, DM1, and DM2. (<b>d</b>) Estimation fluxes and the errors of estimated fluxes, DM1, and DM2.</p>
Full article ">Figure 7 Cont.
<p>Matlab Simulation results with constant speed (300 r/min) under the <math display="inline"><semantics><mrow><mi mathvariant="normal">α</mi></mrow></semantics></math>-axis voltage disturbance (0 V and 0.6 V). (<b>a</b>) Artificially injected Doff and DC-drift estimation error, DM1, and DM2. (<b>b</b>) Speed and position estimation error, DM1, and DM2. (<b>c</b>) Observed speed estimation, DM1, and DM2. (<b>d</b>) Estimation fluxes and the errors of estimated fluxes, DM1, and DM2.</p>
Full article ">Figure 8
<p>Simulation results with constant speed (300 r/min) under the <math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math>-axis voltage disturbance (1 V and 1.5 V). (<b>a</b>) Artificially injected Doff and DC-drift estimation error, DM1, and DM2. (<b>b</b>) Speed and position estimation error, DM1, and DM2. (<b>c</b>) Observed speed estimation, DM1, and DM2. (<b>d</b>) Estimation fluxes and the errors of estimated fluxes, DM1, and DM2.</p>
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<p>Simulation results with constant speed (300 r/min) under the <math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math>-axis voltage disturbance (1 V and 1.5 V). (<b>a</b>) Artificially injected Doff and DC-drift estimation error, DM1, and DM2. (<b>b</b>) Speed and position estimation error, DM1, and DM2. (<b>c</b>) Observed speed estimation, DM1, and DM2. (<b>d</b>) Estimation fluxes and the errors of estimated fluxes, DM1, and DM2.</p>
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<p>Simulation results with constant speed (300 r/min) under the <math display="inline"><semantics><mrow><mi>α</mi><mi>β</mi></mrow></semantics></math>-axis voltage disturbance. (<b>a</b>) Artificially injected Doff and DC-drift estimation error, DM1, and DM2. (<b>b</b>) Speed and position estimation error, DM1, and DM2. (<b>c</b>) Observed speed estimation, DM1, and DM2. (<b>d</b>) Estimation fluxes and the errors of estimated fluxes, DM1, and DM2.</p>
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<p>Simulation results with constant speed (300 r/min) under the <math display="inline"><semantics><mrow><mi>α</mi><mi>β</mi></mrow></semantics></math>-axis voltage disturbance. (<b>a</b>) Artificially injected Doff and DC-drift estimation error, DM1, and DM2. (<b>b</b>) Speed and position estimation error, DM1, and DM2. (<b>c</b>) Observed speed estimation, DM1, and DM2. (<b>d</b>) Estimation fluxes and the errors of estimated fluxes, DM1, and DM2.</p>
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<p>Structure diagram of real-time simulation experimental system for IPMSM based on dSPACE.</p>
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<p>IPMSM experimental platform based on dSPACE.</p>
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<p>Experimental results of drift elimination strategy 1 with 300 RPM speed under the <math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math>-axis voltage disturbance (0 V and 0.6 V). (<b>a</b>) Artificially injected Doff and speed estimation; (<b>b</b>) flux estimation and its enlarged view; (<b>c</b>) angle estimation and its enlarger view; (<b>d</b>) angle and speed estimation errors.</p>
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<p>Experimental results of drift elimination strategy 2 with 300 RPM speed under the <math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math>-axis voltage disturbance (0.6 V and 0 V). (<b>a</b>) Artificially injected Doff and speed estimation; (<b>b</b>) flux estimation and its enlarged view; (<b>c</b>) angle estimation and its enlarger view; (<b>d</b>) angle and speed estimation errors.</p>
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<p>Experimental results of drift elimination strategy 1 with 300 RPM speed under the <math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math>-axis voltage disturbance (1.0 V to 1.5 V). (<b>a</b>) Artificially injected Doff and speed estimation; (<b>b</b>) flux estimation and its enlarged view; (<b>c</b>) angle estimation and its enlarger view; (<b>d</b>) angle and speed estimation errors.</p>
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<p>Experimental results of drift elimination strategy 2 with 300 RPM speed under the <math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math>-axis voltage disturbance. (<b>a</b>) Artificially injected Doff and speed estimation; (<b>b</b>) flux estimation and its enlarged view; (<b>c</b>) angle estimation and its enlarger view; (<b>d</b>) angle and speed estimation errors.</p>
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<p>Experimental results of drift elimination strategy 1 with 300 RPM speed under the <math display="inline"><semantics><mrow><mi>α</mi><mi>β</mi></mrow></semantics></math>-axis voltage disturbance. (<b>a</b>) Artificially injected Doff and speed estimation; (<b>b</b>) flux estimation and its enlarged view; (<b>c</b>) angle estimation and its enlarger view; (<b>d</b>) angle and speed estimation errors.</p>
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<p>Experimental results of drift elimination strategy 2 with 300 RPM speed under the <math display="inline"><semantics><mrow><mi>α</mi><mi>β</mi></mrow></semantics></math>-axis voltage disturbance. (<b>a</b>) Artificially injected Doff and speed estimation; (<b>b</b>) flux estimation and its enlarged view; (<b>c</b>) angle estimation and its enlarger view; (<b>d</b>) angle and speed estimation errors.</p>
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13 pages, 10232 KiB  
Article
Low-Cost Orientation Determination System for CubeSat Based Solely on Solar and Magnetic Sensors
by Yerkebulan Nurgizat, Abu-Alim Ayazbay, Dimitri Galayko, Gani Balbayev and Kuanysh Alipbayev
Sensors 2023, 23(14), 6388; https://doi.org/10.3390/s23146388 - 14 Jul 2023
Cited by 5 | Viewed by 3340
Abstract
CubeSats require accurate determination of their orientation relative to the Sun, Earth, and other celestial bodies to operate successfully and collect scientific data. This paper presents an orientation system based on solar and magnetic sensors that offers a cost-effective and reliable solution for [...] Read more.
CubeSats require accurate determination of their orientation relative to the Sun, Earth, and other celestial bodies to operate successfully and collect scientific data. This paper presents an orientation system based on solar and magnetic sensors that offers a cost-effective and reliable solution for CubeSat navigation. Solar sensors analyze the illumination on each face to measure the satellite’s orientation relative to the Sun, while magnetic sensors determine the Earth’s magnetic field vector in the satellite’s reference frame. By combining the measured data with the known ephemeris of the satellite, the satellite–Sun vector and the magnetic field orientation can be reconstructed. The orientation is expressed using quaternions, representing the rotation from the internal reference system of the satellite to the selected reference system. The proposed system demonstrates the ability to accurately determine the orientation of a CubeSat using only two sensors, making it suitable for installations where more complex and expensive instruments are impractical. Additionally, the paper presents a mathematical model of a low-cost CubeSat orientation system and a hardware implementation of the sensor. The technology, using solar and magnetic sensors, provides a reliable and affordable solution for CubeSat navigation, supporting the increasing sophistication of miniature payloads and enabling accurate satellite positioning in space missions. Full article
(This article belongs to the Section Electronic Sensors)
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<p>Architecture of the proposed CubeSat orientation system.</p>
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<p>Orientation system computation algorithm.</p>
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<p>Electrical circuit of the orientation system.</p>
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<p>Parts setup diagram for making a double-sided circuit board. (<b>a</b>) First side of the board; (<b>b</b>) second side of the board.</p>
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<p>The board is completed using a CNC machine. (<b>a</b>) Printed circuit board; (<b>b</b>) ready-made board with a microcontroller.</p>
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<p>Experimental study using Cubesat.</p>
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<p>Measurement of the cosine of the angle on one side of the CubeSat.</p>
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<p>The fall of a sunbeam on two sides of a satellite. (<b>a</b>) The same angles of incidence of the beam; (<b>b</b>) different angles of incidence of the beam.</p>
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<p>The fall of a sunbeam on three sides of a satellite. (<b>a</b>) The same angles of incidence of the beam; (<b>b</b>) different angles of incidence of the beam.</p>
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<p>1 experiment. The Sun’s rays fall on only two faces of the Cubesat.</p>
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<p>Sensor measurement error.</p>
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<p>Experiment 2. The Sun’s rays fall on the three faces of the CubeSat.</p>
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12 pages, 2448 KiB  
Article
Asymmetric Magneto-Optical Rotation in Magnetoplasmonic Nanocomposites
by Sergey Tomilin, Andrey Karavaynikov, Sergey Lyashko, Olga Tomilina, Vladimir Berzhansky, Alexey Gusev, Wolfgang Linert and Alexander Yanovsky
J. Compos. Sci. 2023, 7(7), 287; https://doi.org/10.3390/jcs7070287 - 13 Jul 2023
Cited by 2 | Viewed by 1455
Abstract
The results of the asymmetric magneto-optical rotation in the magnetoplasmonic nanocomposite study are presented. The asymmetry is observed in spectra of magneto-optical rotation when a magneto-optical medium with a plasmonic subsystem is magnetized along or against the radiation wave vector. The asymmetry is [...] Read more.
The results of the asymmetric magneto-optical rotation in the magnetoplasmonic nanocomposite study are presented. The asymmetry is observed in spectra of magneto-optical rotation when a magneto-optical medium with a plasmonic subsystem is magnetized along or against the radiation wave vector. The asymmetry is observed as vertical displacement of a magneto-optical hysteresis loop too. Such asymmetry is detected in magnetoplasmonic nanocomposite, which consists of a magneto-optical layer of Bi substituted iron-garnet intercalated with a plasmonic subsystem of gold self-assembled nanoparticles. It is shown that the physical reason for the asymmetric magneto-optical rotation is the manifestation of the Cotton–Mouton birefringence effect when the normal magnetization of the sample to a radiation wave vector appears due to the magnetic component of the electromagnetic field of resonating nanoparticles. This effect is additive to the basic magneto-optical Faraday Effect. Full article
(This article belongs to the Special Issue Feature Papers in Journal of Composites Science in 2023)
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<p>(<b>a</b>) SEM image of morphology of self-assembled gold nanoparticles, inset—size dispersion of Au nanoparticles (columns—experiment, curve—approximation by the Gaussian). (<b>b</b>) Change of garnet film thickness <span class="html-italic">h</span><sub>BiIG</sub> along the gradient, inset—the schematic structure of investigated nanocomposite GGG/Au<sub>(NP)</sub>/BiIG(<sub>grad</sub><span class="html-italic"><sub>h</sub></span><sub>)</sub>. (<b>c</b>) The scheme of a “half-shadow” technique for syntheses of gradient BiIG film.</p>
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<p>(<b>a</b>) Transmittance spectra of the GGG/Au<sub>(NP)</sub>/BiIG(<sub>grad</sub><span class="html-italic"><sub>h</sub></span><sub>)</sub> nanocomposite at different thickness of the BiIG layer (<span class="html-italic">h</span><sub>BiIG</sub> is indicated in the legend), inset—transmittance spectra of a GGG/Au gold film (before annealing) and self-assembled GGG/Au<sub>(NP)</sub> nanoparticles (after annealing); (<b>b</b>) the spectral position of various LPR modes along gradient at different thicknesses of garnet film <span class="html-italic">h</span><sub>BiIG</sub> [<a href="#B31-jcs-07-00287" class="html-bibr">31</a>].</p>
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<p>Magneto-optical rotation of the light polarization transmitted through 220 nm thick GGG/BiIG film without a plasmon subsystem (<b>a</b>) and through the GGG/Au<sub>(NP)</sub>/BiIG(<sub>grad</sub><span class="html-italic"><sub>h</sub></span><sub>)</sub> nanocomposite at different values of the thickness <span class="html-italic">h</span><sub>BiIG</sub>: (<b>b</b>) 220 nm; (<b>c</b>) 173 nm; (<b>d</b>) 150 nm; (<b>e</b>) 120 nm; (<b>f</b>) 85 nm. Samples were magnetized along the wave vector (<span class="html-italic">H</span>+) and against it (<span class="html-italic">H</span>−).</p>
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<p>(<b>a</b>) Spectral features of Faraday Effect in the GGG/Au<sub>(NP)</sub>/BiIG(<sub>grad</sub><span class="html-italic"><sub>h</sub></span><sub>)</sub> nanocomposite at different values of the BiIG layer thickness (<span class="html-italic">h</span><sub>BiIG</sub> is indicated in the legend); (<b>b</b>) Change of the factor η of the Faraday Effect enhancement as the function of the garnet layer thickness <span class="html-italic">h</span><sub>BiIG</sub> (due to different LPR modes) [<a href="#B31-jcs-07-00287" class="html-bibr">31</a>].</p>
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<p>(<b>a</b>) Spectra of asymmetric magneto-optical rotation (magneto-optical hysteresis loop displacement) ΔΘ(λ) in the magnetoplasmonic GGG/Au<sub>(NP)</sub>/BiIG(<sub>grad</sub><span class="html-italic"><sub>h</sub></span><sub>)</sub> nanocomposite at different values of the magneto-optical layer thickness <span class="html-italic">h</span><sub>BiIG</sub> (indicated in the legend). (<b>b</b>) Graphical comparative analysis of the spectral dependences ΔΘ(λ) and d<span class="html-italic">T</span>/dλ(λ) obtained at a magnetic layer thickness <span class="html-italic">h</span><sub>BiIG</sub> = 173 nm.</p>
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<p>Results of the analysis of magneto-optical hysteresis loops, which is obtained at different values of the incident radiation wavelength λ for the GGG/Au<sub>(NP)</sub>/BiIG(<sub>grad</sub><span class="html-italic"><sub>h</sub></span><sub>)</sub> sample with a thickness of <span class="html-italic">h</span><sub>BiIG</sub> = 90 nm. (<b>a</b>) Spectra of magneto-optical rotation in the fields <span class="html-italic">H</span>+ and <span class="html-italic">H</span>− (dashed line and the numbers show the spectral ranges where the magneto-optical hysteresis loop was studied, inset shows the corresponding view of magneto-optical hysteresis loop); (<b>b</b>–<b>d</b>) analysis of displacement and deformation of magneto-optical hysteresis loops Θ<span class="html-italic"><sub>i</sub></span> (<span class="html-italic">H</span>) (empty circles—measured loop, filled circles—corrected loop, line—corrective straight line).</p>
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