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Search Results (796)

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13 pages, 3689 KiB  
Article
The Structure and Near-Bottom Magnetic Anomaly Characteristics of the Daxi Vent Field on the Carlsberg Ridge, Northwestern Indian Ocean
by Puchen Zhao, Zhaocai Wu, Xiqiu Han, Yejian Wang, Jialing Zhang and Qiang Wang
J. Mar. Sci. Eng. 2025, 13(3), 488; https://doi.org/10.3390/jmse13030488 - 1 Mar 2025
Viewed by 185
Abstract
Seafloor hydrothermal vent areas are potential sources of polymetallic sulfide deposits and exhibit distinct mineralization structures under different tectonic settings. The Daxi Vent Field (DVF), located on the Carlsberg Ridge in the northwestern Indian Ocean, represents a basalt-hosted hydrothermal system. To investigate the [...] Read more.
Seafloor hydrothermal vent areas are potential sources of polymetallic sulfide deposits and exhibit distinct mineralization structures under different tectonic settings. The Daxi Vent Field (DVF), located on the Carlsberg Ridge in the northwestern Indian Ocean, represents a basalt-hosted hydrothermal system. To investigate the alteration zone structure of the DVF, high-resolution near-bottom bathymetric and magnetic data were collected during the Chinese DY57 expedition in 2019. Based on the results of magnetic anomaly data processing, including reduction to a level surface and Euler deconvolution, the location and depth of the magnetic sources were identified. In addition, two 2.5D magnetic forward models crossing the active and inactive vent fields were constructed. The results indicate that the range of the alteration zone in the active vent at the DVF extends up to 120 m in width and 80 m in depth, while the hydrothermal deposit at the extinct vent on the northeastern side extends up to 220 m along the ridge axis with a thickness of 30 m. Full article
(This article belongs to the Section Geological Oceanography)
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<p>(<b>a</b>) Bathymetric map of the survey area on the Carlsberg Ridge. (<b>b</b>) Location of the Daxi Vent Field (DVF). The bathymetric data were acquired using multibeam sonar during the Chinese DY24 expedition, with a resolution of 50 m. The white rectangle in panel (<b>b</b>) indicates the range of the near-bottom survey area conducted using the autonomous underwater vehicle (AUV).</p>
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<p>(<b>a</b>) Near-bottom bathymetric map of the DVF. (<b>b</b>) Near-bottom magnetic anomaly of the DVF. The white triangles in the central part of the map represent inactive hydrothermal vents and the black triangles indicate active hydrothermal vents. The track lines of the AUV are shown in the figure (black solid lines).</p>
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<p>Schematic diagram of the interpolation-iteration leveling method.</p>
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<p>(<b>a</b>) Leveling results across the active hydrothermal vent of the Central Mound; (<b>b</b>) leveling results across the inactive hydrothermal vent of the NE Mound. The Euler solutions are indicated in the figure.</p>
Full article ">Figure 4 Cont.
<p>(<b>a</b>) Leveling results across the active hydrothermal vent of the Central Mound; (<b>b</b>) leveling results across the inactive hydrothermal vent of the NE Mound. The Euler solutions are indicated in the figure.</p>
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<p>Magnetic susceptibility and NRM of the basalts from mid-ocean ridge hydrothermal and non-hydrothermal zones.</p>
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<p>Forward modeling of magnetic anomalies along profile aa′ (the location shown as the blue line in <a href="#jmse-13-00488-f002" class="html-fig">Figure 2</a>). (<b>a</b>) Observed and calculated magnetic anomalies; (<b>b</b>) magnetic structure and Euler solution distribution. In (<b>b</b>), the blue dots represent Euler solutions, the yellow region denotes altered basalt and massive sulfide deposits, the dark gray region represents fresh basalt from the hydrothermal field, the light gray region indicates basalt from non-hydrothermal areas, and the green region represents gabbro. The blue line represents the observation surface at 100 m above the seafloor. S denotes magnetic susceptibility (SI).</p>
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<p>Forward modeling of magnetic anomalies of the profile bb′ (profile location shown as the red line in <a href="#jmse-13-00488-f002" class="html-fig">Figure 2</a>). (<b>a</b>) Observed and calculated magnetic anomalies; (<b>b</b>) magnetic structure and Euler solution distribution. In (<b>b</b>), the blue dots represent Euler solutions, the yellow region represents hydrothermal sulfide deposits and the network of vein layers, the dark gray region represents fresh basalt from the hydrothermal field, the light gray region indicates basalt from non-hydrothermal areas, and the green region represents gabbro. The blue line represents the observation surface at 100 m above the seafloor. S denotes magnetic susceptibility (SI).</p>
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<p>Schematic cross-sectional diagram traversing both the Central Mound and NE Mound. The SW Mound, not directly intersected by the profile, is projected onto this plane.</p>
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10 pages, 554 KiB  
Article
Can the Solar Atmosphere Generate Very-High-Energy Cosmic Rays?
by Zaza N. Osmanov, D. Kuridze and Swadesh M. Mahajan
Symmetry 2025, 17(3), 366; https://doi.org/10.3390/sym17030366 - 28 Feb 2025
Viewed by 316
Abstract
The origin and acceleration of high-energy particles, constituting cosmic rays, is likely to remain an important topic in modern astrophysics. Among the two categories galactic and solar cosmic rays, the latter are much less investigated. The primary source of solar cosmic ray particles [...] Read more.
The origin and acceleration of high-energy particles, constituting cosmic rays, is likely to remain an important topic in modern astrophysics. Among the two categories galactic and solar cosmic rays, the latter are much less investigated. The primary source of solar cosmic ray particles are impulsive explosions of the magnetized plasma, known as solar flares and coronal mass ejections. These particles, however, are characterized by relatively low energies compared to their galactic counterparts. In this work, we explore the resonance wave–wave (RWW) interaction between the polarized electromagnetic radiation emitted by the solar active regions and the quantum waves associated with high-energy, relativistic electrons generated during solar flares. Mathematically, the RWW interaction problem boils down to analyzing a Klein–Gordon Equation (spinless electrons) embedded in the electromagnetic field. We find that RWW could accelerate the relativistic electrons to enormous energies even comparable to energies in the galactic cosmic rays. Full article
(This article belongs to the Section Physics)
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<p><b>Top left</b>: Image of the sunspot in G-band observed with the Daniel K. Inouye Solar Telescope (DKIST)/Visible Broadband Imager (VBI) on 16 October 2023 in active region NOAA 13645. White dotted lines mark area covered by ViSP spectral scan. <b>Top right</b>: DKIST/ViSP images of intensity (Stokes <span class="html-italic">I</span>) at 630.24 nm. Middle right: Full spectra of Fe <span class="html-small-caps">I</span> 630.1/630.2 nm lines along the slit position marked with blue dotted line in the <b>top right</b> panel. <b>Bottom panels</b>: A typical set of Fe Stokes <span class="html-italic">I</span> and <span class="html-italic">V</span> profiles of a pixel located in a sunspot umbra at 52′′, 14′′ in the <b>top right</b> image. The O<sub>2</sub> telluric line has been removed from the observed spectra.</p>
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<p>The plot of <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </semantics></math>. The set of parameters is: <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>630.2</mn> </mrow> </semantics></math> nm, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math> G, <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>t</mi> <mi>o</mi> <mi>k</mi> <mi>e</mi> <mi>s</mi> <mspace width="0.277778em"/> <mi>V</mi> <mo>/</mo> <msub> <mi>I</mi> <mi>c</mi> </msub> <mrow> <mo>[</mo> <mo>%</mo> <mo>]</mo> </mrow> <mo>=</mo> <mn>25</mn> </mrow> </semantics></math> (black); <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>854.2</mn> </mrow> </semantics></math> nm, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math> G, <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>t</mi> <mi>o</mi> <mi>k</mi> <mi>e</mi> <mi>s</mi> <mspace width="0.277778em"/> <mi>V</mi> <mo>/</mo> <msub> <mi>I</mi> <mi>c</mi> </msub> <mrow> <mo>[</mo> <mo>%</mo> <mo>]</mo> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (blue); <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>1074.6</mn> </mrow> </semantics></math> nm, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> G, <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>t</mi> <mi>o</mi> <mi>k</mi> <mi>e</mi> <mi>s</mi> <mspace width="0.277778em"/> <mi>V</mi> <mo>/</mo> <msub> <mi>I</mi> <mi>c</mi> </msub> <mrow> <mo>[</mo> <mo>%</mo> <mo>]</mo> </mrow> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (red); <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> MHz, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math> G, <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>t</mi> <mi>o</mi> <mi>k</mi> <mi>e</mi> <mi>s</mi> <mspace width="0.277778em"/> <mi>V</mi> <mo>/</mo> <msub> <mi>I</mi> <mi>c</mi> </msub> <mrow> <mo>[</mo> <mo>%</mo> <mo>]</mo> </mrow> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> (magenta).</p>
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<p>The plot of the synchrotron power versus the particle number density. The set of parameters is the same as in the previous figure.</p>
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18 pages, 7376 KiB  
Article
Smart Electronic Device-Based Monitoring of SAR and Temperature Variations in Indoor Human Tissue Interaction
by Filippo Laganà, Luigi Bibbò, Salvatore Calcagno, Domenico De Carlo, Salvatore A. Pullano, Danilo Pratticò and Giovanni Angiulli
Appl. Sci. 2025, 15(5), 2439; https://doi.org/10.3390/app15052439 - 25 Feb 2025
Viewed by 274
Abstract
The daily use of devices generating electric and magnetic fields has led to potential human overexposure in home and work environments. This paper assesses the possible effects of electric fields on human health at low and high frequencies. It presents an electronic monitoring [...] Read more.
The daily use of devices generating electric and magnetic fields has led to potential human overexposure in home and work environments. This paper assesses the possible effects of electric fields on human health at low and high frequencies. It presents an electronic monitoring device that captures the incidence of specific absorption rate (SAR) and temperature variation (∆T) on the human body. The system transmits data to a cloud platform, where a feedforward neural network (FFNN) processes the received information. SAR and surface temperature values are detected in an indoor environment, monitoring stationary and moving subjects. The results effectively assess temperature distribution due to electromagnetic fields. The prototype detected temperature peaks and high SAR values when the subjects remained motionless. Predictive analysis confirms the need for workplaces with materials shielding external electromagnetic signals and attenuating internal sources. Moderate mobile phone use could lower SAR and temperature values. Full article
(This article belongs to the Special Issue Robotics, IoT and AI Technologies in Bioengineering)
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<p>Scenario analysed in indoor environment—(<b>a</b>) body area monitored (head); (<b>b</b>) Wi-Fi source; (<b>c</b>) SAR sensors.</p>
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<p>Measurement environments: (<b>a</b>) stationary subject; (<b>b</b>) moving subject.</p>
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<p>Electric field limit values determined by ICNIRP and HHI for humans.</p>
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<p>Flowchart monitoring system.</p>
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<p>Monitoring board design for SAR and temperature variation signal acquisition.</p>
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<p>Feedforward neural network architecture.</p>
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<p>PCA: dimensionality reduction for SAR and temperature signals.</p>
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<p>Comparison between the SAR and temperature values measured by the device and the normative limits.</p>
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<p>Variation of SAR and temperature on tissues: (<b>a</b>) impact in an indoor environment; (<b>b</b>) impact of SAR on human tissue as the temperature changes.</p>
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<p>Impact of SAR on human tissue: (<b>a</b>) as temperature changes; (<b>b</b>) as source frequency changes.</p>
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<p>Temperature variation (Δ<span class="html-italic">T</span>) as a function of electromagnetic wave frequency (Hz) for a stationary subject at different distances from the source.</p>
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<p>SAR as a function of electromagnetic wave frequency (in GHz) for a subject exposed to electromagnetic sources located at three different distances: 0.5 m, 1.0 m, and 2.0 m.</p>
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<p>FFNN results: (<b>a</b>) true vs. predicted SAR values; (<b>b</b>) residuals distribution.</p>
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22 pages, 7032 KiB  
Article
Magnetic Excitation for Coupled Pendulum and Piezoelectric Wave Energy Harvester
by Wuwei Feng, Xiang Luo, Shujie Yang and Qingping Zou
Micromachines 2025, 16(3), 252; https://doi.org/10.3390/mi16030252 - 24 Feb 2025
Viewed by 239
Abstract
Wave energy is one of the most reliable and promising renewable energy sources that has attracted lots of attention, including piezoelectric wave energy harvesting devices. One of the challenges for piezoelectric wave power generation is the relatively low-frequency wave environments in the ocean. [...] Read more.
Wave energy is one of the most reliable and promising renewable energy sources that has attracted lots of attention, including piezoelectric wave energy harvesting devices. One of the challenges for piezoelectric wave power generation is the relatively low-frequency wave environments in the ocean. Magnetic excitations are one of the techniques used to overcome this issue. However, there is a lack of understanding of the mechanisms to maximize the electric power output of piezoelectric wave energy harvesters through magnetic excitations. In the present study, magnetic excitation experiments were conducted to investigate the power generation of a coupled spring pendulum piezoelectric energy harvester under various magnetic field conditions. Firstly, the mass of the load magnet that can induce the resonance phenomenon in piezoelectric elements was experimentally determined. Then, the power generation of piezoelectric elements was tested under different excitation magnetic spacings. Finally, the influence of different distribution patterns of excitation magnets on the performance of piezoelectric elements was tested. It was found that under the conditions of a load magnet mass of 2 g, excitation magnet spacing of 4 mm, and two excitation magnets stacked on the inner pendulum, optimum power generation of the piezoelectric wave harvester was achieved with a peak-to-peak output voltage of 39 V. The outcome of this study provides new insight for magnetic excitation devices for piezoelectric wave energy harvesting to increase the feasibility and efficiency of wave energy conversion to electrical energy. Full article
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<p>Layout of the coupled spring pendulum and wave energy piezoelectric harvester. 1—universal joint; 2—spring; 3—load magnet; 4—PZT-5H piezoelectric plate; 5—carbon fiber support rod; 6—square magnet carrier box; 7—excitation magnet; 8—five-way base.</p>
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<p>Schematic diagram of the magnetic excitation component.</p>
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<p>Diagram of the magnetic coupling nonlinear vibration system.</p>
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<p>Magnetic excitation experimental system, consisting of an external excitation system, magnetic excitation power generation system, and voltage signal acquisition system.</p>
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<p>(<b>a</b>) Power generation during free vibration of piezoelectric ceramic plates. (<b>b</b>) Spectrum of piezoelectric ceramic plate power generation during free vibration.</p>
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<p>Natural vibration frequency of piezoelectric ceramic plates vs. load magnet mass.</p>
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<p>Frequency spectra of piezoelectric ceramic plates with different load magnet masses under magnetic excitation. (<b>a</b>) For a loaded magnet mass of 2 g, the main vibration frequency of the piezoelectric ceramic plate was about 19 Hz. (<b>b</b>) For a magnet mass was 4 g, the main vibration frequency of the piezoelectric ceramic plate was about 14 Hz. (<b>c</b>) For a loaded magnet mass of 6 g, the main vibration frequency of the piezoelectric ceramic plate was about 12 Hz.</p>
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<p>Vibration frequencies of piezoelectric ceramic plates vs. load magnet mass under magnetic excitation.</p>
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<p>Comparison of the relationship between the natural frequency of the piezoelectric plate (black) and the vibration frequency of the piezoelectric plate with external magnetic excitation (red) under different load magnet masses.</p>
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<p>Voltage signals of piezoelectric ceramic plates under different distances between excitation and load magnets. (<b>a</b>) At an excitation magnet spacing of 1 mm, the piezoelectric plate showed the phenomenon of forced vibration. (<b>b</b>) At an excitation magnet spacing of 4 mm, the piezoelectric plate showed the phenomenon of vibration attenuation, which was close to free vibration. (<b>c</b>) At an excitation magnet spacing of 10 mm, the vibration attenuation of the piezoelectric plate became weaker.</p>
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<p>Maximum voltages of piezoelectric ceramic plates under different excitation magnet spacing.</p>
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<p>The main vibration frequency (blue) and voltage amplitude at resonance frequency (red) of piezoelectric ceramic plates under excitation magnet spacing of 1 to 10 mm.</p>
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<p>The relationship between the voltage amplitude at the resonance frequency of piezoelectric ceramic plates (red) and their peak-to-peak voltage (black) for magnet spacing of 1 to 10 mm.</p>
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<p>Excitation magnets arranged vertically in a single-row experiment.</p>
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<p>Voltage signals of piezoelectric ceramic plates with 1 to 6 excitation magnets stacked vertically in a row. (<b>a</b>) For 2 magnets, the piezoelectric plate showed the vibration attenuation, which was close to free vibration. (<b>b</b>) For 4 magnets, the vibration attenuation of the piezoelectric plate became weaker. (<b>c</b>) For 6 magnets, the vibration attenuation of the piezoelectric plate disappeared completely.</p>
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<p>Maximum voltage of piezoelectric ceramic plates under 1 to 6 stacked magnets.</p>
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<p>Excitation magnet array experiment.</p>
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<p>Voltage signals of piezoelectric ceramic plates under an array with 1 to 6 magnets. (<b>a</b>) When the number of magnets was 2, the piezoelectric plate showed the vibration attenuation. (<b>b</b>) When the number of magnets was 4, the vibration attenuation of the piezoelectric plate became weaker. (<b>c</b>) When the number of magnets was 6, the vibration attenuation of the piezoelectric plate disappeared completely.</p>
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<p>Maximum voltage of piezoelectric ceramic plates under an array with 1 to 6 magnets.</p>
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<p>Comparison of peak-to-peak voltage and amplitude at resonance frequency of the piezoelectric ceramic plate under an array or stacked with 1 to 6 excitation magnets.</p>
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19 pages, 7903 KiB  
Article
Fast Temperature Calculation Method for Spindle Servo Permanent Magnet Motors Under Full Operating Conditions Based on the Thermal Network Method
by Sheng Ma, Yijia Li, Xueyan Hao, Bo Zhang and Wei Feng
Electronics 2025, 14(4), 815; https://doi.org/10.3390/electronics14040815 - 19 Feb 2025
Viewed by 228
Abstract
In CNC machines, the temperature field analysis of spindle servo permanent magnet motors (SSPMMs) under rated load, overload, and weak magnetic conditions is critical for ensuring stable operation and machining accuracy. This paper proposes a temperature calculation method for SSPMMs based on the [...] Read more.
In CNC machines, the temperature field analysis of spindle servo permanent magnet motors (SSPMMs) under rated load, overload, and weak magnetic conditions is critical for ensuring stable operation and machining accuracy. This paper proposes a temperature calculation method for SSPMMs based on the thermal network method, which is used to quickly evaluate the temperature performance of SSPMMs under different operating conditions during design. This method can calculate the steady-state or transient temperature rise under different operating conditions. First, the electromagnetic performance and heat sources of the SSPMMs were analyzed. Then, based on the thermal network method, the equivalent thermal resistances and equivalent heat dissipation coefficients of the motor components were calculated. By iterating the heat balance equation or solving the heat conduction equation for different operating conditions, the temperature distribution of SSPMMs under different operating conditions was obtained. The accuracy of the thermal network model was validated through temperature analysis using fluid–structure interaction simulations and prototype testing. The results show that the relative error between the winding temperature calculated by the proposed equivalent thermal network model and the measured temperature under different operating conditions is less than 5%. This paper provides a theoretical basis for the thermal management of SSPMM, which can quickly and accurately evaluate the temperature rise in the motor during design. Full article
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<p>Structure of water-cooled 12-pole 54-slot SSPMM.</p>
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<p>Efficiency map of SSPMM.</p>
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<p>The thermal network structure of SSPMM.</p>
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<p>The sub-thermal network structure of SSPMM. (<b>a</b>) node 30; (<b>b</b>) node 8; (<b>c</b>) node 17.</p>
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<p>SSPMM temperature calculation flowchart based on thermal network method.</p>
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<p>Three-dimensional model of SSPMM. (<b>a</b>) Spiral waterway structure; (<b>b</b>) three-dimensional structure section view.</p>
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<p>Temperature distributions in SSPMM under rated condition: (<b>a</b>) stator; (<b>b</b>) stator winding; (<b>c</b>) permanent magnet; and (<b>d</b>) cooling water.</p>
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<p>Temperature distributions in SSPMM under high speed condition: (<b>a</b>) stator; (<b>b</b>) stator winding; (<b>c</b>) permanent magnet; and (<b>d</b>) cooling water.</p>
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<p>Prototype temperature test: (<b>a</b>) motor test system; (<b>b</b>) mechanical back-to-back test bench.</p>
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<p>Test temperature curves under rated conditions.</p>
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<p>Test temperature curves under overload condition.</p>
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19 pages, 27035 KiB  
Article
A Highly Stabilized Current Source Topology with Slope Compensation for a High-Power Microwave Guiding Coil
by Dandi Zhang, Hongfa Ding, Zhou He, Wentao Zhou and Ziqi Zhang
Electronics 2025, 14(4), 739; https://doi.org/10.3390/electronics14040739 - 13 Feb 2025
Viewed by 316
Abstract
For the waveguide coil in a High-Power Microwave (HPM) source, a strong repetitive Flat-top Pulsed Magnetic Field (FTPMF) is needed, which requires the power supply system to generate a high load current (3∼5 kA) with high stability (<1000 ppm) and a long pulse-width [...] Read more.
For the waveguide coil in a High-Power Microwave (HPM) source, a strong repetitive Flat-top Pulsed Magnetic Field (FTPMF) is needed, which requires the power supply system to generate a high load current (3∼5 kA) with high stability (<1000 ppm) and a long pulse-width (15∼20 ms). To achieve this, this article proposes a novel topology which includes a capacitor bank as the main power supply to guarantee a long pulse-width, combined with an active current compensator to regulate the load current precisely. A PI control scheme with slope compensation is used to solve the current fluctuation caused by capacitor switching. The novel topology also features a fast rising and falling time, thus it is suitable for repetitive working applications. The parameters of the topology are calculated by analysis to guarantee the working condition of a 45 GHz HPM source, and the operating principle of this topology is verified through low-power-scale experiments. Full article
(This article belongs to the Special Issue Advances in Pulsed-Power and High-Power Electronics)
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<p>Normalized current waveforms of different schemes.</p>
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<p>Schematic of the optimized SFPFN.</p>
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<p>Current waveform of the optimized SFPFN.</p>
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<p>Schematic of the proposed power supply topology for an HPM.</p>
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<p>Theoretical load current waveform and output voltage.</p>
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<p>State trajectory of the proposed topology.</p>
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<p>Equivalent circuits of rise mode.</p>
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<p>Equivalent circuits of flat-top mode.</p>
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<p>Simplified equivalent circuit when studying the current fluctuation of the main power supply.</p>
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<p>Sketch of waveforms of the main power supply.</p>
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<p>Equivalent circuits of fall mode.</p>
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<p>Simplified equivalent circuit when studying the ripple of the output current of the ACC.</p>
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<p>Sketch of the change rate of <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>A</mi> <mi>C</mi> <mi>C</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Situation when the iACC has the theoretical maximum amount of fluctuation.</p>
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<p>Diagram of the closed-loop control system.</p>
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<p>Sketch of the <math display="inline"><semantics> <msub> <mi>I</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>I</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </semantics></math> with slope compensation.</p>
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<p>Sketch of <math display="inline"><semantics> <msub> <mi>i</mi> <mrow> <mi>A</mi> <mi>C</mi> <mi>C</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>I</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>i</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> with slope compensation.</p>
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<p>Waveforms of the simulation result for the optimized SFPFN.</p>
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<p>Waveforms of the simulation result for the proposed topology.</p>
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<p>Details of the load current waveform using the PI controller only.</p>
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<p>Details of the load current waveform using the PI controller with the voltage feed-forward.</p>
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<p>Details of the load current waveform using the PI controller with slope compensation.</p>
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<p>The schematic diagram of the experimental platform.</p>
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<p>The prototype low-power experimental platform.</p>
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<p>Experimental waveforms of <math display="inline"><semantics> <msub> <mi mathvariant="normal">I</mi> <mrow> <mi>l</mi> <mi>o</mi> <mi>a</mi> <mi>d</mi> </mrow> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi mathvariant="normal">I</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="normal">I</mi> <mrow> <mi>A</mi> <mi>C</mi> <mi>C</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Details of <math display="inline"><semantics> <msub> <mi>I</mi> <mrow> <mi>l</mi> <mi>o</mi> <mi>a</mi> <mi>d</mi> </mrow> </msub> </semantics></math> using the conventional PI control scheme.</p>
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<p>Details of <math display="inline"><semantics> <msub> <mi>I</mi> <mrow> <mi>l</mi> <mi>o</mi> <mi>a</mi> <mi>d</mi> </mrow> </msub> </semantics></math> using the PI control scheme with slope compensation.</p>
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23 pages, 12381 KiB  
Article
Structural Design and Vibration Suppression Characteristics Analysis of Semi-Active Eddy Current Damping Seat
by Shaofeng Wu, Xiaoming Zhou, Hongrui Xu and Puwei Mu
Appl. Sci. 2025, 15(4), 1811; https://doi.org/10.3390/app15041811 - 10 Feb 2025
Viewed by 409
Abstract
As components in direct contact with drivers and passengers in complex and challenging road conditions, automotive seats need to effectively absorb and isolate vibrations from the automotive chassis to minimize any adverse effects on the human body. In response to the issue of [...] Read more.
As components in direct contact with drivers and passengers in complex and challenging road conditions, automotive seats need to effectively absorb and isolate vibrations from the automotive chassis to minimize any adverse effects on the human body. In response to the issue of inadequate vibration isolation within multiple frequency bands for car seats, which can lead to discomfort for passengers, a vibration-damping seat structure equipped with an eddy current damper using electromagnets as the magnetic field source is proposed, and its vibration suppression characteristics are studied. First, a semi-active suspension damping structure is designed based on an eddy current damping effect. Second, the theoretical model of the semi-active suspension damping structure based on an eddy current effect is established, and the characteristic parameters of adjustable damping and their relationship with the amplitude response are analyzed. Finally, electromagnetic simulation analysis is conducted, and the results are compared with the theoretical model analysis results to verify the analysis, and the vibration suppression law of the semi-active suspension damping structure based on an eddy current effect is explored. Full article
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<p>The structure schematic diagram of the eddy current damping seat model.</p>
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<p>Arrangement of eddy current damping module.</p>
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<p>Model of an eddy current damping structure with single degree of freedom.</p>
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<p>Schematic diagram of eddy current damping.</p>
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<p>The amplitude response at 60 kg in theoretical model.</p>
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<p>The amplitude response at 70 kg in theoretical model.</p>
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<p>The amplitude response at 80 kg in theoretical model.</p>
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<p>The amplitude response at 90 kg in theoretical model.</p>
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<p>The amplitude response at 100 kg in theoretical model.</p>
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<p>Amplitude response at different loads in theoretical model.</p>
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<p>Simplified model of eddy current damping system.</p>
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<p>Finite element model of 2D electromagnetic field for eddy current damping system.</p>
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<p>Amplitude response at different loads in simulation model.</p>
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<p>The amplitude response at 60 kg in simulation model.</p>
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<p>The amplitude response at 70 kg in simulation model.</p>
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<p>The amplitude response at 80 kg in simulation model.</p>
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<p>The amplitude response at 90 kg in simulation model.</p>
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<p>The amplitude response at 100 kg in simulation model.</p>
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<p>Comparison of amplitude response with or without eddy current damping at 4 Hz.</p>
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<p>Comparison of amplitude response with or without eddy current damping at 8 Hz.</p>
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<p>The eddy damping force response at different loads.</p>
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<p>Magnetic potential value at 60 kg.</p>
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<p>Magnetic potential value at 70 kg.</p>
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<p>Magnetic potential value at 80 kg.</p>
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<p>Magnetic potential value at 90 kg.</p>
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<p>Magnetic potential value at 100 kg.</p>
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<p>Comparison of amplitude response at 60 kg.</p>
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<p>Comparison of amplitude response at 70 kg.</p>
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<p>Comparison of amplitude response at 80 kg.</p>
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<p>Comparison of amplitude response at 90 kg.</p>
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<p>Comparison of amplitude response at 100 kg.</p>
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13 pages, 5350 KiB  
Article
Cosmic Ray Spectra and Anisotropy in an Anisotropic Propagation Model with Spiral Galactic Sources
by Aifeng Li, Zhaodong Lv, Wei Liu, Yiqing Guo and Fangheng Zhang
Universe 2025, 11(2), 53; https://doi.org/10.3390/universe11020053 - 7 Feb 2025
Viewed by 400
Abstract
In our previous work, we investigated the spectra and anisotropy of galactic cosmic rays (GCRs) under the assumption of an axisymmetric distribution of galactic sources. Currently, much observational evidence indicates that the Milky Way is a typical spiral galaxy. In this work, we [...] Read more.
In our previous work, we investigated the spectra and anisotropy of galactic cosmic rays (GCRs) under the assumption of an axisymmetric distribution of galactic sources. Currently, much observational evidence indicates that the Milky Way is a typical spiral galaxy. In this work, we further utilize an anisotropic propagation model under the framework of spiral distribution sources to study spectra and anisotropy. During the calculation process, we adopt the spatial-dependent propagation (SDP) model, while incorporating the contribution from the nearby Geminga source and the anisotropic diffusion of cosmic rays (CRs) induced by the local regular magnetic field (LRMF). By comparing the results of background sources with spiral and axisymmetric distribution models, it is found that both of them can well reproduce the CR spectra and anisotropy. However, there exist differences in their propagation parameters. The diffusion coefficient with spiral distribution is larger than that with axisymmetric distribution, and its spectral indices are slightly harder. To investigate the effects of a nearby Geminga source and LRMF on anisotropy, two-dimensional (2D) anisotropy sky maps under various contributing factors are compared. Below 100 TeV, the anisotropy is predominantly influenced by both the nearby Geminga source and the LRMF, causing the phase to align with the direction of the LRMF. Above 100 TeV, the background sources become dominant, resulting in the phase pointing towards the Galactic Center (GC). Future high-precision measurements of CR anisotropy and spectra, such as the LHAASO experiment, will be crucial in evaluating the validity of our proposed model. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2025—Space Science)
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<p>Fitting to the B/C ratio of the model prediction. The B/C data points are taken from the AMS-02 experiment [<a href="#B66-universe-11-00053" class="html-bibr">66</a>,<a href="#B67-universe-11-00053" class="html-bibr">67</a>].</p>
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<p>Energy spectra of protons (<b>left</b>) and helium nuclei (<b>right</b>) multiplied by <math display="inline"><semantics> <msup> <mrow> <mi>E</mi> </mrow> <mrow> <mn>2.6</mn> </mrow> </msup> </semantics></math>. The dashed blue and red dash-dotted lines are the background fluxes and the fluxes from a nearby Geminga SNR source, respectively. The black solid lines represent the total fluxes. The data points are taken from DAMPE [<a href="#B7-universe-11-00053" class="html-bibr">7</a>,<a href="#B9-universe-11-00053" class="html-bibr">9</a>], AMS-02 [<a href="#B5-universe-11-00053" class="html-bibr">5</a>,<a href="#B6-universe-11-00053" class="html-bibr">6</a>], CREAM-III [<a href="#B10-universe-11-00053" class="html-bibr">10</a>], CALET [<a href="#B12-universe-11-00053" class="html-bibr">12</a>], KASCADE [<a href="#B68-universe-11-00053" class="html-bibr">68</a>], and KASCADE-Grande [<a href="#B69-universe-11-00053" class="html-bibr">69</a>], respectively.</p>
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<p>The all-particle spectra multiplied by <math display="inline"><semantics> <msup> <mi>E</mi> <mrow> <mn>2.6</mn> </mrow> </msup> </semantics></math>. The data points are taken from reference [<a href="#B70-universe-11-00053" class="html-bibr">70</a>]. The solid lines with different colors represent the model predictions of different mass groups, while the black solid line is the total contribution.</p>
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<p>Energy dependences of the amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mn>1</mn> </msub> </semantics></math> (<b>left</b>) and phase <math display="inline"><semantics> <msub> <mi>α</mi> <mn>1</mn> </msub> </semantics></math> (<b>right</b>) of the dipole anisotropies. The data points are taken from MACRO [<a href="#B71-universe-11-00053" class="html-bibr">71</a>], Super-Kamiokande [<a href="#B23-universe-11-00053" class="html-bibr">23</a>], EAS-TOP [<a href="#B33-universe-11-00053" class="html-bibr">33</a>,<a href="#B72-universe-11-00053" class="html-bibr">72</a>], Milagro [<a href="#B25-universe-11-00053" class="html-bibr">25</a>], IceCube [<a href="#B26-universe-11-00053" class="html-bibr">26</a>,<a href="#B28-universe-11-00053" class="html-bibr">28</a>,<a href="#B30-universe-11-00053" class="html-bibr">30</a>], IceTop [<a href="#B29-universe-11-00053" class="html-bibr">29</a>], ARGO [<a href="#B32-universe-11-00053" class="html-bibr">32</a>], Tibet [<a href="#B21-universe-11-00053" class="html-bibr">21</a>,<a href="#B22-universe-11-00053" class="html-bibr">22</a>,<a href="#B73-universe-11-00053" class="html-bibr">73</a>], KASCADE-Grande [<a href="#B34-universe-11-00053" class="html-bibr">34</a>,<a href="#B35-universe-11-00053" class="html-bibr">35</a>] HAWC [<a href="#B36-universe-11-00053" class="html-bibr">36</a>], and HAWC-IceCube [<a href="#B37-universe-11-00053" class="html-bibr">37</a>].</p>
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<p>Two-dimensional anisotropy maps, as a function of right ascension RA and declination DEC, at 10 TeV (<b>up</b>) and 3 PeV (<b>bottom</b>), respectively, i.e., BK (<b>left</b>), BK + Geminga (<b>middle</b>), and BK + Geminga + LRMF (<b>right</b>). The gray circles indicate the GC and galactic anticenter (GAC) directions, and the dark blue square represents the Geminga source, while the black triangle indicates the magnetic field direction measured by IBEX [<a href="#B64-universe-11-00053" class="html-bibr">64</a>].</p>
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18 pages, 10824 KiB  
Article
Pattern-Reconfigurable, Vertically Polarized, Wideband Electrically Small Huygens Source Antenna
by Yunlu Duan, Ming-Chun Tang, Mei Li, Zhehao Zhang, Qingli Lin and Richard W. Ziolkowski
Electronics 2025, 14(3), 634; https://doi.org/10.3390/electronics14030634 - 6 Feb 2025
Viewed by 466
Abstract
A pattern-reconfigurable, vertically polarized (VP), electrically small (ES), Huygens source antenna (HSA) is demonstrated. A custom-designed reconfigurable inverted-F structure is embedded in a hollowed-out cylindrical dielectric resonator (DR). It radiates VP electric dipole fields that excite the DR’s HEM11δ mode, which in [...] Read more.
A pattern-reconfigurable, vertically polarized (VP), electrically small (ES), Huygens source antenna (HSA) is demonstrated. A custom-designed reconfigurable inverted-F structure is embedded in a hollowed-out cylindrical dielectric resonator (DR). It radiates VP electric dipole fields that excite the DR’s HEM11δ mode, which in turn acts as an orthogonal magnetic dipole radiator. The HSA’s unidirectional properties are thus formed. It becomes low-profile and electrically small through a significant lowering of its operational frequency band by loading the DR’s top surface with a metallic disk. The entire 360° azimuth range is covered by each of the HSA’s four 90° reconfigurable states, emitting a unidirectional wide beam. A prototype was fabricated and tested. The measured results, which are in good agreement with their simulated values, demonstrate that the developed wideband Huygens source antenna, with its 0.085 λL low profile and its 0.20 λL × 0.20 λL compact transverse dimensions, hence, electrically small size with ka = 0.89, exhibits a wide 14.1% fractional impedance bandwidth and a 6.1 dBi peak realized gain in all four of its pattern-reconfigurable states. Full article
(This article belongs to the Special Issue Antennas for IoT Devices)
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<p>Basic electric (E) and magnetic (H) field principles of a VP Huygens source antenna: (<b>a</b>) <span class="html-italic">E</span>-plane and (<b>b</b>) <span class="html-italic">H</span>-plane. Labels: E = electric, M = magnetic, H = Huygens.</p>
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<p>DR-based VP HSA configuration.</p>
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<p>Simulated responses of the DR-based VP HSA: (<b>a</b>) S-parameters; (<b>b</b>) Radiation patterns in the <span class="html-italic">E</span>-plane (<span class="html-italic">yz</span>-plane); and (<b>c</b>) <span class="html-italic">H</span>-plane (<span class="html-italic">xy</span>-plane) at the resonance frequency 1.85 GHz.</p>
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<p>Simulated model and field distributions of the horizontal-strip dipole excited DRA: (<b>a</b>) antenna configuration; (<b>b</b>) <span class="html-italic">E</span>-field on the <span class="html-italic">yz</span>-plane within the DRA; and (<b>c</b>) <span class="html-italic">H</span>-field on the <span class="html-italic">zx</span>-plane within the DRA.</p>
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<p>Simulated radiation patterns of the horizontal dipole strip-excited DRA: (<b>a</b>) <span class="html-italic">E</span>-plane (<span class="html-italic">yz</span>-plane); (<b>b</b>) and <span class="html-italic">H</span>-plane (<span class="html-italic">xy</span>-plane).</p>
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<p>Simulation model of the concentric-monopole excited DR antenna and its predicted radiation patterns: (<b>a</b>) configuration; (<b>b</b>) <span class="html-italic">E</span>-plane (<span class="html-italic">yz</span>-plane); and (<b>c</b>) <span class="html-italic">H</span>-plane (<span class="html-italic">xy</span>-plane).</p>
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<p>Configuration of the single-port-fed wideband DR-based VP HSA.</p>
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<p>The components of the single-port-fed wideband DR-based VP HSA together with their corresponding radiation patterns.</p>
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<p>Simulated reflection coefficient of the wideband HSA, Ant II, and the 3D-realized gain patterns at its two resonance frequencies.</p>
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<p>Configurations and simulated |S<sub>11</sub>| values as functions of the source frequency for Ant. I, Ant. II, and Ant. III.</p>
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<p>The equivalent circuit model of Ant. III and the corresponding physical structures in it.</p>
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<p>Pattern-reconfigurable DR-based VP HAS: (<b>a</b>) working principle schematic diagrams; and (<b>b</b>) corresponding radiation patterns in the vertical planes (<b>left</b>) and horizontal plane (<b>right</b>).</p>
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<p>Configuration of the pattern-reconfigurable DR-based VP ESA: (<b>a</b>) 3-D isometric view; and (<b>b</b>) its reconfigurable inverted-F structure.</p>
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<p>Simulated |S<sub>11</sub>| curves for different positions of the shorting pins.</p>
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<p>Simulated |S<sub>11</sub>| values together with the radiation patterns at the second resonance frequency for different top-hat sizes.</p>
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<p>Simulated |S<sub>11</sub>| values together with the radiation patterns at the second resonance frequency for different side-lengths of the square ground plane.</p>
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<p>Fabricated prototype. (<b>a</b>) AUT in the chamber; (<b>b</b>) reconfigurable 3D-inverted-F structure; And (<b>c</b>) state control structure with its DC biasing lines.</p>
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<p>Simulated and measured |S<sub>11</sub>| values together with the 3-D radiation patterns of the ES pattern-reconfigurable VP HSA in each of its four states.</p>
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<p>The corresponding measured and simulated (<b>a</b>) realized gain and (<b>b</b>) OE values of the antenna in each of its four states.</p>
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<p>The corresponding measured and simulated 2D and radiation patterns in each of its four states at 1.4 GHz: (<b>a</b>) State-1; (<b>b</b>) State-2; (<b>c</b>) State-3; and (<b>d</b>) State-4.</p>
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14 pages, 6296 KiB  
Article
Enhanced Coercivity and Tb Distribution Optimization of Sintered Nd-Fe-B Magnets by TbF3 Grain Boundary Diffusion Facilitated by Ga
by Ling Wang, Wenjiao Li, Xiaopeng Wang, Zejun Deng and Shujuan Gao
Molecules 2025, 30(3), 594; https://doi.org/10.3390/molecules30030594 - 28 Jan 2025
Viewed by 653
Abstract
The grain boundary diffusion process employing a mixed diffusion source, comprising heavy rare-earth elements and low-melting metals, significantly enhances the coercivity (Hcj) of sintered Nd-Fe-B magnets. In the present study, Tb and Ga were deposited onto the surface of Nd-Fe-B magnets [...] Read more.
The grain boundary diffusion process employing a mixed diffusion source, comprising heavy rare-earth elements and low-melting metals, significantly enhances the coercivity (Hcj) of sintered Nd-Fe-B magnets. In the present study, Tb and Ga were deposited onto the surface of Nd-Fe-B magnets to serve as a diffusion source for improving hard magnetic properties. The effects of varying deposition sequences of Tb and Ga on the magnetic properties and microstructure of the magnets were analyzed. The findings demonstrate that TbF3 grain boundary diffusion facilitated by Ga effectively increases the efficiency of Tb substitution, leading to enhanced coercivity. When Tb and Ga are deposited simultaneously, coercivity shows a notable improvement of 53.15% compared to the untreated magnet, with no reduction in remanence. Additionally, thermal stability is enhanced, resulting in superior overall magnetic properties. Microstructural analysis reveals that Ga promotes the diffusion of Tb into the magnet. In the magnet where Tb and Ga are co-deposited, the formation of a thinner and more uniform (Nd,Tb)2Fe14B shell–core structure, along with the greater infiltration depth of Tb, leads to a broader distribution of core–shell structures within the magnet. This effectively increases the anisotropy fields (HA) of the main phase grains, preventing the nucleation of antiferromagnetic domains at the edges of main-phase grains, thereby enhancing coercivity. Furthermore, the corrosion resistance of the magnet subjected to mixed diffusion is improved. This study provides a foundation for producing highly efficient magnets with a lower content of heavy rare-earth elements. The simplicity and flexibility of the process make it highly suitable for industrial applications. Full article
(This article belongs to the Special Issue Electroanalysis of Biochemistry and Material Chemistry—2nd Edition)
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<p>(<b>a</b>) Demagnetization curves of the original magnet, Tb magnet, Tb/Ga magnet, Ga/Tb magnet and Tb-Ga magnet at 298 K. (<b>b</b>) The histogram of the magnetic properties.</p>
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<p>The temperature dependence for the B<sub>r</sub> (<b>a</b>) and H<sub>cj</sub> (<b>b</b>) of the original magnet and Tb-Ga magnet at the temperature range of 20–140 °C.</p>
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<p>The dependence of H<sub>cj</sub>/M<sub>s</sub> vs. <span class="html-italic">H</span><sub>A</sub>/M<sub>s</sub> of the original magnet and Tb-Ga magnet.</p>
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<p>EPMA mappings of Tb in the 0–80 μm diffusion region for the Tb magnet (<b>a</b>), Tb/Ga magnet (<b>b</b>), Ga/Tb magnet (<b>c</b>), and Tb-Ga magnet (<b>d</b>).</p>
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<p>Cross-sectional BSE-SEM images of the Tb magnet (<b>a1,a2</b>), Tb/Ga magnet (<b>b1,b2</b>), Ga/Tb magnet (<b>c1,c2</b>), and Tb-Ga magnet (<b>d1,d2</b>). (<b>e</b>) Concentration profiles of line scanning in (<b>b</b>). (<b>f</b>) Concentration profiles of line scanning in (<b>c</b>).</p>
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<p>(<b>a</b>) XRD patterns of the different magnets. (<b>b</b>) The enlarged patterns in the range of 36~40°.</p>
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<p>(<b>a</b>) Potentiodynamic polarization curves of the original magnet and Tb-Ga magnet, (<b>b</b>) Nyquist and (<b>c</b>) Bode plots of the original magnet and Tb-Ga magnet in a 3.5 wt.% NaCl aqueous solution.</p>
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<p>Schematic diagrams of GBD process of (<b>a</b>) Tb magnet, (<b>b</b>) Tb/Ga magnet, (<b>c</b>) Ga/Tb magnet and (<b>d</b>) Tb-Ga magnet.</p>
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28 pages, 451 KiB  
Article
Magnetohyrodynamic Turbulence in a Spherical Shell: Galerkin Models, Boundary Conditions, and the Dynamo Problem
by John V. Shebalin
Fluids 2025, 10(2), 24; https://doi.org/10.3390/fluids10020024 - 23 Jan 2025
Viewed by 563
Abstract
The ‘dynamo problem’ requires that the origin of the primarily dipole geomagnetic field be found. The source of the geomagnetic field lies within the outer core of the Earth, which contains a turbulent magnetofluid whose motion is described by the equations of magnetohydrodynamics [...] Read more.
The ‘dynamo problem’ requires that the origin of the primarily dipole geomagnetic field be found. The source of the geomagnetic field lies within the outer core of the Earth, which contains a turbulent magnetofluid whose motion is described by the equations of magnetohydrodynamics (MHD). A mathematical model can be based on the approximate but essential features of the problem, i.e., a rotating spherical shell containing an incompressible turbulent magnetofluid that is either ideal or real but maintained in an equilibrium state. Galerkin methods use orthogonal function expansions to represent dynamical fields, with each orthogonal function individually satisfying imposed boundary conditions. These Galerkin methods transform the problem from a few partial differential equations in physical space into a huge number of coupled, non-linear ordinary differential equations in the phase space of expansion coefficients, creating a dynamical system. In the ideal case, using Dirichlet boundary conditions, equilibrium statistical mechanics has provided a solution to the problem. As has been presented elsewhere, the solution also has relevance to the non-ideal case. Here, we examine and compare Galerkin methods imposing Neumann or mixed boundary conditions, in addition to Dirichlet conditions. Any of these Galerkin methods produce a dynamical system representing MHD turbulence and the application of equilibrium statistical mechanics in the ideal case gives solutions of the dynamo problem that differ only slightly in their individual sets of wavenumbers. One set of boundary conditions, Neumann on the outer and Dirichlet on the inner surface, might seem appropriate for modeling the outer core as it allows for a non-zero radial component of the internal, turbulent magnetic field to emerge and form the geomagnetic field. However, this does not provide the necessary transition of a turbulent MHD energy spectrum to match that of the surface geomagnetic field. Instead, we conclude that the model with Dirichlet conditions on both the outer and the inner surfaces is the most appropriate because it provides for a correct transition of the magnetic field, through an electrically conducting mantle, from the Earth’s outer core to its surface, solving the dynamo problem. In addition, we consider how a Galerkin model velocity field can satisfy no-slip conditions on solid boundaries and conclude that some slight, kinetically driven compressibility must exist, and we show how this can be accomplished. Full article
(This article belongs to the Section Geophysical and Environmental Fluid Mechanics)
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<p>(Colour online) A comparison: International Geomagnetic Reference Field (IGRF) [<a href="#B83-fluids-10-00024" class="html-bibr">83</a>] spectra <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for the year 2020 at the Earth’s surface, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mi>e</mi> </msub> </mrow> </semantics></math>, and projected down to the CMB, <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mi mathvariant="normal">o</mi> </msub> </mrow> </semantics></math>, with a spectrum that takes into account mantle electrical conductivity, i.e., <math display="inline"><semantics> <mrow> <msubsup> <mi>R</mi> <mi>n</mi> <mi mathvariant="normal">o</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> from reference [<a href="#B59-fluids-10-00024" class="html-bibr">59</a>]. Also shown is the region where Kolmogorov turbulent spectra <math display="inline"><semantics> <msup> <mi>k</mi> <mrow> <mo>−</mo> <mn>5</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </semantics></math> might be expected to appear, the region being bounded by using <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>l</mi> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>l</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math>, where the first ten values of each are shown in <a href="#fluids-10-00024-t001" class="html-table">Table 1</a>. For more details concerning <math display="inline"><semantics> <mrow> <msubsup> <mi>R</mi> <mi>n</mi> <mi mathvariant="normal">o</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math>, please see <a href="#sec9dot2-fluids-10-00024" class="html-sec">Section 9.2</a>.</p>
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18 pages, 6886 KiB  
Article
Single-Stage Power Converter for Magnetic Field Energy Harvesting to Achieve Self-Powered Smart Grid IoT Devices
by Antonio-Miguel Muñoz-Gómez, María Menéndez-Marín, Javier Ballestín-Fuertes and José-Francisco Sanz-Osorio
Electronics 2025, 14(3), 415; https://doi.org/10.3390/electronics14030415 - 21 Jan 2025
Viewed by 850
Abstract
Energy harvesting technologies are becoming increasingly popular as potential sources of energy for Internet of Things (IoT) devices. Magnetic field energy harvesting (MFEH) from current-carrying components, such as power cables, represents a particularly promising technology for smart grid, infrastructure, and environmental monitoring applications. [...] Read more.
Energy harvesting technologies are becoming increasingly popular as potential sources of energy for Internet of Things (IoT) devices. Magnetic field energy harvesting (MFEH) from current-carrying components, such as power cables, represents a particularly promising technology for smart grid, infrastructure, and environmental monitoring applications. This paper presents a single-stage AC/DC power converter, a control architecture, and an energy harvester design applicable to MFEH devices. The power converter consists of a MOSFET full bridge that is used to actively rectify the induced voltage at the transceiver while providing a regulated output voltage. The approach is suitable for a broad range of grid power lines, offering a compact power stage that achieves a reduction in component count while active rectification minimizes energy losses, thereby improving thermal management in power electronics compared with the previous research. The experimental results demonstrate that the power converter provides a stable energy source and offers an alternative to self-powering smart grid IoT devices. Full article
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<p>Magnetic field energy harvester comprising a ferromagnetic core and secondary coil situated within a power line.</p>
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<p>Single-stage MOSFET H-bridge converter with voltage and current measurements for control loop and magnetic field energy harvesting diagram.</p>
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<p>Block diagram of DC bus voltage control scheme in MFEH.</p>
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<p>DC voltage regulator forces a secondary coil short-circuit in the energy harvester to impede any further energy harvesting and prevent overvoltage in DC bus.</p>
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<p>Active rectifier mode operating the corresponding top and bottom MOSFETs in the H-bridge for each positive (<b>a</b>) and negative (<b>b</b>) half-cycle for the active rectification of the voltage from MFEH.</p>
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<p>Simulation diagram of the power converter and control architecture.</p>
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<p>Simulation results for the initial transient of the induced voltage on the MFEH transducer (yellow), the DC bus voltage (blue), and the comparators switching signals of the MOSFETs (green, red, and purple, active at 1).</p>
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<p>Simulation results for the steady state of the induced voltage on the MFEH transducer (yellow), the DC bus voltage ripple (blue), and the comparators switching signals of the MOSFETs (green, red, and purple, active at 1).</p>
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<p>Finite element magnetic simulation of the MFEH transducer with a 60 A power line: (<b>a</b>) with the secondary short-circuited; (<b>b</b>) with the secondary open-circuited; (<b>c</b>) at the maximum power point.</p>
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<p>Power harvested by the MFEH with 50 Hz and 0–600 A primary currents: (<b>a</b>) for different DC voltages; and (<b>b</b>) at maximum power point currents.</p>
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<p>Family of B-H loops (hysteresis loops) and boundaries regions measured at 50 Hz, for a toroidal sample selected of grain-oriented electrical steel.</p>
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<p>Laboratory test bench equipped with MFEH consisting of a transducer and a single-stage AC/DC converter connected to an emulated power line.</p>
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<p>Laboratory measurements of the induced voltage on the MFEH transducer (yellow), the DC bus voltage (blue) and the MOSFET switching signals of the bottom MOSFETs (red and green, active at 0 V) emulating a current of 5% of the maximum power line current (30 A).</p>
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<p>Laboratory measurements of the induced voltage on the MFEH transducer (yellow), the DC bus voltage (blue) and the MOSFET switching signals of the bottom MOSFETs (red and green, active at 0 V) emulating a current of 10% of the maximum power line current (60 A).</p>
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<p>Laboratory measurements of the induced voltage on the MFEH transducer (yellow), the DC bus voltage (blue) and the MOSFET switching signals of the bottom MOSFETs (red and green, active at 0 V) emulating a current of 50% of the maximum power line current (300 A).</p>
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<p>Laboratory measurements of the induced voltage on the MFEH transducer (yellow), the DC bus voltage (blue) and the MOSFET switching signals of the bottom MOSFETs (red and green, active at 0 V) emulating the maximum power line current (600 A).</p>
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11 pages, 423 KiB  
Review
Illuminating the Shadows: Innovation in Advanced Imaging Techniques for Myeloma Precursor Conditions
by Kara I. Cicero, Rahul Banerjee, Mary Kwok, Danai Dima, Andrew J. Portuguese, Delphine Chen, Majid Chalian and Andrew J. Cowan
Diagnostics 2025, 15(2), 215; https://doi.org/10.3390/diagnostics15020215 - 18 Jan 2025
Viewed by 749
Abstract
Monoclonal gammopathy of undetermined significance (MGUS) and smoldering multiple myeloma (SMM), the asymptomatic precursors to multiple myeloma, affect up to 5% of the population over the age of 40. Bone involvement, a myeloma-defining event, represents a major source of morbidity for patients. Key [...] Read more.
Monoclonal gammopathy of undetermined significance (MGUS) and smoldering multiple myeloma (SMM), the asymptomatic precursors to multiple myeloma, affect up to 5% of the population over the age of 40. Bone involvement, a myeloma-defining event, represents a major source of morbidity for patients. Key goals for the management of myeloma precursor conditions include (1) identifying patients at the highest risk for progression to MM with bone involvement and (2) differentiating precursor states from active myeloma requiring treatment. Computed tomography (CT), magnetic resonance imaging (MRI), and positron emission tomography (PET)-CT with [18F]fluorodeoxyglucose (FDG) have improved sensitivity for the detection of myeloma bone disease compared to traditional skeletal surveys, and such advanced imaging also provides this field with better tools for detecting early signs of progression. Herein, we review the data supporting the use of advanced imaging for both diagnostics and prognostication in myeloma precursor conditions. Full article
(This article belongs to the Special Issue Advances in Multiple Myeloma Imaging in 2025)
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<p>Comparison of whole-body imaging modalities for the detection of myeloma bone disease [<a href="#B11-diagnostics-15-00215" class="html-bibr">11</a>,<a href="#B13-diagnostics-15-00215" class="html-bibr">13</a>,<a href="#B20-diagnostics-15-00215" class="html-bibr">20</a>]. Abbreviations: CT, computed tomography; MRI, magnetic resonance imaging; NPV, negative predictive value; PET-CT, positron emission tomography/computed tomography; PPV, positive predictive value; and XR, X-ray.</p>
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56 pages, 48151 KiB  
Article
Excitation of ULF, ELF, and VLF Resonator and Waveguide Oscillations in the Earth–Atmosphere–Ionosphere System by Lightning Current Sources Connected with Hunga Tonga Volcano Eruption
by Yuriy G. Rapoport, Volodymyr V. Grimalsky, Andrzej Krankowski, Asen Grytsai, Sergei S. Petrishchevskii, Leszek Błaszkiewicz and Chieh-Hung Chen
Atmosphere 2025, 16(1), 97; https://doi.org/10.3390/atmos16010097 - 16 Jan 2025
Viewed by 630
Abstract
The simulations presented here are based on the observational data of lightning electric currents associated with the eruption of the Hunga Tonga volcano in January 2022. The response of the lithosphere (Earth)–atmosphere–ionosphere–magnetosphere system to unprecedented lightning currents is theoretically investigated at low frequencies, [...] Read more.
The simulations presented here are based on the observational data of lightning electric currents associated with the eruption of the Hunga Tonga volcano in January 2022. The response of the lithosphere (Earth)–atmosphere–ionosphere–magnetosphere system to unprecedented lightning currents is theoretically investigated at low frequencies, including ultra low frequency (ULF), extremely low frequency (ELF), and very low frequency (VLF) ranges. The electric current source due to lightning near the location of the Hunga Tonga volcano eruption has a wide-band frequency spectrum determined in this paper based on a data-driven approach. The spectrum is monotonous in the VLF range but has many significant details at the lower frequencies (ULF, ELF). The decreasing amplitude tendency is maintained at frequencies exceeding 0.1 Hz. The density of effective lightning current in the ULF range reaches the value of the order of 10−7 A/m2. A combined dynamic/quasi-stationary method has been developed to simulate ULF penetration through the lithosphere (Earth)–atmosphere–ionosphere–magnetosphere system. This method is suitable for the ULF range down to 10−4 Hz. The electromagnetic field is determined from the dynamics in the ionosphere and from a quasi-stationary approach in the atmosphere, considering not only the electric component but also the magnetic one. An analytical/numerical method has been developed to investigate the excitation of the global Schumann resonator and the eigenmodes of the coupled Schumann and ionospheric Alfvén resonators in the ELF range and the eigenmodes of the Earth–ionosphere waveguide in the VLF range. A complex dispersion equation for the corresponding disturbances is derived. It is shown that oscillations at the first resonance frequency in the Schumann resonator can simultaneously cause noticeable excitation of the local ionospheric Alfvén resonator, whose parameters depend on the angle between the geomagnetic field and the vertical direction. VLF propagation is possible over distances of 3000–10,000 km in the waveguide Earth–ionosphere. The results of simulations are compared with the published experimental data. Full article
(This article belongs to the Special Issue Feature Papers in Upper Atmosphere (2nd Edition))
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<p>Electric current in the vicinity of the Hunga Tonga eruption, measured on 13–15 January 2022 (UTC). Time steps of (<b>a</b>) 1 s and (<b>b</b>) 0.1 s are considered.</p>
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<p>Spectral features of Hunga Tonga lightning on 13–15 January 2022 (UTC). Ultra-low frequencies <span class="html-italic">f</span> &lt; 1 Hz are presented with the plots in (<b>a</b>) linear and (<b>b</b>) logarithmic scale.</p>
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<p>The spectra of electric current variations in the ranges (<b>a</b>) of tens of Hz, ELF (blue color—window 50 s, green color—window 500 s), and (<b>b</b>) tens of thousands Hz, VLF (window 1 s).</p>
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<p>(<b>a</b>) Geometry of the 2D problem of determination of directional diagram for VLF radiation from lightning sources; O, K, <math display="inline"><semantics> <mi>α</mi> </semantics></math>, and <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>r</mi> <mo stretchy="false">→</mo> </mover> <mi>j</mi> <mo>′</mo> </msubsup> </mrow> </semantics></math> are the center of coordinates, corresponding to the volcano, the observation point, the angle between the radius-vector <math display="inline"><semantics> <mover accent="true"> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </semantics></math>, and the dot line which is supposed to point at the north, and the radius-vector of the elementary current with the number <math display="inline"><semantics> <mrow> <mi>j</mi> <mo>′</mo> </mrow> </semantics></math>, respectively; <span class="html-italic">F</span> is the circle with the radius <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mrow> <mn>0</mn> </mrow> </msub> <mo>∼</mo> <mn>150</mn> <mrow> <mo> </mo> <mi>km</mi> </mrow> </mrow> </semantics></math>, inside of which the most of elementary currents are placed; (<b>b</b>,<b>c</b>) are directional diagrams for the Fourier components of the lightning current source, averaged in the frequency ranges of, respectively, 10,000 ± 250 Hz (black color, solid line), 20,000 ± 250 Hz (red, dashed), 40,000 ± 250 Hz (blue, dotted). The observation points lie on the circle with the center <span class="html-italic">O</span> with the radius <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1000</mn> <mrow> <mo> </mo> <mi>km</mi> </mrow> </mrow> </semantics></math>; time step 10<sup>−7</sup> s. Arbitrary intervals of time with a duration of 1 s in the neighborhood of high lightning activity are considered: 15 January 2022 05:02:52 (<b>b</b>), 15 January 2022 04:57:23 (<b>c</b>). The data on lightning activity are taken from [<a href="#B7-atmosphere-16-00097" class="html-bibr">7</a>,<a href="#B77-atmosphere-16-00097" class="html-bibr">77</a>]. The directional diagram is calculated with the <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>30</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math> angular steps.</p>
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<p>Geometry of the problem: Penetration of EM fields excited by an external current source of ULF range through LEAIM. In <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>≤</mo> <mi>z</mi> <mo>≤</mo> <msub> <mi>L</mi> <mi>z</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>z</mi> </msub> <mo>≤</mo> <mi>z</mi> <mo>≤</mo> <msub> <mi>z</mi> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> regions, the quasi-stationary and dynamic approaches are used, respectively. There is radiation from the boundary <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> into the magnetosphere region <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>&gt;</mo> <msub> <mi>z</mi> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math>. <math display="inline"><semantics> <mi>θ</mi> </semantics></math> is the angle between the geomagnetic field <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>H</mi> <mo stretchy="false">→</mo> </mover> <mn>0</mn> </msub> </mrow> </semantics></math> and vertical axis <span class="html-italic">OZ.</span> The height <span class="html-italic">z</span> = <span class="html-italic">L<sub>z</sub></span> is about 70–120 km. The coordinate frame, where the coordinates are denoted with primes, relates to the geomagnetic field; the coordinates of the laboratory frame are denoted without primes. Directions of the X and Y axes correspond to meridional and longitudinal directions, respectively.</p>
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<p>Parameters of the ionosphere used in simulations. Part (<b>a</b>) is the electron concentration, (<b>b</b>) is the ion-to-electron mass ratio, (<b>c</b>) is the electron collision frequency, (<b>d</b>) is the ion collision frequency. Curves 1 (black) and 2 (red) are the daytime and nighttime parameters, respectively. The data were taken from [<a href="#B78-atmosphere-16-00097" class="html-bibr">78</a>,<a href="#B79-atmosphere-16-00097" class="html-bibr">79</a>,<a href="#B80-atmosphere-16-00097" class="html-bibr">80</a>,<a href="#B81-atmosphere-16-00097" class="html-bibr">81</a>].</p>
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<p>The simulated ULF tensor impedance components of the ionosphere. The frequency is <span class="html-italic">ω</span> = 0.01 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 1.6 × 10<sup>−3</sup> Hz). Curve 1 is |<span class="html-italic">Z</span><sub>11</sub>|, 2 is |<span class="html-italic">Z</span><sub>12</sub>|, 3 is |<span class="html-italic">Z</span><sub>21</sub>|, 4 is |<span class="html-italic">Z</span><sub>22</sub>|, Curve 5 is the estimated relative error of simulations of the dynamic equations. Part (<b>a</b>) is for nighttime, (<b>b</b>) is for daytime (<span class="html-italic">k<sub>x</sub></span> = <span class="html-italic">k<sub>y</sub></span> = 0).</p>
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<p>The distributions of the electric field |<span class="html-italic">E<sub>x</sub></span>(<span class="html-italic">x</span>,<span class="html-italic">y</span>)| generated by ULF current sources at different frequencies at the height <span class="html-italic">z</span> = 200 km. The parameters of the ionosphere correspond to the nighttime. Panel (<b>a</b>) corresponds to the frequency <span class="html-italic">ω</span> = 0.001 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 1.6 × 10<sup>−4</sup> Hz), (<b>b</b>) is at 0.01 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 1.6 × 10<sup>−3</sup> Hz), the combined simulations only. Panels (<b>c</b>,<b>d</b>) are for the frequency <span class="html-italic">ω</span> = 0.025 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 0.004 Hz), simulated by both the direct dynamic and combined approaches; panels (<b>e</b>,<b>f</b>) are the same as (<b>c</b>,<b>d</b>), but at <span class="html-italic">ω</span> = 0.05 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 0.008 Hz). The center of the current source is at <span class="html-italic">x</span> = <span class="html-italic">y</span> = 1500 km, and the angle between the vertical direction and geomagnetic field is <span class="html-italic">θ</span> = 30°.</p>
Full article ">Figure 8 Cont.
<p>The distributions of the electric field |<span class="html-italic">E<sub>x</sub></span>(<span class="html-italic">x</span>,<span class="html-italic">y</span>)| generated by ULF current sources at different frequencies at the height <span class="html-italic">z</span> = 200 km. The parameters of the ionosphere correspond to the nighttime. Panel (<b>a</b>) corresponds to the frequency <span class="html-italic">ω</span> = 0.001 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 1.6 × 10<sup>−4</sup> Hz), (<b>b</b>) is at 0.01 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 1.6 × 10<sup>−3</sup> Hz), the combined simulations only. Panels (<b>c</b>,<b>d</b>) are for the frequency <span class="html-italic">ω</span> = 0.025 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 0.004 Hz), simulated by both the direct dynamic and combined approaches; panels (<b>e</b>,<b>f</b>) are the same as (<b>c</b>,<b>d</b>), but at <span class="html-italic">ω</span> = 0.05 s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 0.008 Hz). The center of the current source is at <span class="html-italic">x</span> = <span class="html-italic">y</span> = 1500 km, and the angle between the vertical direction and geomagnetic field is <span class="html-italic">θ</span> = 30°.</p>
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<p>The nighttime distributions |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">x</span>,<span class="html-italic">y</span>)| (left, central, and right panels) with all their frequency components for <span class="html-italic">ω</span> ≤ 0.01 s<sup>−1</sup> (<span class="html-italic">ω</span> ≡ <span class="html-italic">2πf</span>) summed up, mV/m units. The source amplitude is <span class="html-italic">j</span><sub>0</sub> = 4.7 × 10<sup>−7</sup> A/m<sup>2</sup>. Matching the quasi-stationary and dynamic problems is at <span class="html-italic">z</span> = 75 km. The altitude from <span class="html-italic">z</span> = 80 km to <span class="html-italic">z</span> = 200 km. The center of the current source is at <span class="html-italic">x</span> = <span class="html-italic">y</span> = 1500 km, and the angle between the vertical direction and geomagnetic field is <span class="html-italic">θ</span> = 30°.</p>
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<p>The nighttime distributions |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">x</span>,<span class="html-italic">y</span>)| (left, central, and right panels) with all their frequency components for <span class="html-italic">ω</span> ≤ 0.01 s<sup>−1</sup> (<span class="html-italic">ω</span> ≡ <span class="html-italic">2πf</span>) summed up, mV/m units. The source amplitude is <span class="html-italic">j</span><sub>0</sub> = 4.7 × 10<sup>−7</sup> A/m<sup>2</sup>. Matching the quasi-stationary and dynamic problems is at <span class="html-italic">z</span> = 75 km. The altitude <span class="html-italic">z</span> = 200 km. The center of the current source is at <span class="html-italic">x = y</span> = 1500 km, and the angle between the vertical direction and geomagnetic field is <span class="html-italic">θ</span> = 50°.</p>
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<p>Magnetic field components |<span class="html-italic">H<sub>x</sub></span>| (<b>a</b>,<b>d</b>), |<span class="html-italic">H<sub>y</sub></span>| (<b>b</b>,<b>e</b>), |<span class="html-italic">H<sub>z</sub></span>| (<b>c</b>,<b>f</b>), excited by Hunga Tonga total ULF lightning current source (see <a href="#sec3-atmosphere-16-00097" class="html-sec">Section 3</a>), on <span class="html-italic">x</span>, <span class="html-italic">y</span> at altitudes <span class="html-italic">z</span> = 80 km (<b>a</b>–<b>c</b>) and <span class="html-italic">z</span> = 200 km (<b>d</b>–<b>f</b>). The units are nT. The center of the current source is at <span class="html-italic">x = y</span> = 1500 km, and the angle between the vertical direction and geomagnetic field is <span class="html-italic">θ</span> = 30°.</p>
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<p>Planar model of excitation of eigenmodes in the Schumann resonator (SR) by external ELF current connected with the Hunga Tonga eruption. Radiation of EM waves into the upper ionosphere is taken into account (see arrows in the Figure at the boundary <span class="html-italic">z</span> = <span class="html-italic">z<sub>max</sub></span>). SR is presented as a one period <span class="html-italic">L</span> of a periodical system. SR occupies the altitude region <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>≤</mo> <mi>z</mi> <mo>≤</mo> <msub> <mi>L</mi> <mi>z</mi> </msub> </mrow> </semantics></math>. Radiation conditions are formulated at the altitude <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <msup> <mover accent="true"> <mi>j</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <msup> <mover accent="true"> <mi>j</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>ω</mi> <mo>,</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> is the external current source, in particular lightning current associated with the Hunga Tonga volcano eruption.</p>
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<p>The dependencies of the components of the permittivity in ELF range at <span class="html-italic">ω</span> = 47.1 s<sup>−1</sup> (<span class="html-italic">f</span> = 7.50 Hz). Panel (<b>a</b>) is the daytime, (<b>b</b>) is the nighttime. The ionosphere parameters correspond to <a href="#atmosphere-16-00097-f006" class="html-fig">Figure 6</a> [<a href="#B78-atmosphere-16-00097" class="html-bibr">78</a>,<a href="#B79-atmosphere-16-00097" class="html-bibr">79</a>,<a href="#B80-atmosphere-16-00097" class="html-bibr">80</a>,<a href="#B81-atmosphere-16-00097" class="html-bibr">81</a>].</p>
Full article ">Figure 14
<p>Excitation of the SR by ELF effective Hunga Tonga current source taken from <a href="#atmosphere-16-00097-f003" class="html-fig">Figure 3</a>a. The used model of SR is a planar waveguide with radiative upper boundary conditions at the magnetosphere; effective periodical boundary conditions are applied in the horizontal (<span class="html-italic">X</span>, <span class="html-italic">Y</span>) directions with the period <span class="html-italic">L</span> = <span class="html-italic">2πR<sub>E</sub></span>; daytime<b>,</b> <span class="html-italic">z</span> = 0, <span class="html-italic">θ</span> = 30°; <span class="html-italic">ω</span> = 46.5 s<sup>−1</sup> (<span class="html-italic">f</span> = 7.40 Hz). Panel (<b>a</b>) is |<span class="html-italic">E<sub>z</sub></span>|, (<b>b</b>) is |<span class="html-italic">H<sub>x</sub></span>|, (<b>c</b>) is |<span class="html-italic">H<sub>y</sub></span>|.</p>
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<p>Excitation of SR by ELF effective Hunga Tonga current source taken from <a href="#atmosphere-16-00097-f003" class="html-fig">Figure 3</a>a, the 1st Schumann mode. Daytime; <span class="html-italic">ω</span> = 47.1 s<sup>−1</sup> (<span class="html-italic">f</span> = 7.50 Hz), <span class="html-italic">θ</span> = 30°; <span class="html-italic">z</span> = 0 (<b>a</b>–<b>c</b>) and <span class="html-italic">z</span> = 200 km (<b>d</b>–<b>f</b>).</p>
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<p>Excitation of SR by ELF effective Hunga Tonga current source taken from <a href="#atmosphere-16-00097-f003" class="html-fig">Figure 3</a>a, the 1st Schumann mode. Nighttime; <span class="html-italic">θ</span> = 30°; <span class="html-italic">ω</span> = 47.1 s<sup>−1</sup> (<span class="html-italic">f</span> = 7.50 Hz); <span class="html-italic">z</span> = 0 (<b>a</b>–<b>c</b>) and <span class="html-italic">z</span> = 200 km (<b>d</b>–<b>f</b>). The narrow peak in the center of the figure (<b>a</b>), as well as in <a href="#atmosphere-16-00097-f014" class="html-fig">Figure 14</a>a and <a href="#atmosphere-16-00097-f015" class="html-fig">Figure 15</a>a, and in <a href="#atmosphere-16-00097-f017" class="html-fig">Figure 17</a>b, <a href="#atmosphere-16-00097-f018" class="html-fig">Figure 18</a>b and <a href="#atmosphere-16-00097-f019" class="html-fig">Figure 19</a>d, presented in the section below, is associated with the current source effect.</p>
Full article ">Figure 17
<p>Comparison of the dependencies of the vertical component of the ELF electric field near the maximum in the spherical geometry |<span class="html-italic">E<sub>r</sub></span>(<span class="html-italic">r = R<sub>E</sub></span>)|, panel (<b>a</b>), and the local plane geometry |<span class="html-italic">E<sub>z</sub></span>(<span class="html-italic">x</span>, <span class="html-italic">y</span>, <span class="html-italic">z</span> = 0)|, panel (<b>b</b>). Panel (<b>b</b>) corresponds to <a href="#atmosphere-16-00097-f016" class="html-fig">Figure 16</a>a, near the maximum of the electric field. Panel (<b>c</b>) is the cross-section of Earth where the correspondence between the distances <span class="html-italic">ρ</span> and <math display="inline"><semantics> <mover accent="true"> <mi>ρ</mi> <mo>˜</mo> </mover> </semantics></math> is seen. Panel (<b>d</b>) is the view from above. The curvilinear axes <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>X</mi> <mo>˜</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>Y</mi> <mo>˜</mo> </mover> </mrow> </semantics></math> are projected to the Cartesian ones <span class="html-italic">X</span>, <span class="html-italic">Y</span> in this view.</p>
Full article ">Figure 18
<p>Excitation of SR by ELF effective Hunga Tonga current source taken from <a href="#atmosphere-16-00097-f003" class="html-fig">Figure 3</a>a, the 1st Schumann mode. Nighttime; <span class="html-italic">θ</span> = 45°; <span class="html-italic">z</span> = 0, <span class="html-italic">ω</span> = 47.1 s<sup>−1</sup> (<span class="html-italic">f</span> = 7.50 Hz). Panel (<b>a</b>) is |<span class="html-italic">E<sub>z</sub></span>|, (<b>b</b>) is |<span class="html-italic">H<sub>x</sub></span>|, (<b>c</b>) is |<span class="html-italic">H<sub>y</sub></span>|.</p>
Full article ">Figure 19
<p>Excitation of SR by ELF effective Hunga Tonga current source taken from <a href="#atmosphere-16-00097-f003" class="html-fig">Figure 3</a>a. Daytime; <span class="html-italic">θ</span> = 30°; <span class="html-italic">z</span> = 0; <span class="html-italic">ω</span> = 70.1 s<sup>−1</sup> (<span class="html-italic">f</span> = 11.2 Hz) (<b>a</b>–<b>c</b>) and the 2nd Schumann mode <span class="html-italic">ω</span> = 94.2 s<sup>−1</sup> (<span class="html-italic">f</span> = 15.0 Hz) (<b>d</b>–<b>f</b>).</p>
Full article ">Figure 20
<p>ELF eigenmodes of coupled Schumann resonator–ionospheric Alfvén resonator (CSIAR). Almost transverse magnetic mode. Daytime, <span class="html-italic">θ</span> = 30°, |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>a</b>,<b>c</b>,<b>e</b>), |<span class="html-italic">H<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>b</b>,<b>d</b>,<b>f</b>). The 1st (<b>a</b>,<b>b</b>), 2nd (<b>c</b>,<b>d</b>), and 3rd (<b>e</b>,<b>f</b>) modes are presented in the vicinity of the 1st Schumann resonance mode. Their frequencies are <span class="html-italic">ω</span><sub>1</sub> = 47.94 + 3.653<span class="html-italic">i</span>, <span class="html-italic">ω</span><sub>2</sub> = 41.56 + 6.076<span class="html-italic">i</span>, and <span class="html-italic">ω</span><sub>3</sub> = 30.69 + 2.383<span class="html-italic">i</span>, in s<sup>−1</sup>. Only the modes with ω″/ω′ &lt; 0.25 are presented.</p>
Full article ">Figure 20 Cont.
<p>ELF eigenmodes of coupled Schumann resonator–ionospheric Alfvén resonator (CSIAR). Almost transverse magnetic mode. Daytime, <span class="html-italic">θ</span> = 30°, |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>a</b>,<b>c</b>,<b>e</b>), |<span class="html-italic">H<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>b</b>,<b>d</b>,<b>f</b>). The 1st (<b>a</b>,<b>b</b>), 2nd (<b>c</b>,<b>d</b>), and 3rd (<b>e</b>,<b>f</b>) modes are presented in the vicinity of the 1st Schumann resonance mode. Their frequencies are <span class="html-italic">ω</span><sub>1</sub> = 47.94 + 3.653<span class="html-italic">i</span>, <span class="html-italic">ω</span><sub>2</sub> = 41.56 + 6.076<span class="html-italic">i</span>, and <span class="html-italic">ω</span><sub>3</sub> = 30.69 + 2.383<span class="html-italic">i</span>, in s<sup>−1</sup>. Only the modes with ω″/ω′ &lt; 0.25 are presented.</p>
Full article ">Figure 21
<p>The same as in <a href="#atmosphere-16-00097-f020" class="html-fig">Figure 20</a>, |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>a</b>,<b>c</b>,<b>e</b>), |<span class="html-italic">H<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>b</b>,<b>d</b>,<b>f</b>), but <span class="html-italic">θ</span><sub>0</sub> = 40°. The frequencies are <span class="html-italic">ω</span><sub>1</sub> = 46.53 + 4.54i, <span class="html-italic">ω</span><sub>2</sub> = 43.21 + 5.35<span class="html-italic">i</span>, and <span class="html-italic">ω</span><sub>3</sub> = 30.48 + 2.60<span class="html-italic">i</span>, in s<sup>−1</sup>.</p>
Full article ">Figure 21 Cont.
<p>The same as in <a href="#atmosphere-16-00097-f020" class="html-fig">Figure 20</a>, |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>a</b>,<b>c</b>,<b>e</b>), |<span class="html-italic">H<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>b</b>,<b>d</b>,<b>f</b>), but <span class="html-italic">θ</span><sub>0</sub> = 40°. The frequencies are <span class="html-italic">ω</span><sub>1</sub> = 46.53 + 4.54i, <span class="html-italic">ω</span><sub>2</sub> = 43.21 + 5.35<span class="html-italic">i</span>, and <span class="html-italic">ω</span><sub>3</sub> = 30.48 + 2.60<span class="html-italic">i</span>, in s<sup>−1</sup>.</p>
Full article ">Figure 22
<p>The same as in <a href="#atmosphere-16-00097-f020" class="html-fig">Figure 20</a>, |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>a</b>,<b>c</b>,<b>e</b>), |<span class="html-italic">H<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (<b>b</b>,<b>d</b>,<b>f</b>), but <span class="html-italic">θ</span><sub>0</sub> = 50°. The frequencies are <span class="html-italic">ω</span><sub>1</sub> = 43.63 + 5.59i, <span class="html-italic">ω</span><sub>2</sub> = 42.99 + 5.07<span class="html-italic">i</span>, and <span class="html-italic">ω</span><sub>3</sub> = 30.31 + 3.58<span class="html-italic">i</span>, in s<sup>−1</sup>.</p>
Full article ">Figure 23
<p>VLF in WGEI and leaking from WGEI into the upper ionosphere–magnetosphere. The tensor impedance method [<a href="#B89-atmosphere-16-00097" class="html-bibr">89</a>] has been developed in [<a href="#B56-atmosphere-16-00097" class="html-bibr">56</a>] and applied for simulating the propagation of electromagnetic beams in a multi-layered/inhomogeneous WGEI. The isotropic medium is at <span class="html-italic">0</span> &lt; <span class="html-italic">z</span> &lt; <span class="html-italic">L<sub>ISO</sub></span>, <span class="html-italic">L<sub>ISO</sub></span> &lt; <span class="html-italic">L<sub>z</sub></span>, where <span class="html-italic">L<sub>ISO</sub></span> = 60–70 km, <span class="html-italic">L<sub>z</sub></span> = 80–120 km. Anisotropic/gyrotropic media are at <span class="html-italic">L<sub>ISO</sub></span> &lt; <span class="html-italic">z</span> &lt; <span class="html-italic">z<sub>max</sub></span> (<span class="html-italic">z<sub>max</sub></span> ≤ 1000 km). The covering layer occupies the region <span class="html-italic">L<sub>z</sub></span> &lt; <span class="html-italic">z</span> &lt; <span class="html-italic">z<sub>max</sub>.</span> WGEI [<a href="#B90-atmosphere-16-00097" class="html-bibr">90</a>,<a href="#B91-atmosphere-16-00097" class="html-bibr">91</a>] includes the isotropic region <span class="html-italic">0</span> &lt; <span class="html-italic">z</span> &lt; <span class="html-italic">L<sub>ISO</sub></span> and anisotropic region <span class="html-italic">L<sub>z</sub></span> &lt; <span class="html-italic">z</span> &lt; <span class="html-italic">z<sub>max</sub></span>. At the upper boundary of the covering layer (<span class="html-italic">z = z<sub>max</sub></span>), the radiation of EM waves into the external region (z &gt; <span class="html-italic">z<sub>max</sub></span>) is accounted for by applying radiative boundary conditions. In the region <span class="html-italic">L<sub>z</sub></span> &lt; <span class="html-italic">z</span> &lt; <span class="html-italic">z<sub>max</sub></span>, both the VLF EM waves leaking from the WGEI and propagating upward in a positive <span class="html-italic">z</span> direction and reflected EM waves propagating in a negative <span class="html-italic">z</span>-direction are taken into account. In the region <span class="html-italic">z</span> &gt; <span class="html-italic">z<sub>max</sub></span>, where the upper ionosphere/magnetosphere is placed, the medium is considered as slowly varying, so the reflection of VLF EM waves downwards is neglected, and only EM waves radiated upwards are accounted for.</p>
Full article ">Figure 24
<p>Typical modes in the planar waveguide model: (<b>a</b>,<b>b</b>) two lower modes of a model planar waveguide [<a href="#B83-atmosphere-16-00097" class="html-bibr">83</a>,<a href="#B84-atmosphere-16-00097" class="html-bibr">84</a>,<a href="#B93-atmosphere-16-00097" class="html-bibr">93</a>] with the ideally conductive upper boundary placed at <span class="html-italic">z</span> = 60 km; (<b>c</b>,<b>d</b>) 1st and 2nd modes of a realistic WGEI, where any “effective upper waveguide boundary” is not prescribed, and the upper boundary condition is radiative in the upper ionosphere at <span class="html-italic">z</span> = 800 km. (<b>e</b>) Exponential factor characterizing field losses at the distance of 1000 km. The normalized absolute values of the field components are shown.</p>
Full article ">Figure 25
<p>Propagation of the two lowest VLF modes in the WGEI; the angle between the vertical direction and geomagnetic field is θ = 30°. Panels (<b>a</b>–<b>e</b>) are for <span class="html-italic">ω</span> = 2.5 × 10<sup>5</sup> s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 4 × 10<sup>4</sup> Hz); daytime; (<b>f</b>–<b>i</b>) are for <span class="html-italic">ω</span> = 1 × 10<sup>5</sup> s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 1.6 × 10<sup>4</sup> Hz); nighttime. Panels (<b>a</b>,<b>b</b>,<b>f</b>,<b>g</b>) show the distributions of |<span class="html-italic">E<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)|, |<span class="html-italic">H<sub>x</sub></span><sub>,<span class="html-italic">y</span>,<span class="html-italic">z</span></sub>(<span class="html-italic">z</span>)| (curves 1, 2, 3) correspondingly, for the 1st mode; panels (<b>c</b>,<b>d</b>,<b>h</b>,<b>i</b>) show the distributions for the 2nd mode. Panel (<b>e</b>) shows the frequency dependence of the wave losses for the 1st and 2nd modes (Curves 1 and 2, respectively) for daytime.</p>
Full article ">Figure 26
<p>Dependence of the permittivity tensor components for the ionosphere on the altitude <span class="html-italic">z</span>. The frequency is <span class="html-italic">ω</span> = 10<sup>5</sup> s<sup>−1</sup> (<span class="html-italic">f</span> ≈ 1.6 × 10<sup>4</sup> Hz). Curves 1, 2, 3 are |<span class="html-italic">ε</span><sub>1</sub>|,|<span class="html-italic">ε</span><sub>3</sub>|,|<span class="html-italic">ε<sub>h</sub></span>|, daytime; 4, 5, 6 are for nighttime. The ionospheric parameters correspond to <a href="#atmosphere-16-00097-f006" class="html-fig">Figure 6</a> [<a href="#B78-atmosphere-16-00097" class="html-bibr">78</a>,<a href="#B79-atmosphere-16-00097" class="html-bibr">79</a>,<a href="#B80-atmosphere-16-00097" class="html-bibr">80</a>,<a href="#B81-atmosphere-16-00097" class="html-bibr">81</a>].</p>
Full article ">Figure 27
<p>Propagation and field distributions in WGEI. Spatial field structure for the transversally magnetic beam at the distances from the input of the system <span class="html-italic">x</span> = 0, part (<b>a</b>), and <span class="html-italic">x</span> = 1000 km, parts (<b>b</b>,<b>c</b>). In (<b>a</b>,<b>b</b>), there are |<span class="html-italic">H<sub>y</sub></span>| distributions, and in c, there is |<span class="html-italic">E<sub>y</sub></span>| one. The fields are in CGS. If we assume that the maximum of the electric field is 1 mV/m, then the magnetic field in <a href="#atmosphere-16-00097-f027" class="html-fig">Figure 27</a>c is 0.03 nT (the problem is linear).</p>
Full article ">Figure 28
<p>Determination of optimal parameters for propagation in WGEI of VLF modes excited by model lightning discharge [<a href="#B63-atmosphere-16-00097" class="html-bibr">63</a>,<a href="#B94-atmosphere-16-00097" class="html-bibr">94</a>]; (<b>a</b>,<b>b</b>) time dependence of the lightning source current normalized to the maximum value and spectral current density, respectively; (<b>c</b>) frequency dependence of the absorption coefficient of VLF waves in WGEI, daytime; (<b>d</b>) frequency dependence of the transmission coefficient of VLF waves in WGEI (see characteristics shown in (<b>a</b>,<b>b</b>)). (<b>e</b>) Transmission coefficient for VLF waves in WGEI, obtained for VLF current source spectrum (<a href="#atmosphere-16-00097-f003" class="html-fig">Figure 3</a>b) from LCSHTE.</p>
Full article ">
13 pages, 4312 KiB  
Article
Numerical Simulation Study of Electromagnetic Pulse in Low-Altitude Nuclear Explosion Source Regions
by Zhaomin Li, Jiarong Dong, Bing Wei and Xinbo He
Electronics 2025, 14(2), 337; https://doi.org/10.3390/electronics14020337 - 16 Jan 2025
Viewed by 641
Abstract
A nuclear electromagnetic pulse (NEMP) is the fourth effect of a nuclear explosion, characterized by a strong electromagnetic field that can instantly damage electronic devices. To investigate the spatial field value distribution characteristics of the source region of low-altitude NEMPs, this study employed [...] Read more.
A nuclear electromagnetic pulse (NEMP) is the fourth effect of a nuclear explosion, characterized by a strong electromagnetic field that can instantly damage electronic devices. To investigate the spatial field value distribution characteristics of the source region of low-altitude NEMPs, this study employed a finite-difference time-domain (FDTD) method based on a rotating ellipsoidal hyperbolic coordinate system. Due to intense field variations near the explosion center, non-uniform grids were employed for both spatial and temporal steps, and an OpenMP parallel algorithm was utilized to enhance computational efficiency. Analysis focused on the following two scenarios: varying angles at a constant distance and varying distances at a constant angle, considering both transverse magnetic (TM) and transverse electric (TE) waves. The results indicate that the spatial field value distribution characteristics differ between the two wave types. For TM waves, the electric and magnetic fields share the same polarity, but their waveform polarities are opposite above and below the explosion center. A TE wave is exactly the opposite. Compared with a TM wave, a TE wave has stronger peak electromagnetic fields but narrower pulse widths and lower overall energy. This research provides significant support for the development of nuclear explosion detection technology and offers theoretical foundations for the protection of surrounding environmental facilities. Full article
Show Figures

Figure 1

Figure 1
<p>Comparison of the relative occurrence rates of three processes as a function of photon energy and atomic number the medium.</p>
Full article ">Figure 2
<p>Schematic diagram of low–altitude NEMP generation.</p>
Full article ">Figure 3
<p>The geometric schematic diagram of the spherical coordinate system (<math display="inline"><semantics> <mrow> <mi>r</mi> <mo>,</mo> <mi>θ</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </semantics></math>) and the rotating ellipsoid–hyperbolic orthogonal coordinate system (<math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>,</mo> <mi>ζ</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </semantics></math>) at the field point P.</p>
Full article ">Figure 4
<p>Comparison of results between the study and existing literature.</p>
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<p>Distribution map of source area under specific conditions.</p>
Full article ">Figure 6
<p>Schematic diagram of nuclear explosion points and observation points from different angles at the same distance.</p>
Full article ">Figure 7
<p>Comparison of field time–domain waveforms during angle variation of TM wave. (<b>a</b>) Electric field; (<b>b</b>) magnetic field.</p>
Full article ">Figure 8
<p>Comparison of field time–domain waveforms during angle variation of TE Wave. (<b>a</b>) Electric field; (<b>b</b>) magnetic field.</p>
Full article ">Figure 9
<p>Schematic diagram of nuclear explosion points and observation points from different distances at the same angle.</p>
Full article ">Figure 10
<p>Comparison of field time–domain waveforms during distance variation of TM wave. (<b>a</b>) Electric field above the explosion center; (<b>b</b>) magnetic field above the explosion center; (<b>c</b>) electric field below the explosion center; (<b>d</b>) magnetic field below the explosion center.</p>
Full article ">Figure 11
<p>Comparison of field time–domain waveforms during distance variation of TE wave. (<b>a</b>) Electric field; (<b>b</b>) magnetic field.</p>
Full article ">
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