Harmonic Field Research Articles

Analysis of P wave induced second-order harmonic field at solid–fluid interface with potential matrix algorithm

Based on the second-order harmonic potential theory, the characteristics of the second-order harmonic field generated at the solid–liquid interface induced by P wave incidence are analyzed. A planar model of the solid–liquid interface is established to study the variation of the second-order displacement field versus the incident angles. The homogeneous solution coefficient matrix, refraction and reflection coefficient matrix are introduced. According to the boundary conditions and Lagrange's various parameters method, the second-order displacement field is obtained, and its dependence on the solid–liquid interface is investigated. The different effects of boundary on the tangential displacement and normal displacement are demonstrated. Numerical simulation shows that the complete solution varies slightly at the incident angle, and the tangential displacement and the normal displacement change sharply at a mutation angle θω due to the boundary effect.

Effects of high-order space harmonics on the operation of five-phase induction machines under unbalance

The paper addresses the effects of high-order space harmonics on the steady-state performance of five-phase induction machines operating under unbalance. We show that the airgap harmonic fields with orders higher than three, although usually disregarded, can produce a significant increase in the torque pulsation and in the Joule losses. We propose a model based on symmetric components which is used to demonstrate that the field produced by each rotor harmonic current is related to two stator sequence currents. Further, the proposed model allows determining additional losses and harmonic torques produced by airgap harmonic fields with orders higher than three, which up to now have not been addressed elsewhere. As a case study, we applied the model to two five-phase induction machines with different designs and assessed the influence of high space harmonics under operation at steady state with one open phase in the stator. The model has been validated by comparing analytical results with results obtained through finite element analysis. Finally, the model validation was also based on experimental results obtained from tests with two prototypes under many different conditions.

Magnetic cross-talk simulation for Iranian Light Source Facility storage ring

Magnetic cross-talk due to the small free space between the magnets of a machine may result in significant distortions of the magnetic field integration and performance distortion of the machine. This paper presents the preparation done at the Iranian Light Source Facility (ILSF) on integrated magnetic components of three storage ring (SR) magnets with minimum space between the yokes, modeled separately in Opera-3D code and accumulatively as in the lattice design. The results show that the integrated quadrupole component of the BE2 dipole magnet remains nearly the same, while the integrated dipole and sextupole components are reduced by 0.13% and 4.69%, respectively. By the same token, the integrated quadrupole component of the Q11 in the lattice is decreased by 0.07%, and the integrated sextupole component of the S4 sextupole is reduced by 8.14%. The probable deviation on the higher-order integrated multipoles together with harmonic fields along the beam trajectory are discussed, and some studies are introduced to cut down any deficient effects.

Realizing the second harmonic acoustic focusing based on an artificial bubble array

Ultrasonic imaging technologies possess extensive applications in modern medical diagnosis and treatment. In this paper, a designed artificial bubble array is utilized to establish a multi-scattering sound field model to describe the nonlinear vibration of the artificial bubble array, combining nonlinear acoustics and multi-scattering theory. With the results of the effective medium model, the correctness and reliability of the multi-scattering model are verified. Furthermore, under different incident frequencies and different bubble array parameters, the distributions of fundamental and second harmonic sound pressure fields produced by nonlinear vibration of the artificial bubble array are investigated. Via a judicious design of structural parameters, both fundamental and second harmonic acoustic focusing at specific locations inside the bubble array and second harmonic acoustic focusing outside the array under a specific incident frequency are realized.

Quench Localization in the High Order Corrector Magnets Using the Harmonic Field Method

INFN LASA, within the CERN-INFN research collaboration for the Hi-Luminosity LHC upgrade project, has been entrusted for the series production qualification of the High Order Corrector magnets. The magnets, designed with a superferric configuration, are tested at 4.2 K in a stacked layout to evaluate the training performance and to characterize the magnetic field. This paper presents an in-depth analysis of different quench events of the High Order Corrector magnets. In this analysis, the reconstruction of the quenched coil position has been performed by measuring the residual magnetic field after the magnet has been discharged. The method used for the quench localization considers the effects of the superconductor coil magnetization, which is canceled by the transition to the normal resistive state only in the quenched coil, on the residual magnetic field. Experimental results of real events during the magnet series tests are presented and analyzed. The model previously developed for the field quality calculation has been extended to consider different quenched coils in the same event. The results are here compared and discussed. From the comparison between the model and the experimental data, the position of the quenched coil/coils has been directly retrieved for all the magnet orders and cross-checked with the acquired voltages from the magnet. The simplicity of this method and its effectiveness make it a promising way to further improve the diagnostic system of the superconducting magnets with a superferric design similar to the High Order Corrector magnets.

A Novel Permanent Magnet Vernier Machine With Coding-Shaped Tooth

It is well known that permanent magnet Vernier machine (PMVM) has multiple flux field harmonics, which can produce stable torque. However, some flux field harmonics would create torque that undermines the total torque output. Such as the 6 slots 26 poles split-tooth PMVM here, of which modulated flux field outputs torque while fundamental flux field undermines torque output. In this article, a 26 pole PMVM with coding-shaped tooth is proposed. The coding-shaped tooth can introduce permeance harmonics with specific phase and amplitude, thus modulating flux fields that all output torque. Air-gap permeance harmonics of the proposed and the regular split-tooth PMVM are obtained via FEA. Based on MMF-permeance model, flux fields of two machines and their contributions to average torque are investigated, proving that the proposed machine has multiple flux fields that all output torque. Moreover, by optimizing geometric parameters of coding-shaped tooth, the proposed machine could obtain largest average torque and smallest torque ripple simultaneously. Electromagnetic performances of the optimized machines are studied comparatively in semianalytical way and FEA. It is proved that with same overall size, PM usage, and copper loss, the proposed machine could achieve 30% larger torque density, 86% smaller cogging torque, and 62% lower torque ripple than its counterpart. Finally, a 16-N·m (rated) prototype is built and tested.

A Pole-Changing Doubly Salient Permanent Magnet Motor

This article presents a new pole-changing (PC) doubly salient permanent magnet (DSPM) motor. According to the general air-gap field modulation theory (GAFMT), the permanent magnet excitation field can be modulated by the stator and rotor teeth to a series of harmonics with different pole-pair numbers and different slot pitch angles. Thus, when the armature winding is connected and reconnected according to the different excitation field harmonics, the PC operation can be realized to obtain a high torque density at the low-speed region and a widened speed regulation range with a simple motor structure. According to the GAFMT, the operating principle of the proposed motor is introduced, and the winding connection is discussed. Then, to verify the validity, the electromagnetic performance of the proposed motor is analyzed by the finite element analysis. Finally, a prototype is built and tested.

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

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

Potentials of Brushless Stator-Mounted Machines in Electric Vehicle Drives—A Literature Review

Brushless stator-mounted traction motors, which are new and emerging, have many potential applications in the electrified transport industry. Brushless stator-mounted machines (BSSMs), with the so-called flux modulation (FM) effects, use asynchronous field harmonics to realize energy conversion by altering the basic principle for conventional machine design which requires the stator and rotor to have the same pole number. The machines show promise of meeting the challenging requirements of electric vehicle (EV) traction motors. Therefore, in this paper, a review is undertaken on the state-of-the-art and potentials of the BSSMs for EV drives. The focus on BSSMs is due to their suitability for high-speed high torque density performance, as well as possessing suitable heat dissipation and flux weakening capabilities. The study is used to first rehash and discuss the design and excitation topologies, operating principles, and some emerging trends based on the basic BSSM variants, e.g., the doubly salient machine, flux reversal machine, and flux switching machine, while also undertaking a bibliometric synthesis on relevant studies highlighting the design and performance candidature of these niche BSSMs in EV applications, especially when compared to the well-developed Prius–IPM motor.

Quantum features of nonlinear coupler with competing nonlinearity

In this work, we examine the quantum features of a multi-waveguide nonlinear coupler exploiting the second-and third-order nonlinearities. The considered system contains four identical channels, each with a single fundamental transverse mode. The essence of this type of nonlinear coupler is to examine the effect of two or more competing nonlinearities on the generated nonclassical features in this class of devices. Here, we consider the case of second harmonic generation, wherein the fundamental harmonic (FH) fields are up-converted in pairs to double-frequency second harmonic (SH) fields, which are then evanescently coupled with the fields from other Kerr nonlinear waveguides. Using the positive P representation of the phase space, the time-evolution of the density matrix could be mapped to the corresponding Fokker–Planck equation of a classical quasiprobability distribution. Using Langevin stochastic equation, an exact representation of the system in phase space led to the demonstration of sub-Poissonian property, squeezing, and entanglement. With more effective squeezing achieved in all channel waveguides, the present system with χ(2)–χ(3) interaction can be a more efficient alternative to other versions of nonlinear couplers such as the quantum optical dimer (QOD) and Kerr nonlinear coupler (KNC). Furthermore, such a structure offers more flexibility in coupled-mode interactions in the form of correlation between the modes in different waveguides. This provides a better mechanism for the generation of enhanced nonclassical effects.

Multiferroic Cantilevers Containing a Magnetoactive Elastomer: Magnetoelectric Response to Low-Frequency Magnetic Fields of Triangular and Sinusoidal Waveform.

In this work, multiferroic cantilevers comprise a layer of a magnetoactive elastomer (MAE) and a commercially available piezoelectric polymer-based vibration sensor. The structures are fixed at one end in the horizontal plane and the magnetic field is applied vertically. First, the magnetoelectric (ME) response to uniform, triangle-wave magnetic fields with five different slew rates is investigated experimentally. Time and field dependences of the generated voltage, electric charge, and observed mechanical deflection are obtained and compared for four different thicknesses of the MAE layer. The ME responses to triangular and sinusoidal wave excitations are examined in contrast. Second, the ME response at low frequencies (≤3 Hz) is studied by the standard method of harmonic magnetic field modulation. The highest ME coupling coefficient is observed in the bias magnetic field strength of ≈73 kA/m and it is estimated to be about 3.3 ns/m (ME voltage coefficient ≈ 25 V/A) at theoretically vanishing modulation frequency ( Hz). Presented results demonstrate that the investigated heterostructures are promising for applications as magnetic-field sensors and energy harvesting devices.

Simulation of Field Oriented Control Algorithm of Permanent Magnet Synchronous Motor Based on SVPWM

Aiming at the problems of large flux pulsation and unstable operation of permanent magnet synchronous motors affected by motor parameters and magnetic field harmonics, this paper proposes a permanent magnet synchronous motor vector control strategy based on SVPMW directional control algorithm to improve motor control performance. This control strategy realizes the effective control of the motor under harmonic interference by establishing a motor model oriented along the air gap magnetic field and the SVPMW regulator algorithm. At the same time, an online query algorithm for current reference values based on mathematical models is established to achieve fast dynamic response of the motor. A simulation model of directional control is established in MATLAB/Simulink. The simulation results show that the modeling method can effectively reduce the interference of harmonics on the flux linkage. It proves that under the interference of harmonics, the directional control of this algorithm has a better control effect, which is practical. The design and debugging of the motor control system provide the basis and ideas.

Spatial and spectral variations of high-order harmonics generated in noble gases

We report on the spatial and spectral variation of high-order harmonics generation from noble gases when driven by high-repetition rate femtosecond laser with different peak intensity and polarization states. Ar, Xe, and Kr were chosen for the generation of coherent extreme ultraviolet radiation. We observe that increasing the intensity of the driving pulses (DPs) leads to disappearance of harmonics yield in the on-axis part of the spatial distribution of the harmonics in Xe target, contrary to Ar and Kr. This observation is attributed to the higher ionization potential of the latter gases. Spectral depletion of harmonics generated in Ar and Xe using radially and azimuthally polarized Gaussian–Laguerre two-color DPs is also observed. The significant depletion in the spectral distribution of harmonics is obtained when two-color pump (TCP) scheme is applied. We demonstrate how TCP scheme with azimuthally polarized DPs can be used as a tool to control the spectral distribution of harmonics generated from gas atoms during strong field by utilizing the presence of second harmonic electromagnetic field.

Multimode Representation of the Magnetic Field for the Analysis of the Nonlinear Behavior of Solar Activity as a Driver of Space Weather

Estimating and predicting space weather is important to the space industry and space missions. The driver of space weather, especially near the Earth, is solar activity, the study of which is an important task. In particular, there is a direction of problems based on models of solar magnetic field generation that require research. In our work, we build a nonlinear dynamic system of equations that describes the behavior of the solar magnetic field harmonics based on the alpha-omega dynamo model. We found that, at the beginning of the magnetic field generation process, when the dynamo number significantly exceeds the threshold, the most rapidly growing waves are in the lead. Then, over time, these waves stop growing quite quickly. In this case, the initially slowly increasing harmonics of the magnetic field become the leaders, which then make the main contribution to the process of magnetic field generation.

Holocene Temperature Variations in Semi-Arid Central Mongolia—A Chronological and Sedimentological Perspective From a 7400-year Lake Sediment Record From the Khangai Mountains

Semi-arid Mongolia is a highly sensitive region to climate changes, but the region’s Holocene paleoclimatic evolution and its underlying forcing mechanisms have been the subject of much recent debate. Here we present a continuous 7.4 ka sediment record from the high-altitude Shireet Naiman Nuur (Nuur = lake) in the central Mongolian Khangai Mountains. We extensively dated the sediments and analyzed elemental composition and bulk isotopes for lake sediment characterization. Our results show that 14C-dating of bulk organic carbon and terrestrial macrofossils provide a robust and precise chronology for the past 7.4 ± 0.3 cal ka BP at Shireet Naiman Nuur and 14C-ages are mostly in stratigraphic order. The 14C-based chronology is confirmed by paleomagnetic secular variations, which resemble the predictions of spherical harmonic geomagnetic field models. The very good chronological control makes paleomagnetic secular variation stratigraphy a powerful tool for evaluating and refining regional 14C-chronologies when compared to the record presented here. The lake sediment proxies TOC, N, log (Ca/Ti) and log (Si/Ti) reveal increased lake primary productivity and high growing season temperatures from 7.4 ± 0.3 to 4.3 ± 0.2 cal ka BP, which is likely the result of stronger summer insolation and pronounced warming. Reduced summer insolation thereafter results in decreased productivity and low growing season temperatures at Shireet Naiman Nuur from 4.3 ± 0.3 cal ka BP until present day. The globally acknowledged 4.2 ka event also appears as a pronounced cooling event at Shireet Naiman Nuur, and additional abrupt cooling events occurred during minima in total solar irradiance at ∼3.4, 2.8 and 2.4 ka BP. Low lake primary productivity and growing season temperatures are likely the result of longer ice cover periods at the high-altitude (2,429 m a.s.l.) Shireet Naiman Nuur. This leads to shorter mixing periods of the lake water which is supported by more positive δ13CTOC because of increased incorporation of dissolved HCO3− by aquatic producers during periods of longer ice cover.

Analysis of Eddy Current Loss of 120-kW High-Speed Permanent Magnet Synchronous Motor

Pulse width modulation current harmonics and space harmonics are some of the major factors affecting the rotor eddy current loss of the high-speed permanent magnet motor. In this study, based on the principle of the equivalent current sheet, a two-dimensional motor model in a rectangular coordinate system was established. Considering the armature reaction, the end effect, and the current harmonics generated by variable frequency power supply, the eddy current loss of the rotor at different frequencies was analyzed and calculated using the analytical and finite element methods (FEM). When the frequency is between 200 Hz and 600 Hz, the variation trend of the rotor eddy current loss with a frequency obtained by analytical calculation and FEM analysis is roughly the same, and the error is still within a reasonable range. However, as the frequency continues to increase, the error between the two becomes larger and larger. Furthermore, based on the two-dimensional FE model, the influence of the sleeve material, the thickness, and the composite structure on the rotor eddy current loss were studied and analyzed. It was found that adding a graphene shielding layer between the permanent magnet and the sleeve can effectively shield the harmonic magnetic field, greatly reduce the eddy current loss of the permanent magnet, and effectively prevent the temperature of the permanent magnet from being too high, which is conducive to the continuous and stable operation of the high-speed permanent magnet motor.

Efficient high-harmonic generation in graphene with two-color laser field at orthogonal polarization

High-order frequency mixing in graphene using a two-color radiation field consisting of the fundamental and the second harmonic fields of an ultrashort linearly polarized laser pulse is studied. It is shown that the harmonics originated from the interband transitions are efficiently generated in the case of the orthogonally polarized two-color field. In this case, the generated high-harmonics are stronger than those obtained in the parallel polarization case by more than two orders of magnitude. This is in sharp contrast with the atomic and semiconductor systems, where parallel polarization case is more preferable. The physical origin of this enhancement is also deduced from the three-step semi-classical electron-hole collision model, extended to graphene with pseudo-relativistic energy dispersion. In particular, we discuss the influence of the many particle Coulomb interaction on the HHG process within dynamical Hartree-Fock approximation. Our analysis shows that in all cases we have an overall enhancement of the HHG signal compared with the free-charged carrier model due to the electron-hole attractive interaction.

Late Holocene Paleomagnetic Secular Variation in the Chukchi Sea, Arctic Ocean

AbstractThe geomagnetic field behavior in polar regions remains poorly understood and documented. Although a number of Late Holocene paleomagnetic secular variation (PSV) records exist from marginal settings of the Amerasian Basin in the Arctic Ocean, their age control often relies on a handful of radiocarbon dates to constrain ages over the past 4,200 years. Here we present well‐dated Late Holocene PSV records from two sediment cores recovered from the Chukchi Sea, Arctic Ocean. The records are dated using 26 14C measurements, with local marine reservoir corrections calibrated using tephra layers from the 3.6 cal ka BP Aniakchak eruption in Northern Alaska. These 14C‐based chronologies are extended into the post‐bomb era using caesium‐137 dating, and mercury isochrons. Paleomagnetic measurements and rock magnetic analyses reveal stable characteristic remanent magnetization directions, and a magnetic mineralogy dominated by low‐coercivity minerals. The PSV records conform well to global spherical harmonic field model outputs. Centennial to millennial scale directional features are synchronous between the cores and other Western Arctic records from the area. Due to the robust chronology, these new high‐resolution PSV records provide a valuable contribution to the characterization of geomagnetic field behavior in the Arctic over the past few thousand years, and can aid in developing age models for suitable sediments found in this region.

Determining patterns in the generation of magnetic fields when using different arc welding techniques

This paper reports a study into the levels of magnetic fields induced by arc welding equipment in various ways in order to assess their impact on the body of welders. It is known that welders are exposed to a magnetic field of high intensity. Depending on the welding technique and the type of welding equipment, it may exceed the maximum permissible levels (MPL). Note that new Ukrainian sanitary standards for magnetic fields have been introduced, which regulate their levels depending on the frequency range. Therefore, it became necessary to carry out their hygienic assessment according to the new standards in order to devise appropriate methods for protecting welders. To this end, it was required to choose a new generation of devices to determine the intensity of magnetic fields induced by welding equipment. Based on the analysis of the constructed oscillograms and spectrograms of magnetic fields, it was found that semi-automatic welding with a metal electrode in carbon dioxide is characterized by an increased level of magnetic field in the frequency range of 50‒1000 Hz. With automatic arc welding under the flux, there are no excess of the maximum permissible levels of individual harmonics of the magnetic field but there is an excess of the total value of all harmonic components of the magnetic field. Manual arc welding with direct current involving a non-melting electrode in argon is characterized by a moderate level of magnetic field in workplace. During manual arc welding with coated electrodes, the exceeded level of the magnetic field is observed only on the electrode cable itself. It is shown that the spectral composition of the magnetic field signal is determined mainly by the welding technique itself, the peculiarities of arc combustion, and the nature of the transfer of electrode metal in the arc gap, as well as the initial parameters of the power supplies of the welding arc

Notes About a Harmonicity on the Tangent Bundle with Vertical Rescaled Metric

In this article, we present some results concerning the harmonicity on the tangent bundle equipped with the vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic with respect to the vertical rescaled metric and we construct some examples of harmonic vector fields. We also study the harmonicity of a vector field along with a map between Riemannian manifolds, the target manifold is equipped with a vertical rescaled metric on its tangent bundle. Next we also discuss the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being whose tangent bundle is endowed with a vertical rescaled metric. Finally, we study the harmonicity of the tangent map also the harmonicity of the identity map of the tangent bundle.