Harmonic Magnetic Field Research Articles

Solar large-scale magnetic field and cycle patterns in solar dynamo

ABSTRACT We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen solution of solar dynamo equations with the growth saturated by a back reaction of the dynamo-driven magnetic field on solar hydrodynamics. The nominal 11(22)-yr cycle as recorded in each mode has a specific phase shift varying from cycle to cycle; the actual length of the cycle varies from one cycle to another and from tracer to tracer. Both the observation and the dynamo model show an exceptional role of the axisymmetric ℓ5 mode. Its origin seems to be readily connected with the formation and evolution of sunspots on the solar surface. The results of observations and dynamo models show a good agreement for the low ℓ1 and ℓ3 modes. The results for these modes do not differ significantly for the axisymmetric and non-axisymmetric models. Our findings support the idea that the sources of the solar dynamo arise as a result of both the distributed dynamo processes in the bulk of the convection zone and the surface magnetic activity.

Investigation of AC loss of superconducting field coils in a double-stator superconducting flux modulation generator by using T-A formulation based finite element method

In order to reliably make use of superconductors in wind generators, a double-stator superconducting flux modulation generator is proposed here to avoid rotation of field coils and armature windings. The superconducting field coils are located in the inner stator while the armature windings are placed in the outer stator. In this way, the stationary-rotatory couplings of current and cryogenic coolants for superconducting field coils and/or armature windings are removed. Because of the modulation effect of the reluctance rotor between the two stators and the armature reaction field, moving AC magnetic fields are acted on superconducting coils in the inner stator. These moving AC magnetic fields are called magnetic field harmonics in the flux modulation generators. The frequencies of these harmonics are multiples of rotor mechanical frequency. Compared to synchronous superconducting generators, the amplitudes of the harmonics are higher. Even though methods to reduce the amplitudes of harmonics have been studied, the level of the AC loss in the superconducting field coils is still unknown. In this paper, numerical simulations based on the T–A formulation are used to estimate the AC loss of the superconducting field coils in a 10 MW double-stator superconducting flux modulation generator. It is found that by choosing a suitable working temperature, the AC loss of the superconducting field coils without any harmonic reduction methods is not very high, but eddy current loss of copper thermal shield inside the cryostat is significantly higher.

Winding Configurations and Pole/Tooth Combinations of Doubly-Fed Flux-Switching Permanent Magnet Machines

The design rules of winding configurations and stator-pole/rotor-tooth (SP/RT) number combinations of doubly-fed flux-switching permanent magnet (DF-FSPM) machines are investigated in this paper based on coil electromotive force (EMF) vectors. The relationships between the components of stator and rotor coil-EMF vector diagrams are unveiled at first, including the numbers of stator and rotor phases, and the numbers of stator and rotor spokes. Then, the SP/RT number combinations are derived considering feasible stator/rotor phase number combinations and different winding configurations. The SP/RT number combinations are optimized considering the winding factors, magnetic field harmonics, unbalanced magnetic forces and machine diameter. It is shown that both of the stator and rotor pitch factors increase when the SP and RT numbers get closer. Furthermore, the influence of winding configurations and SP/RT number combinations on electromagnetic performances of DF-FSPM machines are analyzed by finite-element method. Finally, the analysis results are validated by experiment.

Effect of harmonic magnetic field and pulse magnetic field on microstructure of high purity Cu during electromagnetic direct chill casting

The effects of two types of magnetic fields, namely harmonic magnetic field (HMF) and pulse magnetic field (PMF) on magnetic flux density, Lorentz force, temperature field, and microstructure of high purity Cu were studied by numerical simulation and experiment during electromagnetic direct chill casting. The magnetic field is induced by a magnetic generation system including an electromagnetic control system and a cylindrical crystallizer of 300 mm in diameter equipped with excitation coils. A comprehensive mathematical model for high purity Cu electromagnetic casting was established in finite element method. The distributions of magnetic flux density and Lorentz force generated by the two magnetic fields were acquired by simulation and experimental measurement. The microstructure of billets produced by HMF and PMF casting was compared. Results show that the magnetic flux density and penetrability of PMF are significantly higher than those of HMF, due to its faster variation in transient current and higher peak value of magnetic flux density. In addition, PMF drives a stronger Lorentz force and deeper penetration depth than HMF does, because HMF creates higher eddy current and reverse electromagnetic field which weakens the original electromagnetic field. The microstructure of a billet by HMF is composed of columnar structure regions and central fine grain regions. By contrast, the billet by PMF has a uniform microstructure which is characterized by ultra-refined and uniform grains because PMF drives a strong dual convection, which increases the uniformity of the temperature field, enhances the impact of the liquid flow on the edge of the liquid pool and reduces the curvature radius of liquid pool. Eventually, PMF shows a good prospect for industrialization.

Partitioned Stator Hybrid Excited Machine With DC-Biased Sinusoidal Current

This article proposes a new partitioned stator hybrid excited (PS-HE) machine with dc-biased sinusoidal current. On the inner stator, the consequent pole permanent magnets (PMs) are employed as the PM excitation. On the outer stator, a set of integrated dual three-phase winding is adopted to produce the wound and armature fields at the same time by injecting the sinusoidal current with dc bias. So, the flexible flux regulation can be realized by controlling the dc bias component. The rotor composed of segmented iron cores is sandwiched between two stators. By employing the air-gap field modulation theory, the air-gap magnetic field harmonics are analyzed to explain the operating and flux regulation principle. Furthermore, a design optimization and the electromagnetic performances of the proposed machine are investigated by finite element analysis. When compared with the existing series and parallel PS-HE machines, the proposed machine can avoid the disadvantage of low torque density of PARALLEL HE machine, and it can solve the problem of the poor flux regulation ability of series HE machine as well, which is mainly contributed by the reasonable space allocation of PMs and field winding excitations. Finally, a prototype is built and tested to verify the theoretical analyses.

An Ultrasensitive Debris Microsensor for Oil Health Monitoring Based on Resistance–Inductance Parameter

An ultrasensitive debris sensor based on microfluidic technology is introduced in this article. The microsensor not only achieves the traditional inductance detection, but also proposes a resistance detection method based on coil. The magnetic field distribution in the detection region was obtained by simulation, and the magnetization and eddy current effects of metal particles in harmonic magnetic field were simulated. The frequency characteristics and signal characteristics of inductance and resistance detection were studied through experiments. High-frequency excitation can enhance the eddy current effect inside the metal particles, thereby helping to improve the resistance detection sensitivity, enhance the inductance detection effect of nonferromagnetic metal particles, and reduce the inductance detection effect of ferromagnetic metal particles. The research results showed that inductance parameter has stronger detection ability for ferromagnetic metals, and resistance parameter has stronger detection ability for nonferromagnetic metals. According to the characteristics of inductance and resistance signals, the accurate distinction of metal debris property and size can be realized. And the size measurement error caused by the debris shape can be reduced by the judgment method based on two parameters. This impedance detection based on inductance and resistance parameters provides a new method for high-sensitivity monitoring of metal debris. The debris microsensor can be used as a sensing element of portable oil monitoring devices, and provide technical support for health assessment, state warning, and fault diagnosis of mechanical equipment.

Zonal Harmonics of Solar Magnetic Field for Solar Cycle Forecast

Zonal Harmonics of Solar Magnetic Field for Solar Cycle Forecast

Simplified Brushless Wound Field Synchronous Machine Topology Based on a Three-Phase Rectifier

This paper proposes a novel simplified brushless wound field synchronous machine (BL-WFSM) topology based on an uncontrolled three-phase rectifier. The output of the rectifier is injected into the common point of the star-connected three-phase armature winding. This arrangement develops an armature MMF consisting of two components: the fundamental MMF, which is rotating in nature, and the harmonic pulsating magnetic field, which induces the harmonic current in the specially designed harmonic winding of the rotor. The induced harmonic current is rectified through the full-bridge rectifier, which excites the main rotor field to achieve brushless operation and produce torque while interacting with the main fundamental rotating field of the armature. The proposed brushless topology is simple as it involves a single three-phase rectifier which does not require any complicated control strategy. Furthermore, this topology is a cost-effective solution as compared to the conventional brushless WFSM topologies since it does not require any additional hardware component except for a typical rectifier. In addition, the performance of the proposed brushless topology is better than the existing three-phase rectifier-based brushless scheme in terms of efficiency, output torque, and torque ripple. The proposed simplified BL-WFSM topology is validated through 2-D finite element analysis (FEA) using JMAG-Designer 19.1 to obtain the output torque of the machine.

Аналитический учет внеосевых эффектов в рентгеновском излучении гармоник лазеров на свободных электронах

We give analytical description of generation of harmonics of the undulator radiation (UR) with account for the finite electron beam size, emittance, off-axis beam deviation and electron energy spread, as well as for the constant magnetic components and field harmonics effects. We give exact analytical expressions for the generalized Bessel and Airy functions, which describe the spectrum line shape and intensities in the two-frequency bi-harmonic undulator with account for the above factors. The obtained analytical formulae distinguish contributions of each field component and every undulator and beam parameter on the harmonic radiation in free electron lasers (FEL). The effect of the field on the harmonic radiation is analyzed with account for the beam finite size and its off-axis deviation. The phenomenological model is employed for the FEL modeling; with its help we study the harmonic generation, including even ones, in the experiments LCLS and LEUTL. We demonstrate analytically that strong second FEL harmonic in X-ray FEL at the wavelengths λ = 0.75nm in the LCLS experiment is caused by the deviation of the electron trajectories off the axis in 15 μm on the gain length 1.6 m, which is comparable with the beam size; the strong second FEL harmonic in the LEUTL experiment at the wavelength λ = 192nm can be attributed to interaction of the electrons in wide, ~ 0.2 mm, beam with the photon radiation at the gain length 0.87 m. The modeling results fully agree with the measurements. The developed formalism allows the analysis of projected and built FELs and their radiation, helps minimizing losses and correcting magnetic fields; it also shows physical background and reasons for each harmonic radiated power in the FEL.

Study for Influence of Harmonic Magnetic Fields on Vibration Properties of Core of Anode Saturable Reactor in HVDC Converter Valve System

The cores of anode saturated reactor (ASR) are the main vibration source of the HVDC converter valve system. The ASR is excited with an impulse voltage, which contains many harmonic components, and the magnetostriction of cores is usually the main reason of the ASR vibration. Therefore it is significant to study the influence of the harmonic on the vibration of core of ASR. In this paper, the magneto-mechanical coupling model is established based on the magnetostriction theory and the expression of vibration acceleration in the presence of third harmonic is derived. The vibration test platform is built to test the core's vibration acceleration. The magnetic and magnetostrictive properties of silicon steel sheet under different working conditions are measured. The three-dimensional simulation model of the core is established, and the vibration acceleration under different magnetic flux density is calculated. The comparison of the experiment and simulation results shows the rationality of the magneto-mechanical coupling model. The influence of third harmonic magnetic flux density on vibration is studied by changing the phase of the third harmonic magnetic flux density and the ratio of the third harmonic magnetic flux density to the fundamental magnetic flux density. Both the calculated and measured results show that the third harmonic magnetic flux density affects the vibration acceleration according to the double-frequency components of the third harmonic, as well the sum-frequency and difference-frequency components of the third harmonic and fundamental frequency.

An Improved Sub-Domain Model of Flux Switching Permanent Magnet Machines Considering Harmonic Analysis and Slot Shape

The flux switching permanent magnet motor is a kind of double-salient machine with good speed regulation performances and application prospects. However, in traditional sub-domain models which are used to exactly calculate the magnetic field of the flux switching permanent magnet motor, the orders of major harmonics can not be intuitively obtained. The computational efficiency and practicality of the sub-domain models are limited. Meanwhile, some errors are caused in the equivalent process of iron slot shapes. Aiming at these problems, an improved sub-domain model is proposed in this paper. The major magnetic field harmonics are selected in advance for each sub-domain region by the magnetic permeance function model of the air gap. In addition, the influence of the slot shape equivalence is corrected by the magnetic permeability of slots, and the accuracy of the sub-domain calculation is improved. The proposed model is verified to have the advantages of high accuracy and fast computing speeds by 2-D finite element analysis. A convenient and reliable approach for flux switching permanent magnet motor designs is provided thereby.

Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields

We explore a class of quantum control operations based on a wide family of harmonic magnetic fields that vary softly in time. Depending on the magnetic field amplitudes taking part, these control operations can produce either squeezing or loop (orbit) effects, and even parametric resonances, on the canonical variables. For these purposes we focus our attention on the evolution of observables whose dynamical picture is ascribed to a quadratic Hamiltonian that depends explicitly on time. In the first part of this work we survey such operations in terms of biharmonic magnetic fields. The dynamical analysis is simplified using a stability diagram in the amplitude space, where the points of each region will characterise a specific control operation. We discuss how the evolution loop effects are formed by fuzzy (non-commutative) trajectories that can be closed or open, in the latter case, even hiding some features that can be used to manipulate the operational time. In the second part, we generalise the case of biharmonic fields and translate the discussion to the case of polyharmonic fields. Using elementary properties of the Toeplitz matrices, we can derive exact solutions of the problem in a symmetric evolution interval, leading to the temporal profile of those magnetic fields suitable to achieve specific control operations. Some of the resulting fuzzy orbits can be destroyed by the influence of external forces, while others simply remain stable.

Suppression of nonlinear standing wave excitation via the electrical asymmetry effect

The electrical asymmetry effect (EAE) enables separate control of the ion flux and the mean ion energy in capacitively coupled plasmas (CCP). While a variety of plasma processing applications benefit from this, large-area, very-high-frequency CCPs still suffer from lateral nonuniformities caused by electromagnetic standing wave effects (SWE). Many of such plasma sources are geometrically asymmetric and are operated at low pressure so that high frequency nonlinear plasma series resonance (PSR) oscillations of the RF current are self-excited. These PSR oscillations lead to the presence of short wavelength electromagnetic waves and a more pronounced SWE. In this work, we investigate the influence of the EAE on the nonlinear standing wave excitation in a geometrically asymmetric, low pressure capacitively coupled argon plasma driven by two consecutive harmonics (30 MHz and 60 MHz) with an adjustable phase shift, θ. We use a hairpin probe to determine the radial distribution of the electron density in combination with a high-frequency B-dot probe to measure the radial distribution of the harmonic magnetic field, which in turn is used to calculate the harmonic current density based on Ampere’s law. Our experimental results show that the asymmetry of the discharge can be reduced electrically via the EAE. In this way the self-excitation of high frequency PSR oscillations can be attenuated. By tuning θ, it is, therefore, possible to switch on and off the nonlinear standing wave excitation caused by the PSR and, accordingly, the plasma uniformity can be optimized.

Comparative analysis of the theoretical and experimental spectral properties of X-FELs

The theoretical study of the undulator radiation (UR) from electron beams in free electron laser (FEL) undulators is performed. We analytically account for the magnetic field harmonics and non-periodic field components, off-axis effects, divergence, energy spread and other losses in real installations. The expressions for the UR intensity and spectrum are obtained explicitly in terms of the generalized Bessel and Airy functions. The results are applied to high gain FELs, using the analytical FEL model. They are verified with experiments at SwissFEL, PAL-XFEL, LCLS, SACLA and LEUTL FELs. The spectrum, UR line shape and harmonic power evolution are theoretically analyzed and compared with the available experimental results. The spectral properties of the studied FELs are compared with each other; where the measured data is absent, the theoretical predictions are given.

Optimization of compensation of magnetic field imperfection in K500 superconducting cyclotron

Large first Fourier harmonic of the main magnetic field near the injection and extraction regions of the K500 superconducting cyclotron at VECC, Kolkata adversely affects the beam, guiding it off-center and inducing large amplitude coherent oscillations, thus, making efficient extraction very difficult. Copper-liners over the iron-poles make the poles inaccessible for local iron-shimming. In this paper we discuss an optimal correction of the field imperfection. We consider the magnetic field measurements data, analyze the contributions from different sources of error harmonics and find that it is mostly due to the misalignment of major components of the machine. An algorithm to provide effective correction of the first harmonic of the main magnetic field is proposed and successfully adopted in the K500 beam operation.

Research on inversion method with multi-transceiver distance in underground space based on apparent conductivity

The layered ground under the excitation of a harmonic magnetic field will generate a secondary magnetic field. On the condition of low induction number, the apparent conductivity can be obtained by using the normalized secondary field measured by the instrument directly. By discretizing the integral of relative response function density, the expression of contribution value of conductivity of each layer to the apparent conductivity can be obtained. By using multiple sets of transceiver distance, we can obtain different apparent conductivity observation equations, then the conductivity and thickness of each layer can be solved by Gauss-Newton method. A three-layer medium model containing a V-shaped tunnel is designed for inversion simulation calculations. The results show that the higher the SNR of observed signal, the more stable the inversion result. The maximum relative error of thickness is about 10%.

Research on a damage identification method of harmonic magnetic field detection in steel pipes with cladding

This paper presents a harmonic magnetic field detection technology for damage identification of an in-service coated steel pipeline. Based on the principles of electromagnetic theory and magnetic field detection combined with magnetic focusing technology, an array consisting of a focusing detection probe and a harmonic magnetic field detection system were designed. However, the acquired detection signal includes an excitation signal in addition to the defect information. In order to make the defect information more obvious, the excitation signal needs to be removed to extract the defect feature. Local mean decomposition (LMD) is a new time-frequency analysis method that adaptively decomposes a signal into a set of product function (PF) combinations. The envelope of the PF is the instantaneous amplitude and the instantaneous frequency can be calculated by demodulating the derivative of the phase with a uniform amplitude-modulated signal. This method completely bypasses the Hilbert transform. Therefore, it does not involve the problem of negative frequencies without physical meaning. The effectiveness of LMD is demonstrated by a successful example of damage detection. Combining the data characteristics obtained by the experiment, the data processing algorithm suitable for the test data is written by improving the LMD. The algorithm is easy to use and has high engineering practicability.

Effect of time‐harmonic current on the harmonic leakage inductance of fractional slot concentrated winding permanent magnet synchronous motor

Harmonic leakage inductance occupies a high proportion in the synchronous inductance of fractional slot concentrated winding permanent magnet synchronous motor (FSCW-PMSM), and the synchronous inductance determines the operating performance of the motor. To calculate the harmonic leakage inductance and synchronous inductance of the FSCW-PMSM fed by inverters, two-dimensional finite element analysis and the analytical method are used to study the influence of time-harmonic current on the harmonic leakage inductance of the three-phase FSCW-PMSM in this study, and the influence mechanism is revealed. The relationship between the time-harmonic magnetic field and space harmonic magnetic field is obtained, and the harmonic leakage coefficient and the working harmonic coefficient with different slot-pole combinations are investigated. The results show that the time-harmonic current can reduce the harmonic leakage inductance and increase the magnetising inductance, but has little effect on the synchronous inductance under the unsaturated condition. A prototype was manufactured and tested to verify the accuracy of the analysis model. The research results provide beneficial help for the design of the three-phase FSCW-PMSM fed by inverters.

Generation of Coherent X-ray Harmonic Radiation in a Single-Pass Free-Electron Laser with Phase Shift of Electrons Relative to Photons

Evolution of bunching and harmonic power is theoretically studied for a single-pass free-electron laser (FEL) in which electrons are periodically phase-shifted relative to photons in intervals between undulators with harmonics of magnetic field. Analytical calculations are used to reveal the configuration of magnetic field of an asymmetric elliptical and planar undulators that make it possible to suppress the fundamental and amplify several higher harmonics. The evolution of power and bunching is analyzed using a phenomenological model of FEL that describes violation of bunching between the undulator stages and a relatively high sensitivity of electron–photon interaction at wavelengths of higher harmonics to energy spread, size, deflection of the beam from the axis, etc. Expressions for the Bessel coefficients of the planar and elliptical undulators with field harmonics are analytically studied. Such undulators can be used in phase-shifted FELs for an increase in the power of higher (X-ray) harmonics by a factor of up to 100 in comparison with conventional FELs.

The tooth factor effect on the harmonics of large electrical machines

In the current study, the general mathematical model for the calculation and analysis of asynchronous systems and transient cases in asynchronous synchronous large electrical machines was developed. The theory of magnetic fields in the teeth's circuits with a smooth surface of the rotor was used and at the same time, high harmonics of magnetic fields and its effect on the transient cases was also calculated. Performance curves were investigated using Matlab codes and evaluated under different values of factor. The results confirmed the possibility of improving the noise harmonics on the sinusoidal wave form, which is reflected on the machines starting.