Diffusion Equations of the Electric Charges and Magnetic Flux

Innovative definitions of the electric and magnetic diffusivities through conducting mediums and innovative diffusion equations of the electric charges and magnetic flux are verified in this article. Such innovations depend on the analogy of the governing laws of diffusion of the thermal, electrical, and magnetic energies and newly defined natures of the electric charges and magnetic flux as energy, or as electromagnetic waves, that have electric and magnetic potentials. The introduced diffusion equations of the electric charges and magnetic flux involve Laplacian operator and the introduced diffusivities. Both equations are applied to determine the electric and magnetic fields in conductors as the heat diffusion equation which is applied to determine the thermal field in steady and unsteady heat diffusion conditions. The use of electric networks for experimental modeling of thermal networks represents sufficient proof of similarity of the diffusion equations of both fields. By analysis of the diffusion phenomena of the three considered modes of energy transfer;the rates of flow of these energies are found to be directly proportional to the gradient of their volumetric concentration, or density, and the proportionality constants in such relations are the diffusivity of each energy. Such analysis leads also to find proportionality relations between the potentials of such energies and their volumetric concentrations. Validity of the introduced diffusion equations is verified by correspondence their solutions to the measurement results of the electric and magnetic fields in microwave ovens.

Gyrokinetic simulation of magnetic-island-induced electric potential vortex mode

Ion temperature gradient(ITG)-driven turbulence with embedded static magnetic islands is simulated by utilizing a gyrokinetic theory-based global turbulence transport code(GKNET)in this work.Different from the traditional equilibrium circular magnetic-surface average(EMSA)method,an advanced algorithm that calculates the perturbed magnetic-surface average(PMSA)of the electric potential has been developed to precisely deal with the zonal flow component in a non-circular magnetic surface perturbed by magnetic islands.Simulations show that the electric potential vortex structure inside islands induced by the magnetic islands is usually of odd parity when using the EMSA method.It is found that the odd symmetry vortex can transfer into an even one after a steep zonal flow gradient,i.e.the flow shear has been built in the vicinity of the magnetic islands by adopting the PMSA algorithm.The phase of the potential vortex in the poloidal cross section is coupled with the zonal flow shear.Such an electric potential vortex mode may be of essential importance in wide topics,such as the turbulence spreading across magnetic islands,neoclassical tearing mode physics,and also the interaction dynamics between the micro-turbulence and MHD activities.

Winding Function Model-based Performance Evaluation of a PM Transverse Flux Generator for Applications in Direct-drive Systems

The magnetic flux in a permanent magnet transverse flux generator(PMTFG) is three-dimensional(3D), therefore, its efficacy is evaluated using 3D magnetic field analysis. Although the 3D finite-element method(FEM) is highly accurate and reliable for machine simulation, it requires a long computation time, which is crucial when it is to be used in an iterative optimization process. Therefore, an alternative to 3DFEM is required as a rapid and accurate analytical technique. This paper presents an analytical model for PMTFG analysis using winding function method. To obtain the air gap MMF distribution, the excitation magneto-motive force(MMF) and the turn function are determined based on certain assumptions. The magnetizing inductance, flux density, and back-electro-magnetomotive force of the winding are then determined. To assess the accuracy of the proposed method, the analytically calculated parameters of the generator are compared to those obtained by a 3D-FEM. The presented method requires significantly shorter computation time than the 3D-FEM with comparable accuracy.

Magnetic diagnostics layout design for CFETR plasma equilibrium reconstruction

Plasma equilibrium reconstruction provides essential information for tokamak operation and physical analysis.An extensive and reliable set of magnetic diagnostics is required to obtain accurate plasma equilibrium.This study designs and optimizes the magnetic diagnostics layout for the reconstruction of the equilibrium of the plasma according to the scientific objectives,engineering design parameters,and limitations of the Chinese Fusion Engineering Test Reactor(CFETR).Based on the CFETR discharge simulation,magnetic measurement data are employed to reconstruct consistent plasma equilibrium parameters,and magnetic diagnostics'number and position are optimized by truncated Singular value decomposition,verifying the redundancy reliability of the magnetic diagnostics layout design.This provides a design solution for the layout of the magnetic diagnostics system required to control the plasma equilibrium of CFETR,and the developed design and optimization method can provide effective support to design magnetic diagnostics systems for future magnetic confinement fusion devices.

Three-axis magnetic flux leakage in-line inspection simulation based on finite-element analysis

With the increase of pipelines, corrosion leakage accidents happen frequently. Therefore, nondestructive testing technology is important for ensuring the safe operation of the pipelines and energy mining. In this paper, the structure and principle of magnetic flux leakage （MFL） in-line inspection system is introduced first. Besides, a mathematic model of the system according to the ampere circuit rule, flux continuity theorem, and column coordinate transform is built, and the magnetic flux density in every point of space is calculated based on the theory of finite element analysis. Then we analyze and design the disposition of measurement section probes and sensors combining both three-axis MFL in-line inspection and multi-sensor fusion technology. Its advantage is that the three-axis changes of magnetic flux leakage field are measured by the multi-probes at the same time, so we can determine various defects accurately. Finally, the theory of finite element analysis is used to build a finite element simulation model, and the relationship between defects and MFL inspection signals is studied. Simulation and experiment results verify that the method not only enhances the detection ability to different types of defects but also improves the precision and reliability of the inspection system.

Magnetic Flux Leakage Course of Inner Defects and Its Detectable Depth

As a promising non-destructive testing(NDT)method,magnetic flux leakage(MFL)testing has been widely used for steel structure inspection.However,MFL testing still faces a great challenge to detect inner defects.Existing MFL course researches mainly focus on surface-breaking defects while that of inner defects is overlooked.In the paper,MFL course of inner defects is investigated by building magnetic circuit models,performing numerical simulations,and conducting MFL experiments.It is found that the near-surface wall has an enhancing effect on the MFL course due to higher permeability of steel than that of air.Further,a high-sensitivity MFL testing method consisting of Helmholtz coil magnetization and induction coil with a high permeability core is proposed to increase the detectable depth of inner defects.Experimental results show that inner defects with buried depth up to 80.0 mm can be detected,suggesting that the proposed MFL method has the potential to detect deeply-buried defects and has a promising future in the field of NDT.

Evaluation of Surface Cracks Using Magnetic Flux LeakageTesting

The magnetic field distribution characteristics of surface cracks with various widths are discussed based on finite element (FEM) results. The crack depth was 0.20 mm, the width range was from 0.02 to 1.00 mm. The results showed that crack width and lift-off (the distance between surface and sensor) will influence signals. Discussed in this paper is the influence of various lift-off parameters on the peak to peak values of the normal component in magnetic flux leakage testing. The effects can be applied to evaluate surface breaking cracks of different widths and depths. An idea is presented to smooth narrow, sharp crack tips using alternating current (AC) field magnetization.

Coronal Magnetic Flux Rope Equilibria and Magnetic Helicity

Using a 2.5-dimensional (2.5-D) ideal MHD model, this paper analyzes the equilibrium properties of coronal magnetic flux ropes in a bipolar ambient magnetic field. It is found that the geometrical features of the magnetic flux rope, including the height of the rope axis, the half-width of the ropes and the length of the vertical current sheet below the ropes are determined by a single magnetic parameter, the magnetic helicity, which is the sum of the self-helicity of the rope and the mutual helicity between the rope field and the ambient magnetic field. All the geometrical parameters increase monotonically with increasing magnetic helicity. The implication of this result in solar active phenomena is briefly discussed.

High T_c Superconductor Theoretical Models and Electromagnetic Flux Characteristics

High Tc Superconductors （HTS） have special electromagnetic characteristics and phenomena. Effort has been made in order to theoretically understand the appfied HTS superconductivity and HTS behaviors for practical appfications, various theoretical models related to the HTS electromagnetic properties have been developed. The theoretical models and analytic methods are summarized with regard to understanding the HTS magnetic flux characteristic which is one of the most critical issues related to HTS appfications such as for HTS magnetic levitation application.

Comparative Study of Novel Axial Flux Magnetically Geared and Conventional Axial Flux Permanent Magnet Machines

In this paper,a performance comparison between the novel axial flux magnetically geared machines(AFMG)and the conventional axial flux YASA machine is presented.The AFMG and YASA machines have the same stator construction in which segments are equipped with concentrated windings to form the stator.However,the AFMG machine has two rotors with different pole-pair numbers.Magnetic gear effect can be obtained to increase the torque density.The performance comparisons at no-load and on-load conditions are then studied by 3D-finite element analysis(FEM).Moreover,both machines are prototyped,tested and compared.

A Dynamics Study of a Magnetic Flux Leakage(MFL) Signal and its Application to Defect Location Discrimination in Steel Pipes MFL Testing Equipment

Difference processing was used to the direct current magnetic flux leakage （DC-MFL） signal, emanating from the defects machined artificially on the internal and external surfaces of a steel pipe. Consequently, the loea-tion discriminating index 8 was provided to identify the defect whether it is on the internal surface or the external one. Three characteristics, shape, depth and orientation of the defect, were discussed through a series of experiments on the artificial defects, such as transverse notches, oblique notches and pits on the steel pipe. The approach has been verified effective to address the defect location identifying problem, albeit the limits on the accuracy assessment to those natural defects on steel pipes in service.

Electromagnetic Performance Analysis of Flux-Switching Permanent Magnet Tubular Machine with Hybrid Cores

The performance of traditional flux switching permanent magnet tubular machine(FSPMTM)are improved by using new material and structure in this paper.The existing silicon steel sheet making for all mover cores or part of stator cores are replaced by soft magnetic composite(SMC)cores,and the lamination direction of the silicon steel sheet in stator cores have be changed.The eddy current loss of the machine with hybrid cores will be reduced greatly as the magnetic flux will not pass through the silicon steel sheet vertically.In order to reduce the influence of end effect,the unequal stator width design method is proposed.With the new design,the symmetry of the permanent magnet flux linkage has been improved greatly and the cogging force caused by the end effect has been reduced.Both 2-D and 3-D finite element methods(FEM)are applied for the quantitative analysis.

DEVELOPMENT OF THE CONTROL METHODOLOGY OF THE GIANT MAGNETOSTRICTIVE ACTUATOR BASED ON MAGNETIC FLUX DENSITY

According to the principle of the magnetostriction generating mechanism, thecontrol model of giant magnetostriction material based on magnetic field and the control method withmagnetic flux density are developed. Furthermore, this control method is used to develop a giantmagnetostrictive micro-displacement actuator (GMA) and its driving system. Two control methods whosecontrol variables are current intensity and magnetic flux density are compared with each other byexperimental studies. Finally, effective methods on improving the linearity and control precision ofmicro-displacement actuator and reducing the hysteresis based on the controlling magnetic fluxdensity are obtained.

The Ellerman bomb and ultraviolet burst triggered successively by an emerging magnetic flux rope

Ellerman bombs(EBs)and ultraviolet(UV)bursts are common brightening phenomena,which are usually generated in the low solar atmosphere of emerging flux regions.In this paper,we have investigated the emergence of an initial un-twisted magnetic flux rope based on three-dimensional(3 D)magneto-hydrodynamic(MHD)simulations.The EB-like and UV burst-like activities successively appear in the U-shaped part of the undulating magnetic fields triggered by the Parker instability.The EB-like activity starts to appear earlier and lasts for about 80 seconds.Six minutes later,a much hotter UV burstlike event starts to appear and lasts for about 60 seconds.Along the direction vertical to the solar surface,both the EB and UV burst start in the low chromosphere,but the UV burst extends to a higher altitude in the up chromosphere.The regions with apparent temperature increase in the EB and UV burst are both located inside the small twisted flux ropes generated in magnetic reconnection processes,which are consistent with the previous 2 D simulations that most hot regions are usually located inside the magnetic islands.However,the twisted flux rope corresponding to the EB is only strongly heated after it floats up to an altitude much higher than the reconnection site during that period.Our analyses show that the EB is heated by the shocks driven by the strong horizontal flows at two sides of the U-shaped magnetic fields.The twisted flux rope corresponding to the UV burst is heated by the driven magnetic reconnection process.

Quantum transport through two series Aharonov-Bohm interferometers with zero total magnetic flux

With the help of nonequilibrium Green＇s function technique, the electronic transport through series Aharonov-Bohm （AB） interferometers is investigated. We obtain the AB interference pattern of the transition probability characterized by the Mgebraic sum φ and the difference θ of two magnetic fluxes, and particularly a general rule of AB oscillation period depending on the ratio of integer quantum numbers of the fluxes. A parity effect is observed, showing the asymmetric AB oscillations with respect to the even and odd quantum numbers of the total flux in antiparallel AB interferometers. It is also shown that the AB flux can shift the Fano resonance peaks of the transmission spectrum.

Distribution of Magnetic Flux Density in Soft-Contact EMCC Rectangular Mold

The distribution of the magnetic flux density in a soft-contact electromagnetic continuous casting （EMCC） rectangular mold was investigated. The experimental results show that with an increase in electric power, the magnetic flux density increases. The position where the maximum magnetic flux density appears will shift up when the coil moves to the top of the mold. At the same time, the maximum magnetic flux density will increase and the effective acting range of electromagnetic pressure will widen. As a result, in practice, the coil should be placed near the top part of the mold. The meniscus should be controlled near the top part of the coil, as this not only remarkably improves the billet surface quality but also saves energy. With the same electric power input, the higher the frequency, the lower the magnetic flux density.

Influence of Slot Defect Length on Magnetic Flux Leakage

A key issue, which influences the applications of magnetic flux leakage testing, is defect quantification. There have been many research on the relationship between width, depth and magnetic flux leakage of slot defect. However, the length factor is often ignored. The relationship between characteristics of defect leakage field and defect length was investigated. The magnetic flux leakages of a series of plate specimens with the same width, same depth and different length slot defects were tested under the same magnetizing conditions. Testing results show that defect length is an important parameter needed to consider in quantifying defects.

Effect of Distribution of Magnetic Flux Density on Purifying Liquid Metal by Travelling Magnetic Field

The distribution of the magnetic flux density in the magnetic field generator which provided travelling magnetic field was determined. The experiments using liquid gallium and aluminum silicon alloy to observe the turbulent flow or remove inclusions were performed to obtain the basic principles how the distribution of the magnetic flux density took effect on removing inclusions from molten metal by electromagnetic field. The suitable area in the field for purifying metal was suggested.

The Positions and Number of Flux Loops and Magnetic Probes for the HT-7U Superconducting Tokamak

The plasma shape and other paremeters such as /3P, li is important for the tokamak deveice where the plasma has a non-circular cross-section of sufficient elongation. The measuered signals of magnetic probes and flux loops are used to reconstruct the plasma shape and the current profile in device operation and plasma shape feed back control system. So the number and positions of magnetic probes and flux loops provides the basis of the plasma reconstruction. This paper instroduce how to use EFIT code (equilibrium fitting code) to determine the number and positions of the magnetic probes and flux loops. The simulation result is given also.

Magnetic flux leakage during longitudinal magnetic flux induction heating

A three-dimensional electromagnetic thermal coupled model of a 45#steel strip during longitudinal magnetic flux induction heating was established in this study.The influence of different power levels,frequencies,and electromagnetic shielding on the magnetic induction intensity and the heating of parts of different materials around the inductor was analyzed by calculating the magnetic induction intensity around the longitudinal flux induction heater under different conditions.The results show that leakage flux can be reduced up to 49%by electromagnetic shielding.The higher the frequency,the greater the electromagnetic shielding effect,and the lower the magnetic leakage around the inductor.Conversely,the higher the power,the greater the magnetic induction around the inductor.By adding electromagnetic shielding to reduce magnetic leakage of the inductor and replacing the metal part material around the inductor with stainless steel,the heat generation of the parts around the inductor can be greatly reduced.