Tangential Magnetic Field Research Articles

A method of characterizing axial stress in ferromagnetic members using superficial magnetic flux density obtained from static magnetization by permanent magnet

It is of great significance to obtain the information about the stress of load-bearing ferromagnetic members quickly in order to maintain the safety of the infrastructure. The key point is to accurately and quickly determine the characterization parameters which change sensitively and linearly with the stress. Among the existing electromagnetic methods of determining axial stress in ferromagnetic members, exciting coils are usually adopted to exert a time-varying magnetic field on the ferromagnetic members, which will induce the problems of winding coils, coil heating, and eddy current that influences the test results. What is worse is that it is inevitable to compare the experimental data point by point to determine the adequate magnetic parameter characterizing the stress, which influences the fast determining of the axial stress in ferromagnetic members. In order to break through these limitations, in this paper we propose a method of determining the axial stress in ferromagnetic members by using superficial magnetic flux density obtained from static magnetization in permanent magnets. In this method, permanent magnetizers are adopted to excite the overall damping and local uniform spatially-varying constant magnetic field on ferromagnetic members. A testing probe including Hall chip array is adopted to measure the superficial axial and radial magnetic flux density to determine the axial stress of the ferromagnetic member. The principle is elaborated to choose the adequate superficial magnetic flux density fast and precisely for characterizing the axial stress in ferromagnetic members. According to the theory of demagnetizing field, the continuity of the tangential magnetic field strength and Gauss's law for magnetism, the relational equation between the derivative of superficial axial magnetic flux density with the stress and the derivative of superficial radial magnetic flux density with the stress is established. Then, an experiment is conducted to verify the proposed method. The experimental results show that according to this relational equation, the superficial magnetic flux density with the highest stress sensitivity can be determined quickly and accurately. What is more, the linearity of the superficial magnetic flux density varying with the stress is good, and the goodness of the corresponding linear fitting R2 is greater than 0.98. It means that the determined superficial magnetic flux density can be used as a feature parameter to characterize the stress in ferromagnetic members. The proposed method of determining the axial stress in this paper can provide a new way of on-line detecting the working stress in ferromagnetic components.

Anisotropic slip magneto-bioconvection flow from a rotating cone to a nanofluid with Stefan blowing effects

A mathematical model for two dimensional steady laminar natural convective anisotropic slip boundary layer flows from a rotating vertical cone embedded in ethylene glycol bionanofluid is presented. The influence of Stefan blowing is also taken into account. Four different non-particles namely Copper (Cu), Alumina (Al2O3), Copper Oxide (Cuo), Titanium Oxide (TiO2) are explored. Suitable similarity transformations are used to convert the governing equations into non-linear ordinary differential equations. These are then solved numerically, with appropriate boundary conditions, utilizing an implicit finite difference method (the BVP5C code in MATLAB). During computation Sc, Lb, Le and Lb are presented as unity, whilst Pr is taken as 151. The effects of the governing parameters on the dimensionless velocities, temperature, nanoparticle volume fraction, density of motile microorganisms as well as on the local skin friction, local Nusselt, Sherwood number and motile micro-organism number density are thoroughly examined via tables and graphs. It is found that the skin friction factor increases with tangential slip, magnetic field and Schmidt number whilst it decreases with blowing parameter and spin parameters. It is further observed that both the friction and heat transfer rates are highest for copper nanoparticles and lowest for TiO2nanoparticles. Validation of the BVP5C numerical solutions with published results for several special cases of the general model is included. The study is relevant to electro-conductive bio-nano-materials processing.

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression with Taylor's series. The transmitted field in the homogeneous gyrotropic cylinder is expressed in terms of the series of wave functions based on the integral equation. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions of continuous tangential electric and magnetic fields. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.

Characterisation of case depth in induction-hardened medium carbon steels based on magnetic minor hysteresis loop measurement technique

The magnetic hysteresis behaviours of ferromagnetic materials vary with the heat treatment-induced micro-structural changes. In the study, the minor hysteresis loop measurement technique was used to quantitatively characterise the case depth in two types of medium carbon steels. Firstly, high-frequency induction quenching was applied in rod samples to increase the volume fraction of hard martensite to the soft ferrite/pearlite (or sorbite) in the sample surface. In order to determine the effective and total case depth, a complementary error function was employed to fit the measured hardness-depth profiles of induction-hardened samples. The cluster of minor hysteresis loops together with the tangential magnetic field (TMF) were recorded from all the samples and the comparative study was conducted among three kinds of magnetic parameters, which were sensitive to the variation of case depth. Compared to the parameters extracted from an individual minor loop and the distortion factor of the TMF, the magnitude of three-order harmonic of TMF was more suitable to indicate the variation in case depth. Two new minor-loop coefficients were introduced by combining two magnetic parameters with cumulative statistics of the cluster of minor-loops. The experimental results showed that the two coefficients monotonically linearly varied with the case depth within the carefully selected magnetisation region.

HIS-TORIC: extending core ICRF wave simulation to include realistic SOL plasmas

This paper presents a novel approach to incorporating an arbitrarily shaped edge scrape-off-layer (SOL) plasma and an ion cyclotron range of frequency (ICRF) antenna structure into existing core ICRF wave simulation models. We partition the entire computation domain into two sub-domains: a core and an edge region. Simulations in each domain are performed separately with appropriate numerical solvers. For the core, the TORIC ICRF solver (Brambilla 1999 Plasma Phys. Control. Fusion 41 1) was modified to impose an essential (Dirichlet) boundary condition at its interface with the edge domain. In the edge, a finite element method is used to solve a cold collisional plasma model. The domains are then joined together using the continuity boundary condition for the tangential electric and magnetic fields at their interfaces (Hybrid Integration of SOL to TORIC: HIS-TORIC). The model developed here was tested using an ICRH H minority heating scenario on the Alcator C-Mod tokamak (Hutchinson et al 1994 Phys. Plasmas 1 1511). The simulated pattern of core wave propagation agrees well with a standard TORIC simulation. This approach opens the possibility of using a realistic diverted SOL plasma and a complicated 3D RF antenna together with a rigorous hot core plasma model, while requiring only minimal modification to existing RF codes.

Ultrafast imprinting of topologically protected magnetic textures via pulsed electrons

Short electron pulses are demonstrated to trigger and control magnetic excitations, even at low electron current densities. We show that the tangential magnetic field surrounding a picosecond electron pulse can imprint topologically protected magnetic textures such as skyrmions in a sample with a residual Dzyaloshinskii-Moriya spin-orbital coupling. Characteristics of the created excitations such as the topological charge can be steered via the duration and the strength of the electron pulses. The study points to a possible way for a spatiotemporally controlled generation of skyrmionic excitations.

Increase in water evaporation rate with increase in static magnetic field perpendicular to water-air interface

In the last decades many research on effects of magnetic field on water have been reported but still many arguments and doubts are present. However, increase in water evaporation due to presence of magnetic field is less in conflict. In this article, effects of static magnetic field on the amount of deionized water evaporation in presence of magnetic field with one, two or three permanent ferrite magnets perpendicular to water-air interface have been investigated and showed that tangential magnetic field at the interface does not make changes on the amount of evaporation but when magnetic field is perpendicular to the interface, up to 18.3% increase in water evaporation rate is observed. Another important effect of magnetic field is memory effect, which shows when magnetic field is applied perpendicular to the interface with three magnets for 60min after removing the magnets even up to 40min more evaporation compared to non-magnetic water is still observable. These effects are explained and discussed using the kinetic energy of water molecules and Lorentz force on these moving charged molecules at the interface which causes weakening or breaking hydrogen-bonds.

Nonlinear magnetoelectric effects in flexible composite ferromagnetic – Piezopolymer structures

Nonlinear magnetoelectric (ME) effects in a flexible composite planar structure, containing mechanically coupled layers of amorphous FeBSiC ferromagnet and PVDF piezoelectric polymer have been experimentally investigated. Under the action of a weak harmonic magnetic field h with frequency f=50–1000Hz and tangential bias magnetic field H=1–80Oe, the structure generated a voltage of the same frequency. The efficiency of linear ME conversion reached 3.4V/(cm·Oe) for the optimum bias field Hm≈15Oe. On increasing the excitation field up to h ∼7Oe, the structure generated second and third harmonics with efficiencies of ∼25mV/(cm·Oe2) and ∼2.5mV/(cm·Oe3), respectively. The amplitudes of the harmonics were not monotonous functions on the bias field H and grew with the increase in the alternating field h. Under the action of two alternating fields with different frequencies f1 and f2, the structure generated ac voltages with frequencies equal to the sum and difference frequencies f1±f2. The efficiency of magnetic fields mixing reached a maximum of ∼30mV/(cm·Oe2) in the absence of the bias field. The effects of harmonics generation and magnetic fields mixing arise due to the nonlinear dependence of the ferromagnet’s magnetostriction λ on the bias field H. The efficiency of the nonlinear processes is proportional to the derivatives of the magnetostriction over magnetic field. The nonlinear ME effects in the ferromagnet-piezopolymer flexible structures can be used to design high-sensitivity dual ac/dc magnetic field sensors and energy harvesting devices.

Finite‐difference time‐domain implementation of tensor impedance boundary conditions

Tensor impedance surfaces are modelled using a linear relationship between the tangential electric and magnetic fields at the surface, namely tensor impedance boundary condition (TIBC). To implement TIBC in the finite-difference time-domain (FDTD) method, a problem arises: TIBC boundary condition requires that the tangential components of the electric and magnetic fields to be co-located in both spatial and time grids. However, this requirement is not compatible with the classical leapfrog Yee's algorithm. In this study, the authors present an algorithm for FDTD implementation of TIBC. Numerical examples are presented to demonstrate the stability, and the accuracy of the proposed approach. Validation is achieved by comparison with analytic solutions.

Induction Hardened Layer Characterization and Grinding Burn Detection by Magnetic Barkhausen Noise Analysis

The quality of the ball screw shafts used in the aeronautical sector has to be controlled and certified with the most advanced non-destructive techniques. The capacity of magnetic Barkhausen noise (MBN) as a non-destructive technique to control the quality of ball screw shafts by assuring the appropriate induction hardened layer depth and detecting local overheated regions, known as grinding burns, which may occur during grinding processes is shown in the present work. Magnetic Barkhausen noise measurements were made with a system designed and implemented by the authors and the derived parameters were compared with microhardness measurements made at various depths after the different induction hardening treatments and the grinding processes were applied. A multiparametric study of the MBN signal as a function of the magnetic field in the surface of the sample is done in order to estimate the thickness of the hardened layer and to detect the grinding burns produced during grinding processes. The hardened layer thickness can be characterized with an error of ±200 \(\upmu \)m in the range between 150 and 2500 \(\upmu \)m by the position of the first peak of the MBN envelope in terms of the tangential magnetic field measured at the surface and the grinding burns can be detected with the position of the second peak of the MBN envelope in terms of the tangential magnetic field measured at the surface.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon–polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Electromagnetic control and optimization of high power impulse magnetron sputtering discharges in cylindrical source

High-power impulse magnetron sputtering (HiPIMS), a new physical vapor deposition technique which combines the advantages of the high ionization rates of the sputtered materials and control of electromagnetism, has been widely used to deposit high-performance coatings with a large density and high adhesion. However, HiPIMS has some intrinsic disadvantages such as the low deposition rate, unstable discharge, and different ionization rates for different materials thereby hampering wider industrial adoption. We have recently designed an optimized cylindrical source based on the hollow cathode effect to circumvent the aforementioned limitations. However, during the operation of the cylindrical source, the discharge is inhomogeneous and the etching stripes are nonuniform. In order to determine the underlying mechanism and optimize the electromagnetic control, the discharge in the HiPIMS cylindrical source is simulated. The tangential magnetic field distribution on the target surface of the cylindrical sputtering source is inhomogeneous and electron runaway is serious, resulting in a relatively low plasma density. Two solutions are proposed to improve the situations. The first one is electrical improvement by installing an electron blocking plate, and the second one is magnetic improvement by adding compensating magnets. Our simulation results of the first method show that a potential well is produced by the electron blocking plate to suppress electron runaway and the plasma density is improved significantly, especially around the central cross-section of the cylindrical sputtering source. The discharge becomes homogeneous, and the etching stripes are uniform albeit not full enough. The second method of magnetic improvement significantly improves the homogeneity of the tangential magnetic field distribution on the target surface and the target utilization rate. After adding the optimized compensating magnets, the shape of the effective area (the value of the tangential magnetic field in a range of 25-50 mT) on the target surface can be controlled and made zonal. The target utilization rate increases to over 80% from 60%. In order to obtain the optimal conditions, the two techniques are combined. A larger and more homogeneous etching ring is observed by adopting both the electrical and magnetic improvements as predicted and explained by the simulation results. It can be concluded that the combination of the two improvement techniques can improve and optimize the HiPIMS cylindrical source.

A Method to Reduce Electrode Erosion in a Magnetically Driven Rotating Arc

One or a few current carrying cables are located along the axis outside the concentric arc electrodes. These cables produce a tangential magnetic field in the interelectrode gap, which has different directions at different azimuthal angles. Interaction of this field with the radial arc current causes the arc column to oscillate and slowly drift in axial direction, thus spreading the thermal and erosion load of the electrodes.

Application of a Tangential Magnetic Field and Negative Repetitively Pulsed Bias for Suppression of Vacuum-Arc Copper Macroparticles

The joint effect of magnetic fields normal and tangential to the cathode surface and of short-pulse highfrequency bias potential of negative polarity on the accumulation of macroparticles on the potential target immersed in copper vacuum-arc plasma is studied. It is shown that the application of a vacuum-arc evaporator with the magnetic field tangential to the cathode surface reduces by 5 times generation of copper macroparticles in comparison with an axially symmetric vacuum-arc evaporator in which the magnetic field normal to the working cathode surface is used. It is established that the joint action of the tangential field and short-pulse high-frequency bias potential makes it possible to decrease by 2–3 orders of magnitude the density of copper macroparticles on the target surface.

Efficient computation of coherent synchrotron radiation in a rectangular chamber

We study coherent synchrotron radiation (CSR) in a perfectly conducting vacuum chamber of rectangular cross section, in a formalism allowing an arbitrary sequence of bends and straight sections. We apply the paraxial method in the frequency domain, with a Fourier development in the vertical coordinate but with no other mode expansions. A line charge source is handled numerically by a new method that rids the equations of singularities through a change of dependent variable. The resulting algorithm is fast compared to earlier methods, works for short bunches with complicated structure, and yields all six field components at any space-time point. As an example we compute the tangential magnetic field at the walls. From that one can make a perturbative treatment of the Poynting flux to estimate the energy deposited in resistive walls. The calculation was motivated by a design issue for LCLS-II, the question of how much wall heating from CSR occurs in the last bend of a bunch compressor and the following straight section. Working with a realistic longitudinal bunch form of r.m.s. length $10.4\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and a charge of 100 pC we conclude that the radiated power is quite small (28 W at a 1 MHz repetition rate), and all radiated energy is absorbed in the walls within 7 m along the straight section.

The Non-Destructive Test of Steel Corrosion in Reinforced Concrete Bridges Using a Micro-Magnetic Sensor.

This paper presents a non-destructive test method for steel corrosion in reinforced concrete bridges by using a 3-dimensional digital micro-magnetic sensor to detect and analyze the self-magnetic field leakage from corroded reinforced concrete. The setup of the magnetic scanning device and the measurement mode of the micro-magnetic sensor are introduced. The numerical analysis model is also built based on the linear magnetic charge theory. Compared to the self-magnetic field leakage data obtained from magnetic sensor-based measurement and numerical calculation, it is shown that the curves of tangential magnetic field at different lift-off height all intersect near the edge of the steel corrosion zone. The result indicates that the intersection of magnetic field curves can be used to detect and evaluate the range of the inner steel corrosion in engineering structures. The findings of this work propose a new and effective non-destructive test method for steel corrosion, and therefore enlarge the application of the micro-magnetic sensor.

Nd-Fe-B permanent magnet generator and voltage stabilizing control technology for vehicles

In this study, the tangential magnetic field Nd-Fe-B permanent magnet generator is designed and analyzed. In the generator, the adjacent permanent steel is sequentially arranged on the radial groove by the way of same polarity-oriented manner. The optimal design parameters of the generator are obtained by analyzing the influence rule of the generator leakage magnetic flux and leakage coefficient which is affected by the change in rotor pole pairs, permanent steel thickness, magnetic isolation air width, and air-gap length. The mathematical model of the magnetic field is developed and analyzed using the finite element method. Using the finite element method model, the diagrams of magnetic force line distribution, magnetic flux density modulus value, and magnetic flux density vector are obtained, which can be used to verify the validity of the main design parameters. A three-phase half-wave impulse-type controlled rectifier voltage regulator is developed with the function of regulator and rectifier, which proposes a solution to the output voltage instability of the Nd-Fe-B permanent magnet generator in a wide speed and load range.

Skin Effect Modeling in Conductors of Arbitrary Shape Through a Surface Admittance Operator and the Contour Integral Method

An accurate modeling of skin effect inside conductors is of capital importance to solve transmission line and scattering problems. This paper presents a surface-based formulation to model skin effect in conductors of arbitrary cross section, and compute the per-unit-length impedance of a multiconductor transmission line. The proposed formulation is based on the Dirichlet-Neumann operator that relates the longitudinal electric field to the tangential magnetic field on the boundary of a conductor. We demonstrate how the surface operator can be obtained through the contour integral method for conductors of arbitrary shape. The proposed algorithm is simple to implement, efficient, and can handle arbitrary cross-sections, which is a main advantage over the existing approach based on eigenfunctions, which is available only for canonical conductor's shapes. The versatility of the method is illustrated through a diverse set of examples, which includes transmission lines with trapezoidal, curved, and V-shaped conductors. Numerical results demonstrate the accuracy, versatility, and efficiency of the proposed technique.

An Efficient Time-Domain Integral Solution for a Loaded Rectangular Metallic Enclosure With Apertures

This paper proposes an efficient time-domain mixed potential integral equation (TD-MPIE) technique to analyze the penetrated transient electromagnetic field into a perforated rectangular metallic enclosure loaded with conducting objects. To this end, the surface equivalent principle is applied, and the fields in the interior and the exterior regions of the enclosure are formulated by using the time-domain cavity and free space Green's functions, respectively. Then, the governing TD-MPIE is derived by enforcing the continuity of the tangential magnetic and electric fields on the surface of the apertures and conducting loads inside the shield, respectively. The resultant time-domain equation is then solved by using the marching-on-in time scheme. Here, the spatial integrations and temporal convolutions are carried out analytically which eliminates the need to complicated numerical integration routines and remove the late time instability. In addition, an accelerated algorithm is proposed to scale down the computational complexity from $O(N_{\rm mod } N_t^2 N_s^2)$ down to $O(N_{{\rm mod}} N_t (\log ^2 N_t + 2N_s))$ where $N_{{\rm mod}}$ , $N_{t}$ and $N_{s}$ denote the total number of necessary modes inside the cavity, the number of time steps, and the spatial unknowns, respectively. The accuracy of the proposed technique is validated by comparing the simulated results with the well-known CST Microwave Studio time-domain solver, as well as the frequency-domain solution, and the measurements.

Formation of rupture in a conducting fluid layer under the action of an oscillating tangential magnetic field

Possible equilibrium shapes of the free surface of a conducting fluid layer subjected to oscillating tangential magnetic field are studied. Exact solution corresponding to the formation of rupture in a fluid layer is derived using the conformal mapping method. The width of the rupture has been defined; it depends on the problem parameters, viz. the value of the external magnetic field and the surface tension coefficient.