Magnetic Flux Concentrations Research Articles

MAGNETIC FLUX CONCENTRATION AND ZONAL FLOWS IN MAGNETOROTATIONAL INSTABILITY TURBULENCE

Accretion disks are likely threaded by external vertical magnetic flux, which enhances the level of turbulence via the magnetorotational instability (MRI). Using shearing-box simulations, we find that such external magnetic flux also strongly enhances the amplitude of banded radial density variations known as zonal flows. Moreover, we report that vertical magnetic flux is strongly concentrated toward low-density regions of the zonal flow. Mean vertical magnetic field can be more than doubled in low-density regions, and reduced to nearly zero in high density regions in some cases. In ideal MHD, the scale on which magnetic flux concentrates can reach a few disk scale heights. In the non-ideal MHD regime with strong ambipolar diffusion, magnetic flux is concentrated into thin axisymmetric shells at some enhanced level, whose size is typically less than half a scale height. We show that magnetic flux concentration is closely related to the fact that the magnetic diffusivity of the MRI turbulence is anisotropic. In addition to a conventional Ohmic-like turbulent resistivity, we find that there is a correlation between the vertical velocity and horizontal magnetic field fluctuations that produces a mean electric field that acts to anti-diffuse the vertical magnetic flux. The anisotropic turbulent diffusivity has analogies to the Hall effect, and may have important implications for magnetic flux transport in accretion disks. The physical origin of magnetic flux concentration may be related to the development of channel flows followed by magnetic reconnection, which acts to decrease the mass-to-flux ratio in localized regions. The association of enhanced zonal flows with magnetic flux concentration may lead to global pressure bumps in protoplanetary disks that helps trap dust particles and facilitates planet formation.

Properties of small-scale magnetism of stellar atmospheres

Abstract The magnetic field outside of sunspots is concentrated in the intergranular space, where it forms a delicate filigree of bright ribbons and dots as seen on broad band images of the Sun. We expect this small-scale magnetic field to exhibit a similar behavior in stellar atmospheres. In order to find out more about it, we perform numerical simulations of the surface layers of stellar atmospheres. Here, we report on preliminary results from simulations in the range between 4000 K and 6500 K effective temperature with an initial vertical, homogeneous magnetic field of 50 G strength. We find that the field strength of the strongest magnetic flux concentrations increases with decreasing effective temperature at the height level where the average Rosseland optical depth is one. On the other hand, at the same level, the field is less strong than the thermal equipartition value in the coolest model but assumes superequipartition in the models hotter than 5000 K. While the Wilson depression of the strongest field concentrations is about one pressure scale height in the coolest model, it is more than four times the pressure scale height in the hottest one. We also find that the relative contribution of the bright filigree to the bolometric, vertically directed radiative intensity is most significant for the Teff = 5000 K model (0.6%–0.79%) and least significant for the hottest and coolest models (0.1%–0.46% and 0.14%–0.32%, respectively). This behavior suggests that the effect of the small-scale magnetic field on the photometric variability is more significant for K dwarf stars than for F-type and also M-type stars.

Intense bipolar structures from stratified helical dynamos

We perform direct numerical simulations of the equations of magnetohydrodynamics with external random forcing and in the presence of gravity. The domain is divided into two parts: a lower layer where the forcing is helical and an upper layer where the helicity of the forcing is zero with a smooth transition in between. At early times, a large-scale helical dynamo develops in the bottom layer. At later times the dynamo saturates, but the vertical magnetic field continues to develop and rises to form dynamic bipolar structures at the top, which later disappear and reappear. Some of the structures look similar to $\delta$ spots observed in the Sun. This is the first example of magnetic flux concentrations, owing to strong density stratification, from self-consistent dynamo simulations that generate bipolar, super-equipartition strength, magnetic structures whose energy density can exceeds the turbulent kinetic energy by even a factor of ten.

Three-Dimensional Magnetic Field Analysis for Local Induction Heating of Steel Sheet by Using Magnetic Flux Concentration Plate

In general, the magnetic properties of electrical steel sheets are strongly influenced by mechanical stress. We have reported the measurement results of vector magnetic properties of a non-oriented electrical steel sheet under stress conditions. From these results, it is possible to control the vector magnetic property by applying local mechanical stress. Therefore, we next focus on an induction heating technique that applies mechanical stress in a non-oriented electrical steel sheet. It is very important to control the eddy current distribution inside the non-oriented electrical steel sheet. This paper presents a magnetic flux concentration plate structure to control the eddy current in steel sheets by using an induction heating technique. The magnetic flux concentration plate structure is investigated in a three-dimensional magnetic field analysis by the finite element method.

Investigation of Electrodeposited Nifemo for Application as Flux Concentrator in Magnetic Field Sensors

Introduction To enhance a magnetic field sensor’s sensitivity, flux concentrators made of soft-magnetic materials featuring high permeability and low coercivity are used. By electroplating, these materials can be completely integrated into the sensor design. Whereas Ni81Fe19 is already characterized by high permeabilities of 1,500 to 3,000 [1] and a low coercivity of 16 A/m [2], NiFeMo layers promise even more favorable magnetic characteristics (permeabilities of 2,200 to 20,000 and coercivities in the range of 8-28 A/m [3]). The preferred composition is Ni79Fe16Mo5. The presented investigation deals with the influence of plating conditions and post-treatment on the NiFeMo characteristics. Experiments Based on the plating bath published in [3], the influence of plating parameters like current density, the relationship between forward and reverse current (pulse current relationship), the relationship between the time of forward and reverse current (pulse time relationship) and frequency on the composition of the plated NiFeMo and its magnetic properties are analyzed. Moreover the influence of thermal annealing below and above Curie temperature of NiFeMo on its magnetic characteristics is investigated.The NiFeMo is electroplated into micromolds made of photoresist. The micromold has the geometry of flux concentrators as applied in magnetic field sensors. Fig. 1 shows the deposited structure.The plating parameters are varied in the following ranges:- Current density: 15 – 30 mA/cm2 - Pulse current relationship (Iforward/Ireverse): -10 – +10- Pulse time relationship (tforward/treverse): 1 – 9- Frequency (1/(tforward+treverse)): 50 – 150 HzThe deposition time is adapted according to the aspired deposition height of 2 µm. The magnetic properties are measured by a Vibrating Sample Magnetometer (VSM) and the surface quality is investigated by Atomic Force Microscopy (AFM) and Light Optical Microscopy. For comparison Ni81Fe19layers are plated and thermally treated and the measurement results are finally opposed to the NiFeMo characteristics. Results Main influence on the composition of the electroplated NiFeMo is taken by the current density. The magnetic properties are moreover determined by the pulse time relationship, whereas the composition is not changed significantly.With a higher current density the Fe-content in the layers increases while the Ni and Mo concentration decrease. The highest permeability and lowest coercivity are realized at the targeted composition of Ni79Fe16Mo5. The sample with a composition of Ni62Fe35Mo3 shows the highest saturation flux density. The influence of the pulse time relationship shows that a long time of forward current in relation to the reverse current leads to an increase in permeability. These layers are characterized by a reduced roughness and potentially smaller grains.Annealing the NiFeMo-films above their Curie temperature in a magnetic field for 2 h increases their coercivity.Compared to the plated NiFe-layers, a higher permeability of the plated NiFeMo layers can be achieved, whereas the coercivity is similar. Conclusion NiFeMo is a quite promising material for magnetic flux concentrators in sensor application. Its high permeability enhances the flux concentrator’s ability to focus the magnetic field into the sensitive area of the device and hence increase the sensor’s sensitivity. Its fabrication by electroplating demands an adequate selection of parameters. By choosing an appropriate current density and pulse time relationship, high permeable layers with low coercivity can be deposited.

Magnetic flux concentrations from dynamo-generated fields

The mean-field theory of magnetized stellar convection gives rise to the two possibility of distinct instabilities: the large-scale dynamo instability, operating in the bulk of the convection zone, and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation, but the growth rate of NEMPI is suppressed with increasing rotation rates, although recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an alpha squared mean-field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time. We use both DNS and mean-field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal field. We use the test-field method to compute relevant dynamo coefficients. DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively well reproduced with MFS. As expected, for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity. Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over. For the solar rotation rate, the corresponding turbulent turnover time is about 5 hours, with dynamo action commencing in the layers beneath.

Design of an induction heating coil coupled with magnetic flux concentrators for barrel heating of an injection molding machine

In an injection molding machine, the conventional barrel heating system which uses resistance heating method (RH) has some drawbacks such as low heating rate, long heating time, and energy loss. With induction heating (IH) technique, the barrel can better handle almost all of these disadvantages. However, non-uniform temperature distribution on inside surface of a barrel is the main drawback of induction heaters. A working coil coupled with magnetic flux concentrators via adjustment of magnetic flux concentrator spacing to achieve uniformity of magnetic flux and temperature distribution on the inside surface of a barrel was proposed and experimented. Results showed that, when barrel was heated by induction heating method with the proposed induction heating coil, heating time to reach a specific temperature could be reduced, and heating rate increased compared to resistance heating method. With 8 mm pitch of magnetic flux concentrators on a coil, the temperature distribution was the most uniform.

DETECTION OF COHERENT STRUCTURES IN PHOTOSPHERIC TURBULENT FLOWS

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/SOT magnetograms. Eulerian and Lagrangian coherent structures are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicates that, on average, the deformation Eulerian coherent structures dominate over the vortical Eulerian coherent structures in the plage region. We demonstrate the correspondence of the network of high magnetic flux concentration to the attracting Lagrangian coherent structures (a-LCS) in the photospheric velocity based on both observations and numerical simulations. In addition, the computation of a-LCS provides a measure of the local rate of contraction/expansion of the flow.

A model for the formation of the active region corona driven by magnetic flux emergence

We present the first model that couples the formation of the corona of a solar active region to a model of the emergence of a sunspot pair. This allows us to study when, where, and why active region loops form, and how they evolve. We use a 3D radiation MHD simulation of the emergence of an active region through the upper convection zone and the photosphere as a lower boundary for a 3D MHD coronal model. The latter accounts for the braiding of the magnetic fieldlines, which induces currents in the corona heating up the plasma. We synthesize the coronal emission for a direct comparison to observations. Starting with a basically field-free atmosphere we follow the filling of the corona with magnetic field and plasma. Numerous individually identifiable hot coronal loops form, and reach temperatures well above 1 MK with densities comparable to observations. The footpoints of these loops are found where small patches of magnetic flux concentrations move into the sunspots. The loop formation is triggered by an increase of upwards-directed Poynting flux at their footpoints in the photosphere. In the synthesized EUV emission these loops develop within a few minutes. The first EUV loop appears as a thin tube, then rises and expands significantly in the horizontal direction. Later, the spatially inhomogeneous heat input leads to a fragmented system of multiple loops or strands in a growing envelope.

Magnetic flux concentrations in a polytropic atmosphere

Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers for which the density scale height is constant throughout. We now study the validity of earlier conclusions about the size and growth rate of magnetic structures in the case of polytropic layers, which scale height decreases sharply towards the surface. To allow for a continuous transition from isothermal to polytropic layers, we employ a generalization of the exponential function known as the q-exponential. Now, the top of the polytropic layer shifts with the polytropic index such that the scale height at some reference height is always the same. We use both mean-field and direct numerical simulations of forced stratified turbulence to determine the resulting flux concentrations. Magnetic structures begin to form at a depth where magnetic field strength is about 3-4% the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic one the growth rates decreases for structures deeper down. For vertical fields, magnetic structures of super-equipartition strengths are formed because such fields survive downward advection, unlike NEMPI under horizontal magnetic fields. The horizontal cross-section of such structures is approximately circular. Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon.

Enhanced magnetoelectric effects in composite of piezoelectric ceramics, rare-earth iron alloys, and shape-optimized nanocrystalline alloys

An enhancement for magnetoelectric (ME) effects is studied in a three-phase ME architecture consisting of two magnetostrictive Terfenol-D (Tb(0.3)Dy(0.7)Fe(1.92)) plates, a piezoelectric PZT (Pb(Zr,Ti)O3) plate, and a pair of shape-optimized FeCuNbSiB nanocrystalline alloys. By modifying the conventional shape of the magnetic flux concentrator, the shape-optimized flux concentrator has an improved effective permeability (μ(eff)) due to the shape-induced demagnetizing effect at its end surface. The flux concentrator concentrates and amplifies the external magnetic flux into Terfenol-D plate by means of changing its internal flux concentrating manner. Consequently, more flux lines can be uniformly concentrated into Terfenol-D plates. The effective piezomagnetic coefficients (d(33m)) of Terfenol-D plate and the ME voltage coefficients (α(ME)) can be further improved under a lower magnetic bias field. The dynamic magneto-elastic properties and the effective magnetic induction of Terfenol-D are taken into account to derive the enhanced effective ME voltage coefficients (α(ME,eff)), the consistency of experimental results and theoretical analyses verifies this enhancement. The experimental results demonstrate that the maximum d(33m) in our proposed architecture achieves 22.48 nm/A under a bias of 114 Oe. The maximum α(ME) in the bias magnetic range 0-900 Oe reaches 84.73 mV/Oe under the low frequency of 1 kHz, and 2.996 V/Oe under the resonance frequency of 102.3 kHz, respectively. It exhibits a 1.43 times larger piezomagnetic coefficient and a 1.87 times higher ME voltage coefficient under a smaller magnetic bias of 82 Oe than those of a conventional Terfenol-D/PZT/Terfenol-D composite. These shape-induced magnetoelectric behaviors provide the possibility of using this ME architecture in ultra-sensitive magnetic sensors.

Optimization of sensor design for Barkhausen noise measurement using finite element analysis

The effects of design parameters for optimizing the performance of sensors for magnetic Barkhausen emission measurement are presented. This study was performed using finite element analysis. The design parameters investigated include core material, core-tip curvature, core length, and pole spacing. Considering a combination of permeability and saturation magnetization, iron was selected as the core material among other materials investigated. Although a flat core-tip would result in higher magnetic flux concentration in the test specimen, a curved core-tip is preferred. The sensor-to-specimen coupling is thereby improved especially for materials with different surface geometries. Smaller pole spacing resulted in higher flux concentration.

Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field

Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding the growth rate of this large-scale instability, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached. This results in magnetic spots that are reminiscent of sunspots. Here we want to find out under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. We use a combination of MFS, DNS, and implicit large-eddy simulations to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. We confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using turbulence simulations, we find that magnetic flux concentrations occur for different values of the Mach number between 0.1 and 0.7. DNS and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated.

Mesogranulation and small-scale dynamo action in the quiet Sun

Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at mesogranular boundaries. Our aim is to investigate the small-scale dynamo properties of a convective flow that exhibits both granulation and mesogranulation, comparing our findings with solar observations. Adopting an idealised model for a localised region of quiet Sun, we use numerical simulations of compressible magnetohydrodynamics, in a 3D Cartesian domain, to investigate the parametric dependence of this system (focusing particularly upon the effects of varying the aspect ratio and the Reynolds number). In purely hydrodynamic convection, we find that mesogranulation is a robust feature of this system provided that the domain is wide enough to accommodate these large-scale motions. The mesogranular peak in the kinetic energy spectrum is more pronounced in the higher Reynolds number simulations. We investigate the dynamo properties of this system in both the kinematic and the nonlinear regimes and we find that the dynamo is always more efficient in larger domains, when mesogranulation is present. Furthermore, we use a filtering technique in Fourier space to demonstrate that it is indeed the larger scales of motion that are primarily responsible for driving the dynamo. In the nonlinear regime, the magnetic field distribution compares very favourably to observations, both in terms of the spatial distribution and the measured field strengths.

Study on Induction Heating Coil for Uniform Mold Cavity Surface Heating

Recently, energy saving is one of the important issues for polymer processing industry. Electromagnetic induction heating has many advantages such as fast heating and low energy consumption. Previous studies using electromagnetic induction heating for rapid tool heating have indicated that the temperature uniformity on a cavity surface is not easy to be achieved. In this paper, two different coils were used for heating uniform 7 mm thick hot work tool steel (JIS SKD61) surface. One is a four-row coil with opposite current directions and the other is a two-row coil with identical current directions. Magnetic flux concentrators were used to control magnetic field and heat the workpiece uniformly. The heating experiment results showed that coil with opposite adjacent current directions had more uniform temperature distribution on tool surface. The temperature uniformity was about 94%∼95%. The coil with identical adjacent current directions had higher average temperature and the temperature rose from 50°C to 150°C in 15 seconds.

A Novel Bar-Shaped Magnetic Shielding for Magnetoresistive Sensors in Current Measurement on Printed Circuit Boards

This paper presents the study of a novel bar-shaped magnetic shielding for magnetoresistive (MR) sensors in current measurement on printed circuit boards (PCB). The main physical principles of the shielding effect were studied by using the analytical model of magnetic flux concentration. Finite element analysis (FEA) simulations were used to simulate the shielding effects with changing geometrical parameters of the bar-shaped magnetic shielding. The dependences of the shielding effect on the parameters of length, width and thickness were analyzed. It shows that these parameters are critical for designing magnetic shielding. This new concept of magnetic shielding for MR sensors in current measurement on PCB was experimentally tested and verified in a laboratory setup. The experimental results verify the feasibility and effect of this novel magnetic shielding for MR sensors.

Magnetization Mechanism of Si-Gradient Steel Sheet Manufactured by CVD Siliconizing Process

Si-gradient steel sheet, which has a silicon concentration gradient in the sheet thickness direction, manufactured by Chemical Vapor Deposition (CVD) Siliconizing process, possesses unique magnetic properties. In this paper, the magnetization behaviors of the single crystal of Si-gradient steel sheet are investigated in the direction <100> and <110>, comparing with Si-homogeneous steel sheet, in order to clarify the magnetization mechanism. The internal stress of Si-gradient steel sheet was evaluated. The induced magnetic anisotropy which arose according to the magnetoelastic effect is considered to play an important role in the magnetization process of Si-gradient steel sheet. The reduction of eddy current loss can be explained by the effect of the magnetic flux concentration to the sheet surface resulting from the internal stress.

Design of magnetic field alarm powered by magnetic energy harvesting

Abstract This paper presents a design of magnetic field alarm powered by magnetic energy harvesting. It consists of an energy harvesting module, Cockcroft-walton circuit and piezo buzzer. The energy harvesting module is composed of coil and magnetic flux concentration core. It can generate 200 μW from an environmental magnetic field of 200 μT at 60 Hz. The Cockcroft-walton circuit can converts the ac voltage to a suitable dc voltage for the piezo buzzer. This alarm can notice not only the magnetic field level defined by ICNIRP2010 but also the existence of magnetic field energy to be harvested. It is the first demonstration of a “self-generating component” powered by magnetic energy harvesting.

SELF-ASSEMBLY OF SHALLOW MAGNETIC SPOTS THROUGH STRONGLY STRATIFIED TURBULENCE

Recent studies have demonstrated that in fully developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. In the presence of strongly stratified turbulence, this was shown to lead to a large-scale instability that produces spontaneous magnetic flux concentrations. Furthermore, using a horizontal magnetic field, elongated flux concentrations with a strength of a few per cent of the equipartition value were found. Here we show that a uniform vertical magnetic field leads to circular magnetic spots of equipartition field strengths. This could represent a minimalistic model of sunspot formation and highlights the importance of two critical ingredients: turbulence and strong stratification. Radiation, ionization, and supergranulation may be important for realistic simulations, but are not critical at the level of a minimalistic model of magnetic spot formation.

Metamaterial anisotropic flux concentrators and magnetic arrays

A metamaterial magnetic flux concentrator is investigated in detail in combination with a Halbach cylinder of infinite length. A general analytical solution to the field is determined and the magnetic figure of merit is determined for a Halbach cylinder with a flux concentrator. It is shown that an ideal flux concentrator will not change the figure of merit of a given magnet design, while the non-ideal will always lower it. The geometric parameters producing maximum figure of merit, i.e., the most efficient devices, are determined. The force and torque between two concentric Halbach cylinders with flux concentrators is determined and the maximum torque is found. Finally, the effect of non-ideal flux concentrators and the practical use of flux concentrators, as well as demagnetization issues, is discussed.