Magnetic Vector Research Articles

A Robust Tracking Method for Multiple Moving Targets Based on Equivalent Magnetic Force.

A ferromagnetic vehicle, such as a submarine, magnetized by the Earth's magnetic field produces a magnetic anomaly field, and the tracking of moving targets can be realized through real-time analysis of magnetic data. At present, there are few tracking methods based on magnetic field vectors and their gradient tensor. In this paper, the magnetic field vector and its gradient tensor are used to calculate equivalent magnetic force. It shows the direction of the vector between the detector and the tracking targets for controlling the direction of motion of the detector and achieving the purpose of tracking. Compared with existing positioning methods, the proposed method is relatively less affected by instrument resolution and noise and maintains robustness when the velocity vectors of multiple magnetic targets change randomly.

Artificial compression method for MHD system in Elsässer variables

We introduce an artificial compression (AC) method for simulations of the MHD system in Elsässer Variables. The proposed method decouples unknowns such as pressure, which acts as a Lagrange multiplier ensuring divergence constraints in each equation, from velocity and magnetic field vectors. By advancing for each unknown explicitly in time, the method approximates flow quantities at a lower cost when compared with its fully-implicit counterparts. We propose backward Euler and BDF2 based AC methods for MHD systems. This report presents stability and accuracy analyses of the proposed methods and numerically verifies the theoretical findings.

Model of Ferrite-cored Driver-pickup Coil Probe Application of TREE Method for Eddy Current Nondestructive Evaluation

An analytical model of a driver-pickup coil probe, consists of a cylindrical ferrite core, located above a layered conductor is presented. The truncated region eigenfunction expansion (TREE) method is used and the solution region is truncated with a certain radius around markedasmathitalicz axis. First, the magnetic vector potential of each region of filamentary coil problem is derived and solved with variables separation method using boundary and interface conditions, and then the rectangular cross-section coil problem is solved with superposition method. The expression of induced voltage in pickup coil is obtained and can be calculated with software such as Matlab or Mathematica. Using the proposed analytical model, the influence of the excitation frequency and excitation current in the driver coil on the responses of the pickup coil is examined. Experiments are performed, and the changes of voltage induced in the pickup coil due to the conductor are measured at different excitation frequencies and excitation currents. The analytical calculation results agree with the experimental results very well, verifying the correctness of the proposed analyticalmodel.

An Improved 3D Magnetization Inversion Based on Smoothness Constraints in Spherical Coordinates

In the inverse problem, the traditional way to obtain a stable solution is based on the maximum smoothness criteria. However, this approach cannot generate clearer and more focused images. In this study, we propose an improved inversion method based on the smoothness constraints. In the algorithm, the model weighting functions are updated by adding a model’s total gradient module matrix, which can effectively constrain the boundary of the recovery model in the iterative operation. We invert the 3D magnetization intensity for the three-component magnetic data in the spatial domain by spherical coordinates. The preconditional conjugate gradient algorithm is introduced to improve the efficiency of the solutions. We design two sets of synthetic examples to evaluate the inversion effects, which show that the improved method is more reliable than the smoothness constraint method. The boundary of the magnetic bodies is more precise, and the magnetization ranges are more focused. The method does not rely on the initial model and is suitable for magnetic vector data inversion. We also apply the algorithm to a set of Dabie orogen three-component magnetic data derived from a geomagnetic field model and verify the effectiveness of the inversion method.

A comparative study of finite element schemes for micromagnetic mechanically coupled simulations

Magnetic materials find wide applications in modern technology. For further materials design and optimization, physics-grounded micromagnetic simulations play a critical role, as predictions of properties, regarding the materials to be examined, can be made on the basis of in silico characterizations. However, micromagnetism, in particular, the Landau–Lifshitz–Gilbert equation, poses an interesting but challenging numerical issue, particularly the constraint of the preserved magnetization magnitude far below Curie temperature. Since this requirement is not fulfilled a priori, additional measures must be considered. In this work, four different methods for conserving the length of the magnetization vector in the framework of the finite element method are compared, namely, a projection method, penalty method, a Lagrange multiplier, and the approximation of the magnetization vectors using arithmetical and circular spherical coordinates. By applying the described methods to appropriate numerical examples, the different advantages and disadvantages are worked out so that a clear recommendation for the perturbed Lagrange method can be derived.

Mapping Single Electron Spins with Magnetic Tomography

Mapping the positions of single electron spins is a highly desired capability for applications such as nanoscale magnetic resonance imaging and quantum network characterization. Here, we demonstrate a method based on rotating an external magnetic field to identify the precise location of single electron spins in the vicinity of a quantum spin sensor. We use a nitrogen-vacancy center in diamond as a quantum sensor and modulate the dipolar coupling to a proximate electron spin in the crystal by varying the magnetic field vector. The modulation of the dipolar coupling contains information on the coordinates of the spin, from which we extract its position with an uncertainty of 0.9\,\AA. We show that the method can be used to locate electron spins with nanometer precision up to 10\,nm away from the sensor. We discuss the method's applicability to mapping hyperfine coupled electron spins, and show it may be applied to locating nitroxide radicals. The magnetic tomography method can be utilized for distance measurements for studying the structure of individual molecules.

Analytical model of a fractional slot double‐layer‐winding vernier permanent magnet machine

AbstractThis study presents an analytical model (ANA) for predicting magnetic field and performances of a fractional slot (FS) double‐layer‐winding (DLW) vernier permanent magnet (VPM) machine. Magnetic vector potential equations of a FS DLW VPM machine are analytically solved by the technique of variable separation in three subdomains, that is, regions of permanent magnets (PM), air‐gap, and slots in 2‐D polar coordinate system. Field distributions and performances, such as flux linkage, electromotive force (EMF), torque and inductance of a FS DLW VPM machine are developed. Results from ANA of an 18‐slot/2‐stator‐pole‐pair FS DLW VPM machine prototype have been compared with those from finite element analysis (FEA), which indicates that ANA has a huge advantage in the computing speed in addition to a good accuracy. In the end, a prototype is built and its EMF and torque are tested in experiment platforms in which the results verify ANA. The necessity and importance of the research is that the model is an analytical method which provides a close solution of magnetic field and performances of a FS DLW VPM machine and its calculation time is much less than FEA on the base of a good precision.

Stability of nontrivial magnetic structures in ferromagnetic films with antidots

The paper investigates stability conditions of vortex-like inhomogeneities in perforated ferromagnet films with strong uniaxial anisotropy of the ‘easy plane’ type. It has been demonstrated that the non-trivial magnetic structures, which are characterized by the absence of an exit of the magnetization vector from the film’s plane, can be observed at the absolute values of the anisotropy constant which exceed a certain threshold point. Possible methods (analytical, numeric, and empiric) have been developed to calculate this threshold value. Universally applicable estimates have been obtained of the minimum permissible value of the anisotropy constant for a number of the most important cases. Possible scenarios have been investigated for a loss of stability of the magnetic structure as the film’s material parameters vary.

Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating terms containing the covariant component BΨP of the magnetic field vector with respect to the poloidal flux function ΨP. In an unperturbed plasma, BΨP can be eliminated via exact coordinate transformations, but, in general, one relies on approximations, assuming that the effect of BΨP is small. Here, we are interested in the question whether Hamiltonian conservation laws are still satisfied when BΨP is retained in the presence of fluctuations. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency, and a single toroidal mode number n, we show that simulations using the code ORBIT with and without BΨP yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the appendix), which show that the unabridged GC Lagrangian with BΨP retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) and (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen) modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

Quantifying Inclination Shallowing and Representing Flattening Uncertainty in Sedimentary Paleomagnetic Poles

AbstractInclination is the angle of a magnetization vector from horizontal. Clastic sedimentary rocks often experience inclination shallowing whereby syn‐ to post‐depositional processes result in flattened detrital remanent magnetizations relative to local geomagnetic field inclinations. The deviation of recorded inclinations from true values presents challenges for reconstructing paleolatitudes. A widespread approach for estimating flattening factors (f) compares the shape of an assemblage of magnetization vectors to that derived from a paleosecular variation model (the elongation/inclination [E/I] method). Few studies exist that compare the results of this statistical approach with empirically determined flattening factors and none in the Proterozoic Eon. In this study, we evaluate inclination shallowing within 1.1 billion‐year‐old, hematite‐bearing red beds of the Cut Face Creek Sandstone that is bounded by lava flows of known inclination. Taking this inclination from the volcanics as the expected direction, we found that detrital hematite remanence is flattened with whereas the pigmentary hematite magnetization shares a common mean with the volcanics. Using the pigmentary hematite direction as the expected inclination results in . These flattening factors are consistent with those estimated through the E/I method supporting its application in deep time. However, all methods have significant uncertainty associated with determining the flattening factor. This uncertainty can be incorporated into paleomagnetic poles with the resulting ellipse approximated with a Kent distribution. Rather than seeking to find “the flattening factor,” or assuming a single value, the inherent uncertainty in flattening factors should be recognized and incorporated into paleomagnetic syntheses.

Magnetization Vector Inversion Based on Amplitude and Gradient Constraints

Magnetization vector inversion has been developed since it can increase inversion accuracy due to the unknown magnetization direction caused by remanence. However, the three components of total magnetizations vector are simultaneously inverted and then synthesized into the magnetization magnitude and direction, which increases the inherent non-uniqueness of the inversion. The positions of the three components of the magnetization vector are originally consistent. If there is a lack of constraints between them during the inversion process, they may be misaligned, resulting in a large deviation between the synthesized vector model and the ground truth. To address this issue and at the same time increase the accuracy of the edges of the inversion models, this paper proposes a magnetization vector inversion scheme with model and its gradients’ constraints by sparse Lp norm functions based on the amplitude of the three components of the magnetization vector instead of a single component to improve the accuracy of the inversion result. To evaluate the inversion accuracy performance, an improved evaluation index is also proposed in this paper, which can better evaluate the accuracy of the shape, position and magnetization amplitude of the inversion model. The proposed inversion method can recover the models with higher accuracy compared with traditional methods, indicated by the inverted model and the evaluation indexes. Simulation results based on the open-source SimPEG software and inversion on actual measured Galinge iron ore deposit (China) data verified the effectiveness and advantages of the proposed method.

Design and test validation of a novel permanent magnet eddy current brake

Aiming at slippage and belt breakage of large mechanical conveyor belts, a new type of water-cooled permanent magnet brake (WPMB) is proposed. In order to determine the braking performance of WPMB, a multi-physics coupling model and analysis method of magneto-thermal-structure are built. The braking torque and temperature characteristics of WPMB under different working conditions are obtained. Based on the magnetic vector potential equation, an electromagnetic eddy current model is established, and the variation trend of braking torque with speed is predicted. The temperature field model is built based on the equivalent thermal network method. Using multi-field coupling analysis method and 3-D FEM, the influence factors of WPMB braking torque are analyzed. Two test prototypes with rated speed of 78 rpm, braking torque of 3000 N⋅m are designed and developed. Braking torque characteristic tests and magnetic shielding characteristic tests at different speeds and continuous braking characteristic test are carried out. Experiments show that the proposed method provides very practical results to ensure the continuous and stable operation of WPMB.

Modelling Earth’s lithospheric magnetic field using satellites in low-perigee elliptical orbits

SUMMARYThe sensitivity of magnetic measurements taken by satellites in elliptical orbits to the lithospheric magnetic field is studied by comparing the formal error variances of the lithospheric Gauss coefficients for various satellite orbital constellations. Analytical expressions are presented for the variances of the Gauss coefficients when either all three magnetic vector components or only the radial component are used. We compare the results obtained using a satellite in a near-polar circular orbit at 350 km altitude with those from a satellite in an elliptical orbit with perigee at 140 km (and apogee at 1500 km) and find that the latter leads to Gauss coefficient variances at spherical harmonic degree n = 180 (corresponding to a horizontal wavelength of λ = 220 km) that are 104 times smaller compared to those derived from a similar number of data measured at 350 km altitude. The improvements in variance ratio at degree n = 145 (λ = 275 km) and n = 110 (λ = 360 km) are 103 and 102, respectively. These findings are supported by an analysis of synthetic magnetic data along simulated satellite orbits from which the lithospheric Gauss coefficients are estimated and compared with the original ones used to generate the synthetic data. Coefficients at degree n are successfully determined if the power of the difference between retrieved and original coefficients at that degree is smaller than the power of the lithospheric field (i.e. of the input coefficients). Using 3 yr of simulated data we conclude that magnetic measurements from a satellite in an elliptical orbit with perigee at 140 km allow for a reliable determination of the lithospheric field up to spherical harmonic n ≈ 170 while a satellite in a circular orbit at 350 km height only enables lithospheric field modelling up to n ≈ 100. The analysis demonstrates that low-altitude magnetic data collected by satellites in low-perigee elliptical orbits—although only available for a fraction of each orbit—enable improved global lithospheric field modelling at spatial wavelengths well beyond what is currently possible with data from satellites in circular orbits that do not reach such low altitudes. We applied the approach to the orbital configuration proposed for the Daedalus satellite mission (140 km perigee); the method will however also help in the preparation for other satellite missions in near-polar low-perigee elliptical orbits like the Macau Science Satellite pair MSS-2A and MSS-2B (perigee of 200 km or lower).

Controlling Andreev Bound States with the Magnetic Vector Potential.

Tunneling spectroscopy measurements are often used to probe the energy spectrum of Andreev bound states (ABSs) in semiconductor-superconductor hybrids. Recently, this spectroscopy technique has been incorporated into planar Josephson junctions (JJs) formed in two-dimensional electron gases, a potential platform to engineer phase-controlled topological superconductivity. Here, we perform ABS spectroscopy at the two ends of planar JJs and study the effects of the magnetic vector potential on the ABS spectrum. We show that the local superconducting phase difference arising from the vector potential is equal in magnitude and opposite in sign at the two ends, in agreement with a model that assumes localized ABSs near the tunnel barriers. Complemented with microscopic simulations, our experiments demonstrate that the local phase difference can be used to estimate the relative position of localized ABSs separated by a few hundred nanometers.

Current State of the Gold Mining Waste from the Ores of the Ursk Deposit (Western Siberia, Russia)

The article presents the original results of the investigation of sulfide-bearing mine tailings dumps (Ursk, Western Siberia, Russia), the adjacent territory, and acid mine drainage flows. The novelty of this study is related to integration of geophysical and geochemical data. The geoelectrical structure of the dump and the drainage valley was determined using the electrical resistivity tomography (ERT) method. Magnetic anomalies above the surface of the site were identified using ground magnetic surveys. The orthophotomap and a digital elevation model were obtained on the basis of aerial photography from an unmanned aircraft. The model of thermal imaging allows us to identify a number of temperature anomalies in the upper part of the dump slope and filtration zone in the drainage valley, caused by exothermic reactions. The digital relief model was constructed comprising three zones: (1) oxidation, (2) leaching, and (3) mixing and dilution. The oxidation zone is marked by low electrical resistivity (1–10 Ω·m), low pH values of the drainage waters (pH 3.61), low values of the modulus of the magnetic induction vector, and heating by +5 °C compared to the solid dump material that is not actively exposed to water. The oxidative conditions and low pH values favor the dilution of the Fe2+ compounds in the drainage solutions, which also contain Cu (3000 μg/L), Pb (1200 μg/L), As (1300 μg/L), and Hg (34 μg/L). The zone of the primary geochemical barrier is formed within the first 400 m, where the major proportion of dissolved elements if deposited. The second iron–aluminum sorption geochemical barrier is formed at a distance of 1000 m at the mixing zone with the Ur River. The stable geochemistry of surface waters, formed due to the inflow of drainage waters into the Ur River and further into the reservoir, persists at a distance of up to 7.7 km from the dump.

A 2D Multi-Layer Model to Study the External Magnetic Field Generated by a Polymer Exchange Membrane Fuel Cell

An original innovative two-dimensional (2D) multi-layer model based on the Maxwell–Fourier method for the diagnosis of a polymer exchange membrane (PEM) fuel cell (FC) stack is presented. It is possible to determine the magnetic field distribution generated around the PEMFC stack from the (non-)homogenous current density distribution inside the PEMFC stack. Analysis of the magnetic field distribution can indicate whether the FC is healthy or faulty. In this way, an explicit, accurate and fast analytical model can allow the health state of an FC to be studied. To evaluate the capacity and the efficiency of the 2D analytical model, the distribution of local quantities (i.e., magnetic vector potential and magnetic field) in a PEMFC stack has been validated with those obtained by the 2D finite-element analysis (FEA). The comparisons demonstrate excellent results both in terms of amplitude and waveform. The validation of this 2D analytical model is essential for the subsequent generation of an inverse model useful for the diagnosis of a PEMFC.

Type-II quantum spin Hall effect in two-dimensional metals

The quantum spin Hall (QSH) effect has been observed in topological insulators and long quantum wells using spin–orbit coupling as the probe, but it has not yet been observed in a metal. An experiment is proposed to measure the different Type-II QSH effect of an electron or hole in a two-dimensional (2D) metal by using the previously unexplored but relativistically gauge-invariant form of the generated 2D QSH Hamiltonian. Instead of using the electric field in the surface of the spin-polarized bands of a topological insulator or across the quantum well width as the probe, ones uses an applied azimuthal vector potential and an applied radial electric field as the tools to generate a spontaneously quantized spin current in an otherwise spin unpolarized 2D metal. A long cylindrical solenoid lies normally through the inner radius of a 2D metallic Corbino disk. The current surrounding the solenoid produces an azimuthal magnetic vector potential but no magnetic field in the disk. In addition, a radial electric field is generated across the disk by imposing either a potential difference or a radial charge current I across its inner and outer radii. Combined changes in and in either or I generate spontaneously quantized azimuthal charge and spin currents. The experiment is designed to measure these quantized azimuthal charge and spin currents in the disk consistently. The quantum Hamiltonians for both experiments are solved exactly. A method to control the Joule heating is presented, which could potentially allow the Type-II QSH measurements to be made at room temperature.

Influence of a Constant Magnetic Field on Electrodeposition of CoMo, CoRe, and CoMoRe Alloys from a Citrate Electrolyte

The paper presents a study of the electrodeposition of binary alloys CoMo, CoRe and a ternary alloy CoMoRe from the citrate electrolyte (pH 3.5) depending on the presence of a constant magnetic field and the direction of the magnetic induction vector relative to the surface of the working electrode. It is shown that the use of magnetoelectrolysis makes it possible to significantly increase the current efficiency of all studied alloys, especially the ternary CoMoRe alloy. The modeling of the forces acting in the liquid and on the bubbles of hydrogen released during the reaction in a constant magnetic field was carried out, and it was shown that the creation of convective flows due to the magnetohydrodynamic effect in the solution is not the only and determining factor; in the case of intense outgassing, the ratio of forces varies depending on the size of the bubbles: the conductive force and the Archimedes buoyancy force are the largest for large bubbles (about 100 µm), and the gradient magnetic force is for bubbles (less than 1 µm).

FARADAY EFFECT

This article describes a magneto-optical study of the faraday effect in rare-earth ferrite garnets. The Faraday effect is an odd magneto-optical effect in terms of magnetization, that is, the sign of the Faraday rotation depends on whether the direction of the light propagating in the crystal coincides with the direction of the magnetization vector M, or is antiparallel to the vector M. This circumstance underlies the well-known method of visual observation of magnetic domains in rare-earth ferrites - grenades.

THE NOTES ON ENERGY AND ELECTROMAGNETIC FIELD VECTORS IN THE NULL CONE Q2

In this paper, we characterize the directional derivatives in accordance with the asymptotic orthonormal frame {x,α,y} in Q^2. Also, we express the extended Serret-Frenet relations by using cone Frenet formulas and we explain the geometrical understanding of energy on each asymptotic orthonormal vector fields in null cone. Furthermore, we express the bending elastic energy function for the same particle according to curve x(s,ξ,η) and we finalize our results by providing energy variation sketches according to directional derivatives for different cases. Additionally, we explain a geometrical interpretation of the energy for unit vector fields and we express Maxwell’s equations for the electric and magnetic field vectors in null cone 3-space.