Tangential Magnetic Field Research Articles

Scattering From Graphene-Based Multilayered Spherical Structures

In this paper, modified Mie-Lorentz coefficients for graphene-based multilayered spherical structures are extracted. To this end, electromagnetic fields in each region of the solution domain are expanded in terms of vector spherical harmonics. By properly choosing the geometrical dimensions of the spheres, graphene coatings are considered as thin shells with the surface conductivities calculated by the Kubo formulas. Later, graphene surface currents are incorporated in the boundary conditions on tangential magnetic fields. The aforementioned procedure is conducted at the interface of two adjacent layers to relate the Mie coefficients of the successive layers recurrently. The validity of the extracted equations is verified by calculating the extinction cross section of various graphene-based multilayered spherical structures and comparing them with the results of finite element method. Possibility of tuning the graphene plasmonic resonances in multiple layers by varying graphene carrier doping density is discussed, as well. The potential application of our analysis is scattering shaping of graphene-based multilayered spherical configurations for cloaking, super-scattering, medical treatment, and tagging.

Scattered Fields of a 2-D Rectangular Room Composed of Cinder Block Walls Using Floquet–Fourier Series Expansion

In this paper, the 2-D scattered fields from a rectangular room composed of cinder block walls, illuminated by a source outside are derived. First, we assume that the structure is repeated periodically with a periodicity of $P$ . For analysis of a periodic structure, the Floquet theorem is used. Second, the dielectric profile is expressed by a Fourier series and tangential electric and magnetic fields are given by the Floquet series. In fact, the structure is a multilayer periodic one. By applying the boundary conditions, periodic fields in all layers are obtained. Third, by increasing the periodicity $P$ , estimated fields due to the structure alone are obtained. The numerical results due to excitation by a plane wave, a Gaussian wave, and a line source radiation are all in excellent agreement with those of a finite-element method.

Justification of Prandtl Ansatz for MHD Boundary Layer

The paper aims to justify the high Reynolds numbers limit for the magnetohydrodynamics system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on a velocity field and perfectly conducting wall condition on a magnetic field. Under the assumption that the viscosity and resistivity coefficients are of the same order and the initial tangential magnetic field on the boundary is not degenerate, we justify the validity of the Prandtl boundary layer expansion and give an $L^\infty$ estimate on the error by multiscale analysis.

Local-in-time well-posedness for compressible MHD boundary layer

In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work [27], we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.

Dispersion properties of one-dimensional magnetized ferrite photonic crystals in transverse magnetization configuration for transverse magnetic modes

The dispersion characteristics of electromagnetic wave in one-dimensional magnetized ferrite photonic crystals containing yttrium iron garnets and nickel ferrite in a unit cell is investigated for transverse magnetic mode when external magnetic field is perpendicular to the plane of wave propagation. The dispersion relation is derived using transfer matrix method based on the continuity conditions of tangential electric and magnetic field components. It is observed that dispersion properties and phase index are strongly dependent on the normalized parallel wave vector and the filling factor. At the Brewster angle, width of photonic band gap shrinks to zero. Also, the considered structure indicates its dielectric behavior for electromagnetic wave propagation.

A note on the ill-posedness of shear flow for the MHD boundary layer equations

For the two-dimensional Magnetohydrodynamics (MHD) boundary layer system, it has been shown that the non-degenerate tangential magnetic field leads to the well-posedness in Sobolevspaces and high Reynolds number limits without any monotonicity condition on the velocity field in our previous works.This paper aims to show that sufficient degeneracy in thetangential magnetic field at a non-degenerate critical point of the tangential velocity field of shear flow indeed yields instability as for the classical Prandtl equations without magnetic field studied by Gerard-Varet and Dormy (2010). This partially shows the necessity of thenon-degeneracy in the tangential magnetic field for the stability of the boundary layer of MHD in 2D at least in Sobolev spaces.

MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well‐Posedness Theory

AbstractWe study the well‐posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl‐type equations that are derived from the incompressible MHD system with non‐slip boundary condition on the velocity and perfectly conducting condition on the magnetic field. Under the assumption that the initial tangential magnetic field is not zero, we establish the local‐i‐time existence, uniqueness of solutions for the nonlinear MHD boundary layer equations. Compared with the well‐posedness theory of the classical Prandtl equations for which the monotonicity condition of the tangential velocity plays a crucial role, this monotonicity condition is not needed for the MHD boundary layer. This justifies the physical understanding that the magnetic field has a stabilizing effect on MHD boundary layer in rigorous mathematics. © 2018 Wiley Periodicals, Inc.

Sea Surface Radar Scattering at L-Band Based on Numerical Solution of Maxwell’s Equations in 3-D (NMM3D)

Radar scattering from ocean surfaces is investigated by 3-D numerical solution of Maxwell’s equations [numerical Maxwell’s model in 3-D (NMM3D)] using the ocean surface profiles stochastically generated from a 3-D Durden–Vesecky ocean spectrum. The surface integral equations (SIEs) are formulated for dielectric surfaces using Green’s functions of the air and the ocean permittivities with the surface tangential electric and magnetic fields as the unknowns. In solving the SIEs using the method of moment, a fast matrix solver of the sparse matrix canonical grid is used in conjunction with Rao–Wilton–Glisson basis functions. The computation has been implemented on a high-performance parallel computing cluster for problems with up to six million surface unknowns. Unlike the two-scale model (TSM) approximation, NMM3D does not require division of the surface spectrum into large- and small-scale ocean waves. The results of backscattering simulations are compared to Aquarius satellite radar measurements for wind speeds of 5, 8, and 10 m/s and for incidence angles of 29°, 39°, and 46°. The results show that NMM3D ocean backscattering solutions at L-band are in good agreement with Aquarius satellite radar data for co-polarized VV, HH, and cross-polarized VH returns as well as for the VV/HH ratio. The azimuthal dependence of L-band backscatter is also assessed. Finally, NMM3D results are compared to TSM solutions and are shown to lie close to Aquarius data in observed VV/HH ratio, and their azimuthal dependencies.

Quantitative Prediction of Surface Hardness in 12CrMoV Steel Plate Based on Magnetic Barkhausen Noise and Tangential Magnetic Field Measurements

Both magnetic Barkhausen noise (MBN) and tangential magnetic field (TMF) strength can be applied in the quantitative prediction of surface hardness of ferromagnetic specimens. The prediction accuracy depends on the selected model and the input parameters of the model. In this study, the relationship between the surface hardness of 12CrMoV steel plate and the measured MBN and TMF signals is investigated with multivariable linear regression (MLR) model and BP neural network technique. A comparative study between the MLR and BP model is conducted. The external validation results show that the BP model utilizing four MBN features as the input nodes has a smaller average prediction error (3.7%) than that of the MLR model (13.2%). Features extracted from the MBN and TMF signals are combined together as the input parameters of the BP model in order to achieve high accuracy. After adding two more TMF features into the input nodes of the BP network, the external validation results suggest that the average prediction error is decreased from 3.7 to 3.5%.

Simultaneous quantitative prediction of tensile stress, surface hardness and case depth in medium carbon steel rods based on multifunctional magnetic testing techniques

The simultaneous quantitative prediction of three target properties (tensile stress, surface hardness and case depth) in medium carbon steel rods based on magnetic nondestructive testing techniques was experimentally investigated. A multifunctional sensor is proposed to simultaneously measure the magnetic Barkhausen noise, tangential magnetic field and magnetic hysteresis curve of the tensioned steel rods with different depths of surface hardened layer. Mean impact value evaluation algorithm is introduced to select the optimal combination from the sixteen candidate feature parameters, which are extracted from the measured signals, as the input nodes of BP neural network. For the two types of rods of 45 steel rods and 42CrMo steel, the established BP prediction model possesses good accuracy in simultaneous quantitative prediction of the three target properties. The maximum prediction error for surface hardness is less than 1.6%. The average prediction error for tensile stress case is around 5.1% in 45 steel rods and 5.3% in 42CrMo steel rods. Under the tensile stress higher than 40 MPa, the average prediction error is less than 3.4%. Although the BP prediction model may lose resolution in distinguishing small changes in the case depth around 0.07 mm, the average prediction error of case depth in both types of medium carbon steel rods is lower than 5%.

Analysis and Calculation of Radial Electromagnetic Force on Brushless Doubly Fed Machine

Brushless doubly fed machine has reliable structure, low system cost, and advantages of outstanding application. BDFM achieves electric energy exchange depending on the effective magnetic field components, which leads to some problems of unbalanced radial electromagnetic force, vibration and noise. On the basis of analyzing the mechanism of radial electromagnetic force, the analytical method and finite element method are used to analyze the magnetic field of air gap. Take 4/2 pole and 8/4 pole as the example, the radial electromagnetic force of different pole numbers are obtained by means of tangential magnetic field component. The conclusions are useful for the development and design of brushless doubly fed machine.

Joint influence of steered vacuum arc and negative repetitively pulsed bias on titanium macroparticles suppression

This paper presents the results of an experimental study of titanium macroparticle accumulation on a negatively biased substrate immersed in DC vacuum arc plasma generated by an evaporator with an axial magnetic field and a steered arc evaporator. Using a steered arc with a tangential magnetic field strength of 200 Gs reduced the generation of macroparticles 5-fold compared to a plasma source with an axial magnetic field. The application of repetitively pulsed negative bias significantly decreased macroparticle assembly on the substrate surface for both evaporator designs. After 20 min of ion-plasma treatment with negatively pulsed bias (−2 kV, 7 μs, 105 p.p.s.) and steered arc, the observed macroparticle surface density appeared to be 2 orders of magnitude smaller than after vacuum arc plasma deposition at the anode potential using an evaporator with an axial magnetic field. The possibility of high–frequency short–pulse plasma immersion ion implantation by implementing DC vacuum arc plasma is discussed.

Adaptive finite element for 3D time-domain airborne electromagnetic modeling based on hybrid posterior error estimation

Airborne electromagnetic (AEM) forward modeling has been extensively developed in past years. However, not much attention has been paid to the adaptive numerical algorithms for time-domain electromagnetic modeling. We have created an adaptive method that can generate an effective mesh for time-domain 3D AEM full-wave modeling using an unstructured finite-element method and a backward Euler scheme. For the estimation of the posterior error in the adaptive process, we use a hybrid technique based on the continuity of the normal current density for modeling the off-time channels, and on the continuity of the tangential magnetic field for the on-time channels. To improve the stability of the forward modeling and control the number of grids in the adaptive process, a random grid-selection technique is applied. We check the modeling accuracy of the algorithm by comparing our adaptive results with the semianalytical solution for a time-domain AEM system over a homogeneous half-space. Furthermore, we test the effectiveness of our algorithm for multiple-source time-domain AEM systems by analyzing the meshes generated by the adaptive method and the model results. Finally, we study the topographic effect by calculating time-domain AEM responses over a hill model with an abnormal body embedded.

Magnetic Nature of Light Transmission through a 5-nm Gap

Slot antennas have been exploited as important building blocks of optical magnetism because their radiations are invoked by the magnetic fields along the axes, as vectorial Babinet principle predicts. However, optical magnetism of a few-nanometer-width slit, for which fascinating applications are found due to the colossal field enhancement but Babinet principle fails due to the nonnegligible thickness, has not been investigated. In this paper, we demonstrated that the magnetic field plays a dominant role in light transmission through a 5-nm slit on a 150-nm-thick gold film. The 5-nm slit was fabricated by atomic layer lithography, and the transmission was investigated for various incident angles by experiment and simulation at 785-nm wavelength. We found that, due to the deep subwavelength gap width, the transmission has the same incident angle dependence as the tangential magnetic field on the metal surface and this magnetic nature of a nanogap holds up to ~100-nm width. Our analysis establishes conditions for nanogap optical magnetism and suggests new possibilities in realizing magnetic-field-driven optical nonlinearities.

Face-Centered Anisotropic Surface Impedance Boundary Conditions in FDTD

Thin-sheet models are essential to allow shielding effectiveness of composite enclosures and vehicles to be modeled. Thin dispersive sheets are often modeled using surface-impedance models in finite-difference time-domain (FDTD) codes in order to deal efficiently with the multiscale nature of the overall structure. Such boundary conditions must be applied to collocated tangential electric and magnetic fields on either side of the surface; this is usually done on the edges of the FDTD mesh cells at the electric field sampling points. However, these edge-based schemes are difficult to implement accurately on stair-cased surfaces. Here, we present a novel face-centered approach to the collocation of the fields for the application of the boundary condition. This approach naturally deals with the ambiguities in the surface normal that arise at the edges on stair-cased surfaces, allowing a simpler implementation. The accuracy of the new scheme is compared to edge-based and conformal approaches using both planar sheet and spherical shell canonical test cases. Staircasing effects are quantified and the new face-centered scheme is shown have up to 3-dB lower error than the edge-based approach in the cases considered, without the complexity and computational cost of conformal techniques.

An inverse problem for Maxwell’s equations with Lipschitz parameters

We consider an inverse boundary value problem for Maxwell’s equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric permittivity, and magnetic permeability are uniquely determined by knowledge of all tangential electric and magnetic fields on the boundary of the body at a fixed frequency.

Hybrid Prediction Method for the Electromagnetic Interference Characteristics of Printed Circuit Boards Based on the Equivalent Dipole Model and the Finite-Difference Time Domain Method

In this paper, we propose a hybrid modeling method for analyzing the electromagnetic compatibility characteristics of printed circuit boards (PCBs). The method uses an equivalent magnetic dipole array deduced from near-field scanning results obtained at a certain height over the PCB surface under test and the finite-difference time domain (FDTD) algorithm. The array of dipoles can simulate the PCB electromagnetic emissions, including the ground plane effect at a particular high frequency; the equivalent dipole array can then be imported into the FDTD calculation space for calculating the electromagnetic fields generated by the dipole array. In our experiment, we obtained the tangential magnetic field distribution of the PCB surface using near-field scanning, from where the tangential magnetic field component, orientation, and the magnitude and phase of the dipoles could be deduced. We used the proposed method to model two different modules on a highly integrated circuit. The results of the proposed method and those obtained by near-field scanning are nearly the same, which demonstrates the effectiveness and accuracy of the proposed method. We therefore conclude that the proposed modeling approach presents a new technique for studying the electromagnetic interference of PCBs.

A Radio Continuum and Polarization Study of SNR G57.2+0.8 Associated with Magnetar SGR 1935+2154

Abstract We present a radio continuum and linear polarization study of the Galactic supernova remnant (SNR) G57.2+0.8, which may host the recently discovered magnetar SGR 1935+2154. The radio SNR shows the typical radio continuum spectrum of a mature supernova remnant with a spectral index of and moderate polarized intensity. Magnetic field vectors indicate a tangential magnetic field, expected for an evolved SNR, in one part of the SNR, and a radial magnetic field in the other. The latter can be explained by an overlapping arc-like feature, perhaps a pulsar wind nebula, emanating from the magnetar. The presence of a pulsar wind nebula is supported by the low average braking index of 1.2, which we extrapolated for the magnetar, and the detection of diffuse X-ray emission around it. We found a distance of 12.5 kpc for the SNR, which identifies G57.2+0.8 as a resident of the Outer spiral arm of the Milky Way. The SNR has a radius of about 20 pc and could be as old as 41,000 yr. The SNR has already entered the radiative or pressure-driven snowplow phase of its evolution. We compare independently determined characteristics like age and distance for both the SNR and the soft gamma repeater SGR 1935+2154, and conclude that they are physically related.

Effects of magnetic fields on capillary-gravity waves in the presence of magnetic surfactants

The stability of capillary-gravity wave motion on horizontal free surface of viscous noncompressible fluid in the presence of magnetic surfactant in an external magnetic field was studied. It is shown that for normal as well as for tangential external magnetic field the horizontal free liquid surface is unstable for field strength exceeding some critical value that does not depend on the elastic constant of the surfactant film. However, for oblique external magnetic field the stability of the free surface depends not only on the field value but also on the surfactant elastic constant.

Generation of surface plasmon-polaritons by edge effects

By using numerical and analytical methods, we describe the generation of fine-scale lateral electromagnetic waves, called surface plasmon-polaritons (SPPs), on atomically thick, metamaterial conducting sheets in two spatial dimensions (2D). Our computations capture the two-scale character of the total field and reveal how each edge of the sheet acts as a source of an SPP that may dominate the diffracted field. We use the finite element method to numerically implement a variational formulation for a weak discontinuity of the tangential magnetic field across a hypersurface. An adaptive, local mesh refinement strategy based on a posteriori error estimators is applied to resolve the pronounced two-scale character of wave propagation and radiation over the metamaterial sheet. We demonstrate by numerical examples how a singular geometry, e.g., sheets with sharp edges, and sharp spatial changes in the associated surface conductivity may significantly influence surface plasmons in nanophotonics.