A 3-D finite element formulation for calculating Meissner currentsin superconductors

A three-dimensional (3-D) finite element formulation for calculating Meissner currents in superconductors is presented. The authors have chosen a magnetic vector potential formulation, which also enables them to simulate ferromagnetic shielding. The equations are written so that the problem can be solved by the use of a conjugate gradient algorithm without preconditioning. Numerical results on normal-superconductor junctions and on superconducting lines are compared with analytical solutions     

Magnetic field attenuation of nonlinear shields

The analysis of shielding performance of planar shields against near field sources is carried out in the time domain to account for the nonlinear behavior of ferromagnetic materials used in low frequency applications. To this end, the Schelkunoff approach for shielding problems has been reformulated in the time domain introducing the transient wave impedances which relates transient electric and magnetic field components and appear in the integrodifferential boundary conditions. The final equation system is solved by means of a numerical procedure based on the finite element method. The obtained results are compared with analytical and measured data in different configurations     

Magnetization oscillations in a ferromagnet/nonmagnetic metal/ferromagnet nanostructure under the action of the spin-polarized current

Oscillations of magnetization of a ferromagnetic disk included in the ferromagnet/nonmagnetic metal/ferromagnet nanostructure under the action of the spin-polarized current are studied in the macrospin approximation. Conditions for switching and oscillations of magnetization are determined for four cases of the magnetic crystallographic anisotropy near the transition instability region depending on the ratio between disk dimensions and current density. It is shown that the region of disk magnetization instability corresponds to the minimum values of the current density that are necessary for excitation of the oscillations or switching of magnetization. Depending on the value and direction of the anisotropy and the relaxation parameter, the frequency of the observed oscillations varies within 0.1–30 GHz.     

Electromagnetic scattering from objects composed of multiplehomogeneous regions using a region-by-region solution

The paper presents an efficient procedure to calculate the electromagnetic field scattered by an inhomogeneous object consisting of N+1 linear isotropic homogeneous regions. The procedure is based on surface integral equation (SIE) formulations and the method of moments. The method of moments (MM) is used to reduce the integral equations for each homogeneous dielectric region into individual matrices. These matrices are each solved for the equivalent electric current in terms of the equivalent magnetic current. A simple algebraic procedure is used to combine these solutions and to solve for the magnetic current on the outer dielectric surfaces of the scatterer. With the magnetic current determined, the electric current on the outer surface of the scatterer is calculated. Because the matrix corresponding to each dielectric region is solved separately, the authors call this procedure the region-by-region method. The procedure is simple and efficient. It requires less computer storage and less execution time than the conventional MM approach, in which all the unknown currents are solved for simultaneously. To illustrate the use of the procedure, the bistatic and monostatic radar cross sections (RCS) of several objects are computed. The computed results are verified by comparison with results obtained numerically using the conventional numerical procedure as well as via the series solution for circular cylindrical structures. The possibility of nonunique solutions has also been investigated     

Design of Shielded Cables Using Saturable Ferromagnetic Materials

Previously, a numerical solution was evolved that may be used to analyze the effect of material saturation on the low frequency shielding characteristics of a thin ferromagnetic cable shield. Numerical solutions are difficult to employ in design problems and so a simplified theory has also been developed. This supplemental theory, described here, yields simple equations useful in the design of ferromagnetic cable shields to provide protection against some anticipated intense low frequency environment.     

sd-Exchange emission in ferromagnetic junctions

The spin-injection emission in a ferromagnetic junction at terahertz frequencies is theoretically analyzed. It is demonstrated that the efficiency of the emission caused by the sd-exchange interaction of the injected spin in which the electromagnetic field is involved strongly depends on the orientation angle of the magnetization of the active region relative to the magnetization direction of the injecting region. The fact that the calculated radiation frequency and power are close to the experimental results shows that the sd-exchange emission must be taken into account in the interpretation of the observed terahertz emission in magnetic junctions.     

Geometrical aspects of magnetic shielding at extremely lowfrequencies

The magnetic shielding effectiveness for closed and open shield structures is studied at extremely low frequencies. Analytical solutions are used for simple geometries, while more complex structures are evaluated using a finite-element method. Both highly conductive and ferromagnetic materials are studied, and their different shielding behavior is shown. Ferromagnetic shields give good results for small and closed shields and they also give a large field attenuation at close range to the source for open shield geometries. Highly conductive materials, on the other hand, are found to be suitable for large shield sizes. The attenuation is, however, reduced in the close vicinity of the source. Comparisons of numerical results with analytical calculations and measurements confirmed the high accuracy of the finite-element model     

Analysis of the Shielding Characteristics of Saturable Ferromagnetic Cable Shields

A numerical technique is developed that may be used to analyze the shielding characteristics of a cable with a saturable ferromagnetic outer sheath in an intense low-frequency environment. The solution relates the center conductor current to the total current exciting a coaxial cable with a ferromagnetic sheath. Several examples are given to illustrate how saturation effects the shielding properties of a ferromagnetic sheath.     

均匀外磁场中铁质球体系统磁场的镜像解析解

均匀外磁场中铁质球体系统磁场的计算一般是比较困难的,这是因为铁质球体之间的相互磁化比较难处理.从点磁荷与磁介质球系统中的镜像法出发,对磁介质球中的镜像线磁荷进行简化等效,推导出铁质球体系统中镜像磁偶极子和镜像磁荷的表达式.然后计算铁质球体之间各阶相互磁化而产生的附加磁场,进而求出铁质球体系统磁场的镜像解析解,并分析讨论了镜像解析解最大阶数的选择.仿真实验结果表明,镜像解析解的误差非常小,且适用于各种相对磁导率下铁质球体系统磁场的计算.     

Numerical Study of the Shielding Properties of Macroscopic Hybrid Ferromagnetic/Superconductor Hollow Cylinders

We study the magnetic shielding properties of hybrid ferromagnetic/superconductor (F/S) structures consisting of two coaxial cylinders, with one of each material. We use an axisymmetric finite-element model in which the electrical properties of the superconducting tube are modeled by a nonlinear $E$ -$J$ power law with a magnetic-field-dependent critical current density whereas the magnetic properties of the ferromagnetic material take saturation into account. We study and compare the penetration of a uniform axial magnetic field in two cases: 1) a ferromagnetic tube placed inside a larger superconducting tube (Ferro-In configuration) and 2) a ferromagnetic tube placed outside the superconducting one (Ferro-Out configuration). In both cases, we assess how the ferromagnetic tube improves the shielding properties of the sole superconducting tube. The influence of the geometrical parameters of the ferromagnetic tube is also studied: It is shown that, upon an optimal choice of the geometrical parameters, the range of magnetic fields that are efficiently shielded by the high-temperature superconductor tube alone can be increased by a factor of up to 7 (2) in a Ferro-Out (Ferro-In) configuration. The optimal configuration uses a 1020 carbon steel with a thickness of 2 mm and a height that is half that of the superconducting cylinder (80 mm).      

Analytic modeling of transit-time device drift regions with field-dependent transport coefficients

An iterative procedure for obtaining two-carrier d.c. solutions in regions of rapidly varying carrier concentration is presented. The procedure uses an analytic solution for the carrier concentrations in a region of linear spatial electric field variation. Field-dependent diffusion and field-dependent velocities are assumed. A single-carrier small-signal model for a drift region with a spatially varying field and field-dependent transport properties is presented. When applied to a BARITT device, results consistent with published experimental data are obtained. The importance of momentum relaxation effects in Si BARITT drift regions is discussed.     

Macroscopic numerical evaluation of heat generation in a bulk highTc superconductor during pulsed field magnetization

Pulsed-field magnetization of a bulk high Tc superconductor (HTS) is evaluated by using a macroscopic numerical simulation code. Local heat generation in the HTS during the pulsed-field magnetization is discussed to clarify the dynamic magnetization process. Nonlinear dependence of shielding current on the dynamic magnetic field is considered by using the flux flow-creep model. Dependence of flow resistivity on the magnetic field and temperature are also evaluated with the Bardeen-Stephen and the Tinkham models. It is numerically confirmed that reported experimental results are due to a decrease of the shielding current caused by local heat generation     

Frequency splitting effect of degenerate modes in ferrite resonators

The splitting of magneto-dielectric modes frequency in disk ferrite resonators in a magnetic field is considered.Asimplified formula is obtained for estimation of the splitting magnitude. Theoretical and experimental results of the frequency splitting effect in magneto-dielectric modes in the millimeter wave range are compared. The use of the splitting of the magneto-dielectric modes frequencies as an alternative to ferromagnetic resonance in devices with magnetic frequency tuning is suggested, with values of the magnetization fields being an order of magnitude lower than for ferromagnetic resonance. The features of the splitting modes effect in different ferrite classes are investigated and it is shown that it occurs in both microwave and optical ranges. The estimated magnitude of the mode frequency splitting in the iron-yttrium garnet (YIG) transparency window can reach 9 GHz, which is comparable to the 5 GHz splitting in the millimeter range. The frequency ranges where frequency splitting effect is of practical interest are discussed. In particular, the effect in barium hexaferrite can be used both in post-resonance and pre-resonance regions, which is almost impossible for ferrogarnates and ferrospinels.     

Ferromagnetic high-permeability alloy alone can provide sufficientlow-frequency and eddy-current shieldings for biomagnetic measurements

A low cost, two-shell ferromagnetic shielded room large enough for a person to enter and prepare experiments was constructed for biomagnetic measurements. No aluminium or copper shell was used for eddy-current shielding. A high-permeability nickel-iron-molybdenum alloy (1.57 mm thick) was used for both ferromagnetic and eddy-current shieldings. The shielding factor was 60 dB at DC and 40 dB between 0.1 Hz and about 3 Hz. The eddy-current shielding due to the alloy alone provided a shielding factor of 55 dB at 30 Hz and 66 dB at 60 Hz. The shielding factor was sufficiently high in all the frequency range for biomagnetic measurements with a first-order superconducting gradiometer     

Magnetic effects of direct ion implantation of Mn and Fe into p-GaN

In p-GaN implanted with Mn (3×10¹⁶ cm⁻² at 250 keV), the material after annealing shows ferromagnetic properties below 250 K. Cross-sectional transmission electron microscopy (TEM) revealed the presence of platelet structures with hexagonal symmetry. These regions are most likely Ga_xMn_1−xN, which produce the ferromagnetic contribution to the magnetization. In p-GaN implanted with Fe, the material after annealing showed ferromagnetic properties at temperatures that were dependent on the Fe dose, but were below 200 K in all cases. In these samples, TEM and diffraction analysis did not reveal any secondary phase formation. The results for the Fe implantation are similar to those reported for Fe doping during epitaxial growth of GaN.     

Interleaving Cavity Resonances for Shielding Enhancement in Topologically Definable Spaces

Shielding enhancement can be obtained via resonance interleaving when applied to complex, layered shielded enclosures. Resonance interleaving assumes that the enclosure is subject to topological decomposition into weakly coupled separate regions. For each region a set of unperturbed resonances is found by eliminating outside coupling. Resonance interleaving is achieved by adjusting the geometries or boundary conditions on the separate regions to minimize overlapping of the unperturbed resonances of adjacent regions. It is shown mathematically how this reduces the energy transfer between adjacent regions. Various means of obtaining the unperturbed resonances so that interleaving can be performed are discussed. An example of the shielding effect is examined and from it a qualitative estimate of a ~ 12 dB shielding effectiveness increase over critical frequency intervals is made. It is noted that the cost of using this approach in designing enclosures is minimal, in that only small geometry changes may be sufficient, and the concept can be used to locate design problems in pre-existing designs.     

Anisotropic Interlayer Dzyaloshinskii–Moriya Interaction in Synthetic Ferromagnetic/Antiferromagnetic Sandwiches

The interfacial Dzyaloshinskii–Moriya interaction (DMI) in ferromagnetic/non-magnetic-metal bilayers is essential to stabilize chiral spin textures for potential applications. Recent works reveal that the interlayer DMI is beneficial to designing 3D chiral spin textures that possess fundamental importance and the associated technological promises. Here, the interlayer DM constants are determined quantitatively in synthetic ferromagnetic/antiferromagnetic Pt/Co/Pt/Ru/Pt/Co/Ta structures. The results demonstrate that the interlayer DMI shows uniaxial anisotropic characteristics. The first-principles calculations elucidate that the anisotropic interlayer DMI is induced by the in-plane symmetry breaking along two high symmetric directions, which favors the magnetization of adjacent ferromagnetic layers canting in different directions. The anisotropic interlayer DMI is also confirmed by spin-orbit torque driven asymmetric magnetization switching. Moreover, the interlayer DMI can be tuned by the Ru-layer-thickness and beneficial to designing 3D spin textures for future spintronic devices.     

Electromagnetic Pulse Transmission Through a Thin Sheet of Saturable Ferromagnetic Material of Infinite Surface Area

A numerical solution is presented for determining the shielding properties of a thin sheet of saturable ferromagnetic material of infinite surface area. Several examples are given to indicate the behavior of ferromagnetic shields in an intense electromagnetic environment. These examples illustrate that only a few numerical results are required to determine the electric field transmitted through the material for a given incident pulse of any amplitude.     

Survey of Techniques for Measuring RF Shielding Enclosures

An intensive literature survey has been conducted to review existing techniques for measuring the effectiveness of RF shielding enclosures. Prevalent methods of measuring E- and H-field components and for sensing the total field are discussed and evaluated. The procedures described in the literature are tabulated into groups determined by their similarities in method or theory and are compared by listing the advantages and disadvantages inherent in each. (A weighting system is devised to aid in evaluating each of the principal methods discussed.) Also discussed are the theoretical considerations underlying each of the methods listed, as applicable to the measurement of shielding effectiveness. Among these are the concepts of the resultant wave impedance of the E-M field at a point inside a shielded enclosure and the relationship of low-impedance and high-impedance fields in the near field regions of antenna systems. Techniques for extending the frequency and intensity of illuminating fields are also discussed, as well as the insertion loss method of determining leakage from a shield. Limitations and deficiencies of this latter procedure are noted.     

Pulse shielding by nonferrous and ferromagnetic materials

The problems encountered in pulse shielding by ferromagnetic materials are discussed. A limiting nonlinear shielding theory for magnetic materials based on the classic switching theory of ferromagnetism is established and verified experimentally. The limiting nonlinear theory includes the influence of saturation induction, coercive force, electrical conductivity, and pulse charge. The pulse shielding effectiveness of many different shielding materials, both ferrous and nonferrous, is analyzed. The material costs and weights are compared. It is shown that below a certain pulse current level, nickel-iron alloys produce the lightest shields. Above that current level, nonferrous materials become lighter because they are less dense. Suggestions for the improvement of ferrous alloys are included.