A simple theory for optimizing finite width ELF magnetic fieldshields for minimum dependence on source orientation

The effectiveness of single layer, finite width, planar extremely low frequency (ELF) magnetic field shields is strongly dependent upon the orientation of the field sources. Since source information is difficult to obtain, the issue of designing shields which are independent of source orientation is important. Here, a simple analytic model for shielding by multiple layer, finite width, planar shields constructed from perfect electric and perfect magnetic material is presented. This is augmented by a study of conditions for which the perfect material approximation is valid. The simple model is used to determine strategies for designing shields which are independent of source orientation. It is found that two layer perfect electric/magnetic shields perform significantly better than single layer shields     

Transient electromagnetic field propagation through infinite sheets, into spherical shells, and into hollow cylinders

Gaussian electromagnetic field pulses of several durations are propagated through infinite sheets into the interior of hollow cylinders and into the interior of spherical shells. The plates, spheres and cylinders are made of aluminum and contain no slots. The time history of the propagated pulses is computed. Finally, the time sequence of the electric field is calculated in the interior of a cylinder of finite length when connected at its ends by wires to a generator delivering a current pulse of Gaussian shape. The dimensions of the cavities are assumed to be sufficiently small so that resonances are not excited by the highest significant frequency contained in the shortest pulse considered. The numerical study is restricted to thin-walled aluminum shields 1/32 inch, 1/16 inch, 1/8 inch and 1/4 inch thick. The half-amplitude widths of the pulses employed lie in the range14 musec to2400 musec. It is shown that the resultant Gaussian pulse electric fields defined on the surface of the plates and cylinders are propagated with little diminution in amplitude. This is understandable due to the requirement that the tangential fields are continuous across the interfaces, and to the fact that skin effect is almost nonexistent at low frequencies. The incident (as contrasted to resultant) field pulse undergoes reflection at the boundary surface. Hence, the attenuation sustained by the incident field is great, since reflection is the chief mechanism of attenuation of fields at low frequencies. Thin spherical shells form effective magnetic shields. The electric field is small in the interior of thin-walled cylinders carrying extremely large transient currents.     

Uniform magnetic field generated by two orthogonal sheet currentloops

A uniform-magnetic-field generating source (UMFGS) comprising two orthogonal sheet current loops, which gives a uniform magnetic field at low frequency over a much larger region than either a Helmholtz coil or wrapped wires, is presented. The H-field distribution inside the UMFGS is studied under quasi-static conditions. The UMFGS is shown to generate a well-defined magnetic field distribution, and the direction of the generated H field can be adjusted in the range 0-360° in the horizontal plane. Experimental data show good agreement with numerical results. The properties of the UMFGS need to achieve an optimal structure are predicted theoretically. Optimum design equations obtained with the aid of the computer are presented     

Reduction of Lightning-Induced Magnetic Fields and Voltages Inside Struck Double-Layer Grid-Like Shields

This paper presents a numerical analysis of the reduction of lightning-induced magnetic fields and voltages inside double-layer grid-like spatial shields typically used in reinforced concrete buildings, e.g., nuclear power plants. The calculations are performed with the CONCEPT computer code, which solves Maxwell's equations using the method of moments in the frequency domain. The computer code is extended with the well-known transmission line model (TL-model) in order to simulate direct lightning strikes. The structure under study comprises a cubic cage of 2 m side length having single- or double-layer grid-like spatial shields with square meshes of 0.25 m width. Three lightning-channel attachment points are considered at the cage roof, namely, the center, the midedge, and the corner. The simulated lightning currents are the positive, the negative first, and the negative subsequent strokes at lightning protection level I (LPL I) according to the international standard series IEC 62305. The computed quantities comprise the currents through some selected wires of the grid-like spatial shields, the magnetic fields, the magnetic-field derivatives, and the induced voltage across a typical installation loop inside the shield. The results of the single-layer shield are compared to those of the double-layer one to evaluate the additional reduction of the latter shield.      

Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity

An efficient numerical technique is presented for the calculation of induced electric currents on coupled wires and multiconductor bundles placed in an arbitrary shaped cavity and excited by an external incident plane wave. The method is based upon the finite-difference time-domain (FD-TD) formulation. The concept of equivalent radius is used to replace wire bundles with single wires in the FD-TD model. Then, the radius of the equivalent wire is accounted by a modified FD-TD time-stepping expression (based on a Faraday's law contour-path formulation) for the looping magnetic fields adjacent to the wire. FD-TD computed fields at a virtual surface fully enclosing the equivalent wire are then obtained, permitting calculation of the currents on the wires of the original bundle using a standard electric field integral equation (EFIE). Substantial analytical and experimental validations are reported for both time-harmonic and broad-band excitations of wires in free space and in a high-Qmetal cavity.     

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     

The Effect of Cylindrical Ferromagnetic Shells on the Self and Mutual Inductance of Parallel Wires

The effect of ferromagnetic shields on the self and mutual inductances of the wires enclosed by a ferromagnetic shell has been theoretically analyzed. Some theoretical equations based on a simplified model, which assumes that the driving wires and returning wires are located within two separated magnetic shells, are derived. The analysis shows that the effect of the ferromagnetic shells on the inductance of the wires depends strongly on the separation of the two magnetic shells; the closer the two magnetic shells, the stronger the effect. For a configuration of two identical ferromagnetic shells of internal radius 0.65 cm and separated by 10 cm, it is estimated that the self and mutual inductances are increased by about 30 percent for a wire of radius 0.06 cm. The changes of the self and mutual inductances are essentially due to the interactions between the ferromagnetic shells and the induced fields of the current elements.     

On volume integral equations

The focus of this paper is on the volume integral representations to be used in constructing integral equations for composite volume media. The major thrust of the paper is to identify where derivatives of a discontinuous function arise in the derivation of the volume representation. Three different derivation methods are presented, resulting in identical representation independent of the derivation method. These representations agree with some in the existing literature and disagree with others. When an electric field formulation is considered, the source of disagreement manifests itself only when magnetic materials are present. Likewise, for the dual situation, the inconsistency appears for a magnetic field formulation of dielectric materials. This paper identifies the sources of error in the incorrect representations and its major contribution is the rigorously correct derivation of the representations to be used in volume integral equations. We also present numerical results for an integral equation derived from our representation. The numerical results employ only the E-field as the unknown and the singularity is handled in a manner analogous to a standard numerical treatment of the electric field integral equation.     

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     

Far-field performance of linear antennas determined from near-fielddata

The main plane far-field radiation pattern of an antenna under test from the corresponding main plane near-field data, using a circular-line acquisition, is presented. The method is based on the reconstruction of equivalent magnetic currents (EMCs) using decoupled integral equations and one-dimensional source components. The resultant fast procedure is applicable to linear and quasilinear array antennas. Experimental data results and comparison with complete spherical acquisition and center-line acquisition are presented     

A simple hybrid method for ELF shielding by imperfect finite planar shields

A simple method is described for calculating the shielding performance of a two-dimensional (2-D) thin finite-width shield made of imperfect material in the presence of the magnetic field from line source conductors. First, solutions to two canonical problems with closed-form simple analytic formulas are presented; shielding by reflection from and absorption in thin planar shields of infinite extent and shielding by perfect conductor shields of finite width. Then the method for calculation of magnetic-field shielding by perfect conductor finite-width shields is extended using the simple interpolation method, to thick shields made of imperfect material. Finally, the hybrid solution is developed by adding the two results in quadrature. The result is a simple theory for shielding by finite-width shields made of any real shielding material of arbitrary thickness. Its accuracy has been validated by comparison to finite-element method solutions and existing measurements.     

Transient Analysis of a Stripline Having a Corner in Three-Dimensional Space

The transient analysis of electromagnetic fields has shown its utility not only in clarifying the variation of the fields in time but also in gaining information on mechanisms by which the distributions of an electromagnetic field at the stationary state are bronght about. We have recently proposed a new numerical method for the transient analysis in three-dimensioual space by formulating the equivalent circuit based on Maxwell's equation by Bergeron's method. The resultant nodal equatiou is uniquely formulated in the equivalent circuit for both the electric field and the magnetic field. In this paper, we deal with the stripline which should be analyzed essentially in three-dimensionaf space because of its structure, The time variation of the electric and magnetic field of the stripline having a comer is analyzed and the remarkable changing of distribution of the field is presented as a parameter of time and of conditions imposed by the corner stucture.     

Galerkin solution for the thin circular iris in aTE11-mode circular waveguide

An integral equation for the transverse electric (TE) field in the aperture of a concentric circular iris in a transverse plane of a circular waveguide is approximately solved using Galerkin's method. The aperture field is represented by a finite sum of normal TE and TM (transverse magnetic) circular waveguide modes that fit the circular aperture. The numerical convergence of the Galerkin solution is demonstrated using the resultant aperture field distributions and equivalent shunt susceptance for the case of dominant TE₁₁-mode excitation. The resultant aperture electric field distribution closely resembles that of the TE₁₁ aperture mode alone, except for edge contribution behavior at the edge of the iris. A resonant or capacitive iris is possible over a restricted range of frequencies     

A Nonmodal Formulation for Electromagnetic Transmission through a Filled Slot of Arbitrary Cross Section in a Thick Conducting Screen

This paper considers the two-dimensional problem of electromagnetic transmission through a filled slot of arbitrary cross section in a thick perfectly conducting screen. The equivalence principle is used to divide the original problem into three isolated parts where postulated equivalent sources radiate into unbounded, homogeneous media. These equivalent electric and magnetic currents are chosen to ensure continuity of the tangential components of electric and magnetic fields at each aperture. An integral equation is written for each of the three parts with the equivalent currents as unknowns. The resulting set of coupled integral equations is solved by the method of moments. It is shown in the Appendix that this set of equations has a unique solution. The primary quantities computed are the equivalent magnetic and electric currents on each aperture and the electric current on the remaining portions of the slot cross section. These results are compared with those obtained from a modal solution, where the fields in the slot cross section are expressed in terms of parallel-plate waveguide modes.     

Numerical analysis of MOS magnetic field sensors

A new method of numerical analysis of MOS magnetic field sensors is described, which is based on a lumped discrete approach and the application of a general-purpose circuit-analysis program. The channel region of the device is represented by a network of identical L-type circuit cells. A cell consists exclusively of conventional MOS devices, independent voltage sources and controlled current sources, while the magnetic field appears as a parameter in some of these devices. The method allows for an accurate two-dimensional numerical analysis of MOS sensors, including effects which have been neglected hitherto, such as transverse current flow and nonuniform charge density across the channel. Numerical results are given for conventional MOS plates, split-drain MOS devices and distributed current source biased MOS Hall plates.     

A sheet impedance approximation for electrically thick multilayered shields

This paper describes an extension of the sheet impedance concept to treat inhomogeneous or multilayered shields that may be thick in terms of material shield wavelengths. For shields with magnetic materials, a simple relation between the equivalent electric and magnetic currents representing the shield is obtained. This allows the magnetic current to be treated as a dependent unknown and the electric current to be found as the solution of a single surface integral equation shown to be a perturbation of that for a perfect electric conducting (PEC) surface. By using the proper interior equivalent problem, it is shown that the method produces accurate and stable results for shielding by a rectangular box.     

半空间VMD 的磁场垂直分量精确镜像理论解

精确有效计算Sommerfeld型广义积分是分析导电媒质半空间电磁波辐射和散射问题的关键。基于精确镜像理论,详细推导了导电媒质平面上方垂直磁偶极子激励的磁场垂直分量。该表达式快速收敛,易于数值计算,适用于源点与场点为任意位置、导电媒质参数任意的情形。首先利用源点与场点均位于分界面处特殊情形下磁场垂直分量的精确解析表达式,验证了精确镜像理论退化至特殊条件下给出的磁场表达式。然后计算了源与场点位于某一高度的场强。文中结果在可以等效为磁偶极子的小电流圆环场强计算中具有重要的应用价值。     

Electromagnetic Transmission through a Filled Slit in a Conducting Plane of Finite Thickness, TE Case

A solution is developed for computing the transmission characteristics of a slit in a conducting screen of finite thickness placed between two different media. The slit may be filled with Iossy material while the two regions on either side of the screen are assumed Iossless. A magnetic line source excitation is used (TE case) which is parallel to the axis of the slit. The equivalence principle is invoked to replace the two slit faces by equivalent magnetic current sheets on perfect electric conductors. Two coupled integral equations containing the magnetic currents as unknowns are then obtained and solved for by the method of moments. Pulses are used for the expansion and testing functions. Quantities computed are equivalent magnetic currents, the transmission coefficient, the gain pattern, and the normalized far field pattern.     

Time-domain analysis of magnetic-coated wire antennas

The interaction of transient electromagnetic pulses (EMP) with perfect electric conductor thin wires with a thin magnetic coating, or mixed (dielectric and magnetic) coating, is studied in the time domain. The numerical procedure is based on the solution of the thin-wire electric field integral equation (EFIE) by the method of moments (MM), using a marching-on-in-time procedure. Numerical results are compared with measurements and with other authors' data     

Coupling of finite element and moment methods for electromagneticscattering from inhomogeneous objects

A hybrid formulation which combines the method of moments (MM) with the finite element method (FEM) to solve electromagnetic scattering and/or absorption problems involving inhomogeneous media is discussed. The basic technique is to apply the equivalence principle and transform the original problem into interior and exterior problems, which are coupled on the exterior dielectric body surface through the continuities of the tangential electric field and magnetic field. The interior problem involving inhomogeneous medium is solved by the FEM, and the exterior problem is solved by the MM. The coupling of the interior and exterior problems on their common surface results in a matrix equation for the equivalent current sources for the interior and exterior problems. Combining advantages of both methods allows complicated inhomogeneous problems with arbitrary geometry to be treated in a straightforward manner. The validity and accuracy of the formulation are checked by two-dimensional numerical results, which are compared with the exact eigenfunction solution, the unimoment solution, and Richmond's pure moment solution