Tangential Magnetic Field Research Articles

Solution for jump conditions at fast shocks in an anisotropic magnetized plasma

We study the magnetic field and plasma parameters downstream of a fast shock as functions of normalized upstream parameters and the rate of pressure anisotropy (defined as the ratio of perpendicular to parallel pressure). We analyse two cases: with the shock (i) perpendicular and (ii) inclined with respect to the magnetic field. The relations on the fast shock in a magnetized anisotropic plasma are solved taking into account the criteria for the mirror instability and firehose instability bounding the pressure anisotropy downstream of the shock. Our analysis shows that the parallel pressure and the parallel temperature as well as the tangential component of the velocity are the parameters that are most sensitive to the rate of pressure anisotropy. The variations of the other parameters, namely density, normal velocity, tangential component of the magnetic field, perpendicular pressure, and perpendicular temperature are much less pronounced, in particular when the perpendicular pressure exceeds the parallel pressure. The variations of all parameters increase substantially for a very low rate of anisotropy, which is bounded by the firehose instability in the case of inclined shocks. Using the criterion for mirror instability as a closure relation for the jump conditions at the fast shock, we obtain the plasma parameters and the magnetic field downstream of the shock as functions of the Alfvén Mach number. For each Alfvén Mach number, the criterion for mirror instability determines the minimum jumps in such parameters as density, tangential magnetic field component, parallel pressure, and temperature, and determines the maximum values of the velocity components and the perpendicular temperature. Ideal anisotropic magnetohydrodynamics (MHD) has wide applications for space plasma physics. Observations of the field and plasma behaviour in the solar wind as well as in the Earth's magnetosheath have highlighted the need for an MHD model where the plasma pressure is treated as a tensor.

A FEM formulation to treat 3D eddy currents in laminations

A method is presented to compute the eddy current losses in laminated nonsaturated iron cores based on the finite element method. In the first step, a three-dimensional model of the core treated as a bulk of anisotropic material with low conductivity in the direction normal to the lamination is analyzed. Each laminate is taken into account in the second step by writing the field components in it as fundamental solutions of the diffusion equation so that the averages of the tangential electric and magnetic field components over the thickness of the sheet equal the averages obtained in the first step.

Experimental validation of a stable method of moments procedure in time domain for the scattering from arbitrarily shaped conducting bodies

In this paper, numerical results obtained by the application of a stable marching‐on‐in‐time solution scheme of the electric field integral equation are compared against experimental data, assuming as a testing case that of electromagnetic scattering from perfectly electrically conducting bodies. The experiments have been performed in an electromagnetic pulse hardware simulator, reproducing plane wave illumination conditions. The surface current densities induced on the metallic bodies have been measured by means of probes sensitive to the tangential magnetic fields. The measured current densities have therefore been processed in order to eliminate the effects of the measuring instrument chain. Near‐field measurements have been performed by using probes sensitive to the electric field. Experimental data show a good agreement with numerical predictions.

Characteristic-Based Finite-Volume Time-Domain Method for Scattering by Coated Objects

The characteristic-based finite-volume time-domain method is applied to analyze the scattering from conducting objects coated with lossy dielectric materials. Based on the characteristic-based finite-volume scheme, two numerical strategies are developed to model the electromagnetic propagation across different dielectric media. One introduces a connecting boundary to separate the total-field region from the scattered-field region. The other employs the scattered field formulation throughout the computational domain. These two strategies are verified by numerical experiments to be basically equivalent. A numerical procedure compatible with the finite-volume scheme is developed to guarantee the continuity of the tangential electric and magnetic fields at the dielectric interface. Rigorous boundary conditions for all the field components are formulated on the surface of the perfect electric conducting (PEC) objects. The numerical accuracy of the proposed technique has been validated by comparison with theoretical results.

Theoretical and experimental characterization of the EMP-interaction with composite-metallic enclosures

A numerical procedure is developed for the prediction of the electric and magnetic field distribution inside an enclosure having aluminum and carbon-fiber reinforced composite (CFRC) walls, illuminated by a transient electromagnetic plane wave. The composite panel is simulated by an effective layer model; time-domain surface impedance boundary conditions are enforced on the external faces of the composite slab, to express the relations among the tangential electric and magnetic field components. A coupling model for the calculation of the current induced along thin wires inside the enclosure is presented. The proposed models are implemented in a three-dimensional (3-D) finite-difference time-domain (FDTD) procedure, which is applied to the analysis of the shielding performances of an aluminum box with one CFRC face, illuminated by a transient electromagnetic wave. The computed results are compared with measured data obtained by using a full scale EMP generator.

Exact surface impedance/admittance boundary conditions for complex geometries: theory and applications

A methodology useful to derive exact and higher order surface impedance/admittance boundary conditions (HOI/ABC's) for complex geometries is presented. It is shown that exact surface boundary conditions are always expressed through dyadic integral operators involving the tangential magnetic and electric fields all over the surface of the body. Quasi-local surface boundary conditions that include curvature effects are shown to be computable through an asymptotic approximation of the integral operators. Finally, an example of a surface admittance boundary condition useful to analyze a structure exhibiting discontinuities along its surface boundary is presented. Practical examples to demonstrate the feasibility of the proposed methodology, as well as the accuracy of the resulting surface boundary conditions are also presented.

Statistical studies of plasma waves and backstreaming electrons in the terrestrial electron foreshock observed by Geotail

We present statistical studies of the direction finding of 2ƒp radiation and the spatial distribution of plasma waves and energetic particles in the terrestrial electron foreshock observed by Geotail. First, we investigate the geometry of the electron foreshock which is assumed to be the “2ƒp radio source.” The 2ƒp radio source is likely to be in the leading region of the electron foreshock where the most intense Langmuir waves are observed. The Langmuir wave activities and the population of energetic electrons gradually decrease in the region beyond 10 RE from the contact point. The decreasing rate of Langmuir wave activity is very small, about 10−0.008/RE. We also find that in the region around the contact point of the tangential interplanetary magnetic field (IMF) lines and the bow shock, the observed amplitude of the 2ƒp radiation seems to become weak. We think that it is due to the weak activities of Langmuir waves in the region close to the contact point and/or the directivity of 2ƒp radiation along the tangential IMF line. Next, we investigate the influence of the solar wind conditions on the activities in the electron foreshock. We confirm a positive correlation of the 2ƒp radio activity with the solar wind kinetic energy flux and a decrease of 2ƒp radio activity with decreasing IMF cone angle resulting in IMF lines tangent to the far flank of the bow shock. The 2ƒp radio activity is more affected by both parameters than the amplitude of Langmuir waves is affected. This suggests that the 2ƒp radio emissivity is very sensitive to the energy of Langmuir waves as expected from the generation process of 2ƒp radiation. Such high sensitivity also supports the concentration of the radio emissivity in the leading region of the electron foreshock and the limitation of the radio source extension along the magnetic field line. We also reinvestigate the comparison between the terrestrial and Venusian foreshocks. The differences between them suggest the nonsimilarity of shocks with different sizes.

2117 磁性液滴の衝突現象に及ぼす表面粗さの効果 : 第 2 報水平磁場の場合

2117 磁性液滴の衝突現象に及ぼす表面粗さの効果 : 第 2 報水平磁場の場合

A simple method for measuring the dielectric constant of solids

This paper presents a simple method for determining the dielectric constant of a solid material. The method consists of measuring the return loss due to a slab of such material inserted into a rectangular waveguide. The dielectric slab presents a discontinuity inside the waveguide, and the electric field at each interface of the slab is described as a summation of weighted sinusoidal basis functions. The scattered magnetic field on either side of the slab is determined using the modal expansion approach. These weights are solved by using the method of moments on the boundary conditions of continuity of the tangential magnetic field at the interfaces. The component of the electric field (scattered) for the dominant TE/sub 10/ mode can then be determined in terms of these weights, and from this result the reflection coefficient can be theoretically evaluated. A comparison between the experimentally obtained reflection/transmission coefficient and the theoretical values provide a figure for the dielectric constant of the material.

Evolution of long waves and chaos in magnetohydrodynamics

The evolution equation for a wavepacket travelling on the surface of a conducting fluid of finite depth in 2+1 dimensions in the long-wave approximation is studied in the context of magnetohydrodynamics. The amplitude equation thus obtained is the well-known Kadomtsev–Petviashvili equation with modified coefficients in the presence of a tangential magnetic field. By taking the double limit of this equation, Schrödinger–Poisson type equations are obtained. A nonlinear evolution equation is sought, in order to study Rayleigh–Taylor instability. It is shown that the magnetic field and surface tension have a stabilizing influence on the formation of bubbles arising owing to this instability. By incorporating forcing and damping terms in the Kadomtsev–Petviashvili equation, a condition for the existence of transverse homoclinic orbits giving rise to chaotic motions is obtained by using the Melnikov function method. It is shown that the chaotic motions can be suppressed by applying a suitably strong magnetic field. A study of subharmonic bifurcation leading to surface waves is also undertaken. The tangential magnetic field has a stabilizing influence on such motions.

Tangential magnetic field induced structure in a thin layer of viscous magnetic fluid when developing Rayleigh–Taylor instability

In the framework of the small amplitude Rayleigh–Taylor instability model, one derives an equation describing an evolution of a free surface shape of a thin layer of a viscous magnetic fluid located on the lower side of a horizontal flat plate under a uniform tangential magnetic field. The analytical expressions for a velocity field and a time-dependent pressure perturbation in the fluid layer are obtained. The influence of the magnetic field upon the Rayleigh–Taylor instability is examined. Obtained theoretical results are compared with the experimental observations of the final stage of the disintegration of the layer.

Dual formulations of a hybrid FEM/MOM method for nonlinear analysis [of EM fields

Hybrid FEM/MOM methods use the equivalence theorem to transform the actual problem into equivalent problems in the exterior and interior regions. In this paper, dual edge element differential formulations in terms of two-component vector potentials are used to solve the interior problem. In the exterior problem, the method of moments (MOM) has been used. A nonlinear matrix equation for the problem solution is obtained by forcing the continuity of the actual tangential electric and magnetic fields on the boundary of the nonlinear solid bodies. Two-dimensional numerical results are used to show the characteristics of the method.

Inhomogeneous magnetostriction states in uniaxial ferromagnetic films

Surface magnetoelastic Love waves and nonuniform distributions of the magnetization and elastic strains are investigated in a uniaxial ferromagnetic film on a massive nonmagnetic substrate in a tangential external magnetic field. A new inhomogeneous phase is predicted having spatial modulation of the order parameter, arising from magnetostrictive coupling of the magnetization with lattice strains near the interface of the magnetoelastic and elastic media. It is shown that, at some critical magnetic field Hc, different from the orientational transition field in an isolated sample, a magnetoelastic Love wave propagating parallel to the magnetization vector in the film plane becomes unstable. The frequency and group velocity of the wave vanish at wave number k=kc≠0 and the wave freezes, forming a domain structure localized in the film and adjoining substrate.

Scattering of a Perfectly Conducting Square Plate By Using On-Surface Measured Equation of Invariance Method

In this paper, on-surface measured equation of invariance (OSMEI) method is applied to 3-D problems. The scattering of a perfectly conducting square plate illuminated by a normally incident plane wave is used as a testing example. Rather than 2-D OSMEI formulations, the new formulations in 3-D, which describe a local relationship between tangential vector potential and tangential magnetic field, require the least number of unknowns and generate a highly sparse system matrix. Numerical calculation shows that the results of the OSMEI are in good agreement with the results of method of moments (MoM) .

Uniqueness of electromagnetic inversion by local surface measurements

Assume that a bounded body has been embedded in a homogeneous half-space. Our aim is to reconstruct the electromagnetic material parameters, namely the electric permittivity, conductivity and magnetic permeability, of the body from local field measurements on the surface of the half-space. All fields are supposed to be governed by time-harmonic Maxwell equations. We consider two kinds of initial data. The first data set consists of tangential electric and magnetic field vectors of a tangential magnetic dipole for all field and source points in an open subset of the surface. The second data set is one that we know locally on the surface - the admittance map - which, by definition, associates the tangential magnetic field with the tangential electric field. The purpose of this paper is to show that both of the data sets determine the material parameters uniquely.

Measurements of AC losses in different former materials

A high temperature superconducting cable may be based on a centrally located cylindrical support, a so-called former. If electrically conductive, the former can contribute to the AC losses through eddy current losses caused by unbalanced axial and tangential magnetic fields. With these measurements we aim at investigating the eddy current losses of commonly used former materials. A one layer cable conductor was wound on a glass fibre reinforced polymer (GFRP) former. By inserting a variety of materials into this, it was possible to measure the eddy current losses of each of the former candidates separately; for example copper tubes, stainless steel braid, copper braid, corrugated stainless steel tubes, etc. The measured data are compared with the predictions of a theoretical model. Our results show that in most cases, the losses induced by eddy currents in the former are negligible. However, for materials with a low resistivity the eddy current losses may become significant, e.g., for high purity Cu or Al.

Rayleigh-Taylor Instability of A Thin Magnetic Fluid Layer in A Tangential Magnetic Field

A viscous magnetic fluid layer in a uniform horizontal magnetic field is considered. The upper boundary of the layer is a horizontal rigid wall and the lower boundary a the free surface. It is assumed that at the initial instant the free surface represents a randomly weakly deformed horizontal plane. A dispersion relation for the waves in a layer of arbitrary thickness is obtained within the framework of the linearized system of ferrohydrodynamic equations describing the evolution of spatial perturbations. The effect of a tangential magnetic field on the breakdown of a thin layer is investigated theoretically and experimentally.

Flow shear across solar wind discontinuities: WIND observations

We examine the tangential magnetic field and velocity shears across directional discontinuities (DDs) with significant change in magnetic field intensity observed by WIND in slow and fast solar wind streams. The magnetic field rotation sense in fast wind DDs is that predicted by theory for outward propagating rotational discontinuities (RDs), but flow shear magnitude and orientation do not always satisfy RD theory. Alternatively, DDs with small normal magnetic field can be regarded as tangential discontinuities (TDs); the observed shears imply that the length scale over which the proton velocity distribution changes at the discontinuity can be both smaller or larger than that of the electron distribution. The slow wind includes a larger fraction of DDs that disagree with RD theory. It is shown that the flow shear orientations allowed in a TD provide a continuous transition between the opposite orientations for RDs propagating along or against the magnetic field direction.

A hybrid FEM/MOM formulation for nonlinear electromagnetic analysis

A hybrid method for nonlinear electromagnetic analysis that combines the Method of Moments (MOM) and the Finite Element Method (FEM) is presented. By using the equivalence principle, an interior and an exterior problem are used to study the actual problem. The MOM is used for the solution of the exterior problem where equivalent surface currents replace the solid bodies and generate the fields in the free space. The FEM is used to solve the interior problem defined into the solid bodies with given conditions at their boundaries. Considering that the actual fields are given by the sum of the fields in the two problems, a nonlinear matrix equation for the problem solution is obtained by forcing the continuity of the actual tangential electric and magnetic fields on the boundary of the nonlinear solid bodies. Two-dimensional numerical results are used to show the characteristics of the method by the analysis of test cases and by comparison with other numerical methods.

An Effective Hybrid Method for Electromagnetic Scattering From Inhomogeneous Objects - Summary

An effective hybrid method is proposed, which combines the method of moments (MoM), the finite element method (FEM) and the wavelet transform method (WTM) (referred to as MoM/FEM/WTM method) for efficient solutions of scattering problems involving inhomogeneous media. The hybrid technique applies the equivalence principle to transform the original problem into interior and exterior problems which are coupled on the shared boundary through the continuity conditions of the tangential electric and magnetic fields. The MoM and the WTM are used for efficient solutions of the exterior problem and the FEM for the interior problem. In contrast to other traditional hybrid techniques, the new hybrid method, which combines the advantages of the MoM, the FEM and the WTM, can always produce highly sparse moment matrix equations which can be solved efficiently. This is of particular importance for large-size electromagnetic problems. Numerical results are given to demonstrate the merit of the method.