Computation of electromagnetic fields scattered by a cylindrical inhomogeneity in a homogeneous medium of infinite extent

Summary A method is presented for computing time harmonic electromagnetic fields scattered by a cilindrical inhomogeneity in a homogeneous medium of infinite extent. Geometrically, the homogeneity is a cylinder of arbitrary cross-section. Outside a circular cylinder that completely surrounds the inhomogeneity, the electromagnetic field is expanded in terms of wave functions of the circular cylinder. Inside this cylinder, the electromagnetic field equations are transformed into a system of ordinary differential equations in the radial direction. The relevant system behaves numerically unstable and is therefore transformed into a stable one through a specific transformation scheme. To elucidate the validity and the versatility of the method, numerical results are presented for fields scattered by a number of different cylindrical inhomogeneities.     

压电复合材料中圆孔边Ⅲ型非对称裂纹的场强度因子

研究了压电复合材料中圆孔边4个非对称裂纹在远处受面内电载荷和面外力载荷共同作用下的断裂行为。利用复变函数方法和新映射函数将问题转化为Cauchy积分方程组。通过求解Cauchy积分方程组,得到了电非渗透型和电渗透型两种边界条件下裂纹尖端电弹性场和场强度因子的解析解。所得结果不仅可退化为已有解,而且可模拟出若干新的缺陷构型,如压电复合材料中圆孔边三裂纹、半无限压电复合材料中半圆孔边单裂纹及半无限压电体中边界裂纹。将所得结果与有限元结果进行比较,吻合很好,证实了文中方法的正确性和有效性。数值算例分析了缺陷的几何参数对场强度因子的影响规律。     

A perturbational approach to magneto-thermal problems of a deformed sphere levitated in a magnetic field

This paper presents a perturbation method for the solution of the electromagnetic and thermal problems of a deformed sphere levitated in an alternating magnetic field. The analytical solutions of the electromagnetic field distribution, the Joule heat generation, the magnetic lifting force and the temperature field are obtained based on a linear perturbation theory. The Maxwell equations are first simplified in terms of the vector potential and then solved by the method of separation of variables. The time-averaged Joule-heat source is calculated and coupled to the Fourier heat-conduction equation. The coupled equation is solved for temperature distributions within the deformed sphere by a combined approach of series expansion and variation of parameters. Both asymptotic and numerical analyses are provided. The total power absorption and temperature field for both single and multiple coils are also discussed.     

Analytical solutions for the transverse deflection of a piezoelectric circular axisymmetric unimorph actuator

This paper presents analytical solutions to the transverse deformation shape of a circular axisymmetric piezoelectric-metal composite unimorph actuator. The solutions account for both the influence of an applied electric field and a concentrated or uniformly distributed mechanical load. Using piezoelectric constitutive equations, combined with thin plate and small bending elastic theory, the generalized equation of motion for bending of thin piezoelectric-metal composite plates has been derived. Our approach predicts that there is an optimum thickness ratio between the piezoelectric and metal plates, which leads to a maximum combination of deflection and load carrying capabilities. Derived formulas are very simple that offer a quick method for engineering design and optimization of a circular unimorph piezoelectric actuator.     

Generation of nondiffracting quasi-circular polarization beams using an amplitude modulated phase hologram

We propose an approach to the generation of nondiffracting quasi-circularly polarized beams by a highly focusing azimuthally polarized beam using an amplitude modulated spiral phase hologram. Numerical verifications are implemented in the calculation of the electromagnetic fields and Poynting vector field near the focus based on the vector diffraction theory, and the polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the electric field, magnetic field, and Poynting vector field can simultaneously be uniform and nondiverging over a relatively long axial range of ~7.23λ. In the transverse plane, the ellipticity and azimuthal angle of the local polarization ellipse varies from point to point. No polarization singularity and phase singularity are found at the beam center, which makes the bright spot possible.     

Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields

This paper presents an analysis on electromagneto-thermo-mechanical behaviors of conductive plates, an analytical solution is given for a conductive circular plate in a time-dependent magnetic field by using a T-method of the eddy current which is widely used in the eddy current analysis of conductive and superconductive structures. The solution is expressed in an analytical series form and it is suitable for a circular plate under any arbitrary axisymmetric magnetic fields changing in time. Some interesting results including the eddy current, the increment of temperature, and the electromagneto-thermal stresses are investigated, respectively, in this paper. Some characteristics such as the distribution of temperatures, the in-plane electromagnetic stresses and the dynamic response of the conductive plate are first studied and displayed. This study not only reveals some characteristics on the eddy current, the temperature of the plate, the in-plane electromagnetic thermal stresses and the dynamic responses of the conductive plate which is in a time-dependent magnetic field, but presents a new possible way to simplify the analysis of the electromagnetic coupling problem for conductive structures.     

载流悬臂柱壳的非线性数值分析

针对在电磁场和机械场耦合作用下的载流柱壳的非线性变形问题的数值解法进行了研究。给出了载流柱壳在耦合场作用下的几何方程、物理方程、二维电动力学方程、磁弹性非线性运动方程和洛仑兹力表达式,建立了差分格式和线性化迭代方程,给出了这些方程的数值解系统,并以悬臂柱壳为例,计算了该壳在电磁场和机械载荷耦合作用下的应力及变形;讨论了其应力及变形与外加电磁参量之间的关系;证明了变化电磁参量可以对壳的工作状态实施控制。     

A dynamic theory for polarizable and magnetizable magneto-electro thermoviscoelastic,electrically and thermally conductive anisotropic solids having magnetic symmetry

A unified dynamic theory for polarizable and magnetizable magneto-electro thermoviscoelastic. electrically and thermally conducting anisotropic solids possessing magnetic symmetry is developed for time-dependent electromagnetic fields. Considering the Chu formulation of the Maxwell equations, the balance equations of nonrelativistic continuum mechanics and the boundary conditions together with the constitutive equations for anisotropic materials are given. It is shown that the entropy, polarization. magnetization and the nondissipative part of stress are derivable from a potential while the dissipative part of stress, electric current and heat flux vectors satisfy a residual inequality. The theory developed for a general anisotropy and interaction is applied to special cases.     

Monochromatic electromagnetic fields with maximum focal energy density

The monochromatic electromagnetic fields that achieve maximum focal energy density for a given input power and directional spread are found through a variational approach. It is found that the polarization of the fields at the focal point must be perpendicular to the main direction of propagation. Parametric expressions relating the directional spread and focal energy density of these fields (and others that achieve stationary focal irradiance) are found, both in the optical (electric field only) and in the electromagnetic cases.     

Shear circular dislocation loops investigated with elasticity theory and atomistic simulations

The elastic fields of displacements, strains, and stresses for a shear circular loop are obtained with the Burgers formula. In addition, interactions between two shear circular loops are obtained based on elasticity theory. A series of molecular dynamics (MD) simulations on a shear circular partial dislocation loop in copper have been performed to examine the elastic solutions. It is found that the results of the MD simulations are in good agreement with those of elasticity theory for a loop with radius 7.5 nm.     

Computation of transient electromagnetic fields radiated by atransmission line: An exact model

A novel time domain analytical method for predicting electromagnetic field transients resulting from power line switching operations is presented in this paper. This method, which is directly derived from electromagnetic field theory of a power transmission line, allows the field transients to be accurately and efficiently calculated. It will be shown that conventional numerical methods for computing transmission line transient electromagnetic fields are in fact degenerative approximate models for this analytical method     

Piezoelectrically actuated flextensional micromachined ultrasound transducers--I: theory

This series of two papers considers piezoelectrically actuated flextensional micromachined ultrasound transducers (PAFMUTs) and consists of theory, fabrication, and experimental parts. The theory presented in this paper is developed for an ultrasound transducer application presented in the second part. In the absence of analytical expressions for the equivalent circuit parameters of a flextensional transducer, it is difficult to calculate its optimal parameters and dimensions and difficult to choose suitable materials. The influence of coupling between flexural and extensional deformation and that of coupling between the structure and the acoustic volume on the dynamic response of piezoelectrically actuated flextensional transducer are analyzed using two analytical methods: classical thin (Kirchhoff) plate theory and Mindlin plate theory. Classical thin plate theory and Mindlin plate theory are applied to derive two-dimensional plate equations for the transducer and to calculate the coupled electromechanical field variables such as mechanical displacement and electrical input impedance. In these methods, the variations across the thickness direction vanish by using the bending moments per unit length or stress resultants. Thus, two-dimensional plate equations for a step-wise laminated circular plate are obtained as well as two different solutions to the corresponding systems. An equivalent circuit of the transducer is also obtained from these solutions     

Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture by using Borgnis potentials. I. General theory

A method is proposed, on the basis of the vector electromagnetic theory, for the numerical calculation of the diffraction of a converging electromagnetic wave by a circular aperture by using Borgnis potentials as auxiliary functions. The diffraction problem of vector electromagnetic fields is simplified greatly by solving the scalar Borgnis potentials. The diffractive field is calculated on the basis of the boundary integral equation, taking into consideration the contribution of the field variables on the diffraction screen surface, which is ignored in the Kirchhoff assumption. An example is given to show the effectiveness and suitability of this method and the distinctiveness of the diffractive fields caused by the vector characteristics of the electromagnetic fields.     

Computation of 3-D Sensitivity Coefficients in Magnetic Induction Tomography Using Boundary Integral Equations and Radial Basis Functions

This paper presents a method for the numerical computation of 3-D sensitivity coefficients of a target object in magnetic induction tomography (MIT). The sensitivity coefficient at a point is defined as the dot product of electromagnetic fields produced by unit current flowing in the excitation and the detector coil. In this paper, the fields are governed by a set of boundary integral equations (BIEs). Numerical results demonstrate that the fields on the boundary and interior volume domain of the target can be accurately represented by radial basis functions (RBFs). The paper compares numerical solutions of the BIEs based on RBFs with analytical solutions and boundary element solutions.      

Degree of polarization in tightly focused optical fields

We analyze the degree of polarization of random, statistically stationary electromagnetic fields in the focal region of a high-numerical-aperture imaging system. The Richards-Wolf theory for focusing is employed to compute the full 3 x 3 electric coherence matrix, from which the degree of polarization is obtained by using a recent definition for general three-dimensional electromagnetic waves. Significant changes in the state of partial polarization, compared with that of the incident illumination, are observed. For example, a wave consisting of two orthogonal and uncorrelated incident-electric-field components produces rings of full polarization in the focal plane. These effects are explained by considering the distribution of the spectral densities of the three electric field components as well as the correlations between them.     

Propagation-invariant electromagnetic fields: Theory and experiment

Abstract

The vector concept of the propagation invariance is formulated to be applied to the stationary electromagnetic fields. The analysed exact solutions of the Maxwell equations are obtained on the basis of general propagation-invariant solutions of the scalar Helmholtz equation. A possible classification of the propagation-invariant fields based on quantities which appear in the complex Poynting theorem is proposed. The longitudinal periodicity of the electromagnetic field obtained due to the superposition of two Bessel beams is verified by a simple experiment.     

Dynamics of electron–positron pairs in a vacuum polarized by an external radiation field

The polarization of the vacuum under the action of an external classical field of electromagnetic radiation is investigated in the stationary regime. The electron–positron pairs interact both with the external field and with their own polarization field. For a macroscopic piece of vacuum the pairs are condensed on the low-momenta states and tend to form a quasi-localized electron–positron plasma of pairs, with single-particle states labeled by the position vector. In the polarization process under the action of a classical field of radiation the electron–positron and photon dynamics can be treated by means of classical fields. Under these circumstances, the corresponding coupled non-linear equations of motion are solved. It is shown that the pair dynamics consists of quasi-stationary single-particle states, while the polarization field reduces to a static magnetic field. The single-particle ‘energy’ (temporal phase) due to a monochromatic external field exhibits a spatial distribution characteristic of a stationary wave. Both the pair energy and the polarization energy are computed. Their values are extremely small, even for highly focused, reasonably high, external fields. The number of pairs is determined by the external energy. Under the action of a classical field the polarized vacuum is magnetized, and the corresponding (very low) magnetic susceptibility (the refractive index of the vacuum) is computed.     

On the propagation of waves in an electromagnetic elastic solid

The coupling of electromagnetic and elastic waves is considered from the standpoint of linear elasticity and a linearized electromagnetic theory. The problem of plane waves traveling through a uniform magnetostatic field is considered and couplings of the waves are studied. An investigation of the same problem for a uniform electrostatic field shows that the usual plane waves propagate without any change in their phase velocities but that the mechanical waves are accompanied by small fluctuating electromagnetic fields. The problem of the vibration of a free infinite elastic plate in a large magnetostatic field is examined under the assumption that the resulting electromagnetic fields are quasistationary. Frequency equations are obtained for both symmetric and antisymmetric vibrations and the damping caused by the field for both the first two symmetric and antisymmetric modes is obtained as a linear correction to the usual free plate frequencies.     

A generalized plane-strain theory for transversally isotropic plates

Summary.  By adopting Kane and Mindlin's assumption that the through-the-thickness extensional strain is uniform through the plate thickness, a generalized plane-strain theory is developed for transversely isotropic plates. The three-dimensional governing equations are successfully reduced to two coupled equations in the two-dimensional space. With the new theory, explicit solutions of the three-dimensional stresses, especially the through-the-thickness component, around a circular hole and a V-shaped notch in a transversely isotropic plate of arbitrary thickness are derived. The analytical solutions are verified by comparing with finite element results. Received September 5, 2002 Published online: March 20, 2003     

Analytical solution for transient, diffusing fields inside a ring conductor with rectangular cross section

Electromagnetic launch involves diffusing fields and currents and finite-element analyses are usually employed to compute the transients in launch systems. The simulation times of interest in launch components such as sliding electrical contact systems and pulsed power systems vary from a few microseconds to a few milliseconds. Numerical solutions in such short time scales require very fine meshes to avoid instabilities. Benchmarking and validation of codes with finite-element analyses of coupled electromagnetic equations require checks on errors and instabilities. For this purpose, analytical series solutions have been derived here to describe the diffusing field transients in a few milliseconds in a ring conductor with rectangular cross section. A linearly ramped or step voltage is imposed on one axial end of the ring conductor, whereas the other axial end is grounded and maintained at zero potential. The coupled transient, one-dimensional diffusion equations have been solved using classical methods in applied mathematics. The distributions of currents and fields inside the conductor and the stored magnetic energy with time have been computed. The method presented here can be applied to any general excitation encountered in electromagnetic launch.