Solution For Electromagnetic Field Research Articles

An analytic formalism for the emission of coherent transition radiation from an oblique finite thin metallic target screen

Long-wavelength coherent transition radiation is commonly used in electron beam diagnostics for the determination of bunch lengths. Typically the spectrum of coherent transition radiation for a short bunch accelerator is settled in the low or sub-THz regime. Hereby, we present a theoretical model based on physical optical techniques in order to calculate emission characteristics for transition radiation, for both the radiating near-field and the far-field. This approach yields analytic solutions for the emitted electromagnetic fields without the need to solve integral equations. The simulated intensity distribution is compared with measurements showing good agreement.

A PIC Microcontroller Based Electromagnetic Stirrer

A microcontroller based rotating magnetic stirring system has been developed in this study. A mathematical model is proposed to get electromagnetic field solutions. The magnetic stirring system consists of four-phase half-wound coils with phase currents of lambda/2 radian phase difference to achieve a rotating magnetic field. During the application, the liquid to be stirred is placed on the stirrer in a beaker and a magnetic stir bar in the form of a magnet rod is dipped in. The magnetic stir bar, influenced by the magnetic field supplied by the system, stirs the liquid rotating around the center of the rotational field. An adjustment of the frequencies of the voltage applied to these coils is done through a supply circuit with a developed PIC microcontroller. Within the scope of this study, operating principle and the mathematical model of the rotating magnetic stirring system have been discussed. Experimental results for the initial prototype are also presented in detail. Furthermore, parameter optimization for the stirrer is performed.

Coupling impedances of a gap in vacuum chamber

A gap in the vacuum chamber stands between a beam and the outside world, and the theoretical elucidation of the interaction mechanism between the gap and the beam is of great importance to understand the interaction of any device with the beam. In this paper, we will present the formulas for the longitudinal and transverse impedances due to a gap in the beam chamber. In this process, we will derive the complete solutions of electromagnetic fields effective in the entire region, including the inside and the outside of the chamber, in a form that they can be easily numerically evaluated. The newly developed technique can provide new methods of solutions of electromagnetic fields also for a rather broad class of structures such as cavities. The numerical results of impedances are consistent with the ABCI results and their behavior in high frequency agrees well with the prediction of the diffraction theory. Our theory can also accurately reproduce the behavior of the impedance near and above the cutoff frequencies. In addition, our theory is applicable even to the impedances for nonrelativistic beams. We found that the broadband impedance of the small cavitylike structure can be estimated from the gap size and the chamber radius only, regardless of the exact shape of the structure. We also found that the transverse impedance of a gap has a large resonance peak at the frequency where the wavelength is equal to the chamber circumference. This resonance peak appears around 1\char21{}2 GHz in most of the cases, and we should be careful to design a ceramic break so that this transverse mode will not leak out to interact with nearby devices.

Experimental and modelling analysis of ferroresonant electric circuits

This paper presents a numerical and an experimental investigation on the ferroresonance in a LCR series electric circuit with the aim of deepening the effects of the magnetization phenomena in the ferromagnetic core. In the experiments an Epstein-like FeSi core, enabling an accurate material characterization under the same test conditions, constitutes the non-linear inductance. The model couples the circuit equations with a finite element solution of the one-dimensional electromagnetic field along the lamination thickness. The analysis of the numerical results, which are confirmed by experiments, shows that the accurate prediction of ferroresonance requires the use of detailed constitutive models, when the role of the magnetic losses is significant.

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes

The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series.

A FEM Domain Decomposition Method for Photonic and Electromagnetic Band Gap Structures

This paper introduces an efficient domain decomposition algorithm for the solution of time-harmonic electromagnetic fields arising in three dimensional, finite-size photonic band gap and electromagnetic band gap structures. The method is based on the finite element approximation and a nonoverlapping domain decomposition method. A set of "cement" unknowns on the inter-domain interfaces has been explicitly introduced to enforce the appropriate field continuities. The introduction of these extra unknowns allows for nonconforming/nonmatching triangulations across domain, eliminating the need for periodic mesh. To ensure and improve the convergence of the outer iteration loop, Robin transmission condition is used to communicate information across interfaces. The resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm. In this algorithm, the method solves, in the preprocessing step, for the Robin primal subdomain problems multiple times, by exciting one dual unknown at a time. This step generates an iteration matrix that is then used to update the dual unknowns in the outer-loop iteration. The present method becomes extremely efficient for problems with geometric repetitions, such as, photonic and electromagnetic band gap structures.

Material Design of Functionally Graded Plates with Function of Electromagnetic Noise Suppression (Quantitative Evaluation on Suppression Effect of Electromagnetic Noise)

The purpose of this paper is to present a method of material design of functionally graded material (FGM) plates with a function of electromagnetic noise suppression under an incidence of electromagnetic plane wave. The FGM plates are considered as multilayered plates while electromagnetic properties are homogeneous inside the same layer. The approximate analytical solutions of electromagnetic field in the multilayered plates are therefore derived for electromagnetic plane waves. The expressions for reflection and transmission coefficients are then obtained based on the above analytical solutions. In this paper epoxy resin/titanium oxide FGM plates for numerical calculations were used with a graded composition expressed in the form of power function. The effects of the graded composition and thickness on the reflection and transmission coefficients were then quantitatively evaluated, and the suppression effect of electromagnetic noise was discussed.

3D micromagnetic solution by finite formulation

In this paper, a method for the numerical solution of micromagnetic problems in 3D cases is presented. These problems require the solution of electromagnetic field coupled with Landau–Lifshitz–Gilbert equation, governing magnetization dynamics. Finite formulation of electromagnetic fields (FFEF) is used to compute the magnetostatic contribution to the effective field in terms of line integrals of magnetic vector potential, while integral boundary conditions are obtained computing magnetic scalar potential using magnetization values as source. Magnetization dynamics is evaluated by an implicit formulation. Results on benchmark configurations are shown.

Disks Surviving the Radiation Pressure of Radio Pulsars

The radiation pressure of a radio pulsar does not necessarily disrupt a surrounding disk. The position of the inner radius of a thin disk around a neutron star, determined by the balance of stresses, can be estimated by comparing the electromagnetic energy density generated by the neutron star as a rotating magnetic dipole in vacuum with the kinetic energy density of the disk. Inside the light cylinder, the near zone electromagnetic field is essentially the dipole magnetic field, and the inner radius is the conventional Alfven radius. Far outside the light cylinder, in the radiation zone, = , and the electromagnetic energy density is S/c ∝ 1/r2, where S is the Poynting vector. Shvartsman argued that a stable equilibrium cannot be found in the radiative zone because the electromagnetic energy density dominates over the kinetic energy density, with the relative strength of the electromagnetic stresses increasing with radius. In order to check whether this is also true near the light cylinder, we employ the Deutsch global electromagnetic field solutions for rotating oblique magnetic dipoles. Near the light cylinder the electromagnetic energy density increases steeply enough with decreasing r to balance the kinetic energy density at a stable equilibrium. The transition from the near zone to the radiation zone is broad. The radiation pressure of the pulsar cannot disrupt the disk for values of the inner radius up to about twice the light cylinder radius if the rotation axis and the magnetic axis are orthogonal. This allowed range beyond the light cylinder extends much farther for small inclination angles. The mass flow rate in quiescent phases of accretion-driven millisecond pulsars can occasionally drop to values low enough that the inner radius of the disk goes beyond the light cylinder. The possibilities considered here may be relevant for the evolution of spun-up X-ray binaries into millisecond pulsars, for some transients, and for the evolution of young neutron stars if there is a fallback disk surrounding the neutron star.

Construction of Integral Objective Function/Fitness Function of Multi-Objective/Multi-Disciplinary Optimization

To extend an available mono-objective optimization method to multi-objective/multi-disciplinary optimization, the construction of a suitable integral objective function (in gradient based deterministic method-DM) or fitness function (in genetic algorithm-GA) is important. An auto-adjusting weighted object optimization (AWO) method in DM is suggested to improve the available weighted sum method (linear combined weighted object optimizationLWO method). Two formulae of fitness function in GA are suggested for two kinds of design problems. Flow field solution is obtained by solving Euler equations. Electromagnetic field solution is obtained by solving Maxwell equations. Bi-disciplinary optimization computation is carried out by coupling these two solutions with a nonlinear optimization method. Numerical results show that the needed Pareto solutions can be effectively obtained by using these suggested methods to meet the original design requirements. (Less)

Global formulation of 3D magnetostatics using flux and gauged potentials

AbstractThe use of algebraic formulation for the solution of electromagnetic fields is becoming more and more widespread. This paper presents the theoretical development of two algebraic formulations of the magneto‐static problem and their implementation in a three dimensional computational procedure based on an unstructured tetrahedral mesh. A complete description of the variables used and of the solution algorithm is provided together with a discussion about the performances of the method. The performances of the two procedures are tested and assessed versus cases with known solutions. Copyright © 2004 John Wiley & Sons, Ltd.

Comparative Evaluation of a Novel Series Approximation for Electromagnetic Fields at Dielectric Corners With Boundary Element Method Applications

This paper presents a series solution for the longitudinal electromagnetic fields at arbitrary dielectric corners. We apply versions of the method that are up to sixth-order accurate to our recently proposed full vector boundary element method (BEM) mode solver. Our results indicate that our previous formulation models corner fields with high precision.

Analysis of electromagnetic scattering by a plasma anisotropic sphere

An analytical solution of electromagnetic fields in homogeneous plasma anisotropic media is obtained in this paper. In the source‐free plasma anisotropic media, the source‐free Maxwell's equations are utilized, where the expansion of plane wave factors is made in terms of the spherical vector wave functions in isotropic media, and the Fourier transformation is then applied. As a result, the field expressions represented using eigenfunctions are obtained in spectral domain. Applying boundary conditions on the spherical interface between air and plasma anisotropy, the electromagnetic fields of the plane wave scattered by a plasma anisotropic sphere are derived. Numerical results for the very general plasma dielectric material media are obtained, and those in a special case are compared between the present method and the Method of Moments (MoM) speeded up with the Conjugate‐Gradient Fast‐Fourier‐Transform (CG‐FFT) approach. The formulations in this paper can be generalized to those of more complex cases, such as layered plasma anisotropic sphere, plasma sheath, as well as plasma anisotropic material coated conducting sphere.

A generalized Milne solution for the correlation effects of multiple light scattering with polarization

The Wiener-Hopf method is used to obtain a generalized Milne solution for scalar and electromagnetic fields with single-scattering anisotropy. For the scalar field, the solution found for the time correlation function and the interference component of backscattering is in good agreement with available experimental data. A solution of the Milne problem is constructed for the electromagnetic field. Given anisotropy, the generalized Milne equation is solved in the P1 approximation for the quantity that describes the degree of depolarization of the scattered light. It is shown that the depolarization of the scattered light can change sign at large anisotropies.

Coupled finite-element codes for armature design

This paper discusses the development of a design tool that couples two-dimensional (2-D) electromagnetics (EM) with three-dimensional (3-D) dynamic structural mechanics. The resulting model has the capability for rapid performance assessment of railgun and armature structures. The coupling of codes is one-way in that no deformations are provided to the EM code once the calculations begin. An efficient and accurate 2-D EM code is used to generate the thermal and mechanical loads. It is well known that the 2-D EM solution for a solid armature railgun grossly compromises the calculation as compared to the 3-D formulation for isolated regions in the armature and conducting boundary. However, despite this drawback, some success has been obtained in comparing experimental results to the 2-D computations with velocity skin effect, as well as favorable comparisons between 2-D and static 3-D computations. At the present time, there is no code available that accurately captures the entire launch process and physics leading up to and including transition of the armature contacts. It is anticipated that with development of design rules and methodology, the electromagnetic field solution can be extended to 3-D as well as automated to the point that very little computer time and user intervention are required.

The solution of electromagnetic fields by equivalent magnetical network

A simple and explicit derivation is given for the analyzed electromagnetic fields by an equivalent magnetical network. By the circuit-oriented finite element method the vector wave equation problem is transformed in an algebraical system and solved. The original method is theoretically formulated and is applied in test configurations. The results of the simulations are then compared with those obtained by the traditional edge element finite element method solution.

Electromagnetic field diffusion in axisymmetric hysteretic cores

This paper presents a finite-element procedure for the solution of the voltage-driven transient electromagnetic fields in axisymmetric structures involving hysteresis. The approach handles the presence of eddy currents, flowing along circular paths, which significantly influence the diffusion of the magnetic field within the core. Some results performed on an electromagnet-like structure, under different supply conditions, are presented. The role of eddy currents and magnetic hysteresis is finally discussed.

3D electrostatic field solution with dual mesh

The paper presents an application of the "Finite formulation of electromagnetic field" to the analysis of electrostatic field. This new formulation proposes a direct expression of Maxwell laws in terms of global variables (fluxes, circulations, etc) and exploits duality present in these equations. In this way, it is well suited for the numerical solution of electromagnetic field and makes this process similar to the study of an electrical network. A field solver is thus implemented using tetrahedral elements and several comparisons versus analytical solutions are presented and discussed.

Generalized Telegraphers' and Helmholtz Equations for Conformal Structures With Bi-Anisotropic Loading Materials

This paper introduces a proper set of rotations and variable changing in order to write Maxwell's equations in the generalized orthogonal curvilinear reference system just as in the Cartesian case. These transformations are very useful to strongly minimize the analytical difficulties that arise when handling equations involved in the solution of electromagnetic fields for conformal structures. First, a new set of telegrapher-like equations, called the "Generalized Transmission Line (GTL) equations", is obtained, relating the transverse field components in general conformal structures loaded with bi-anisotropic materials. Then, new Helmholtz equations formally identical to the Cartesian ones, but effective in the generalized curvilinear reference system, are also derived.

The solution of electromagnetic fields by equivalent magnetic network

A simple and explicit derivation is given for the analyzed electromagnetic fields by an equivalent magnetic network. By the circuit-oriented finite element method the vector wave equation problem is transformed into an algebraical system and solved. The original method is theoretically formulated and applied in test configurations. The results of the simulations are then compared with those obtained by the traditional edge element finite element method solution.