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2004-06-08
PIER
Vol. 46, 313-333, 2004
download: 260
Inhomogeneous Magnetic Media: Wave Propagation and Magnetic Permeability Reconstruction
Konstantinos Baganas
In this paper we study the electromagnetic (EM) wave propagation in a perfect magnetic medium with continuously varying magnetic permeability m(z) in one direction. We consider the inhomogeneity to be arbitrary and described by an infinite power series of z and use the Frobenious method to solve the governing differential equation of the problem in the frequency domain. We also give special attention to the first cut-off frequency of the main mode TM11 and we propose a good estimation for it by means of the mean value of the magnetic permeability profile. The results from the mathematical analysis are applied to solve the direct problem of wave propagation in a system of three waveguides having two homogeneous filling materials and one that exhibits such inhomogeneous characteristics. We finally confront the inverse problem of magnetic permeability reconstruction by handling simulation data and a genetic optimization algorithm.
INHOMOGENEOUS MAGNETIC MEDIA: WAVE PROPAGATION AND MAGNETIC PERMEABILITY RECONSTRUCTION
2004-06-08
PIER
Vol. 46, 265-312, 2004
download: 403
A General Framework for Constraint Minimization for the Inversion of Electromagnetic Measurements
Tarek Habashy and Aria Abubakar
In this paper, we developed a general framework for the inversion of electromagnetic measurements in cases where parametrization of the unknown configuration is possible. Due to the ill-posed nature of this nonlinear inverse scattering problem, this parametrization approach is needed when the available measurement data are limited and measurements are only carried out from limited transmitter-receiver positions (limited data diversity). By carrying out this parametrization, the number of unknown model parameters that need to be inverted is manageable. Hence the Newton based approach can advantageously be used over gradient-based approaches. In order to guarantee an error reduction of the optimization process, the iterative step is adjusted using a line search algorithm. Further unlike the most available Newton-based approaches available in the literature, we enhanced the Newton based approaches presented in this paper by constraining the inverted model parameters with nonlinear transformation. This constrain forces the reconstruction of the unknown model parameters to lie within their physical bounds. In order to deal with cases where the measurements are redundant or lacking sensitivity to certain model parameters causing non-uniqueness of solution, the cost function to be minimized is regularized by adding a penalty term. One of the crucial aspects of this approach is how to determine the regularization parameter determining the relative importance of the misfit between the measured and predicted data and the penalty term. We reviewed different approaches to determine this parameter and proposed a robust and simple way of choosing this regularization parameter with aid of recently developed multiplicative regularization analysis. By combining all the techniques mentioned above we arrive at an effective and robust parametric algorithm. As numerical examples we present results of electromagnetic inversion at induction frequency in the deviated borehole configuration.
A GENERAL FRAMEWORK FOR CONSTRAINT MINIMIZATION FOR THE INVERSION OF ELECTROMAGNETIC MEASUREMENTS
2004-06-08
PIER
Vol. 46, 245-264, 2004
download: 187
Rigorous and Fast Convergent Analysis of a Rectangular Waveguide Coupler Slotted in Common Wall
Hongting Jia , Kuniaki Yoshitomi and Kiyotoshi Yasumoto
Rigorous and fast convergent analysis of a coupler slotted in common wall between two dissimilar rectangular waveguides is described by a mode-matching method combined with Fourier transform technique and consideration of the singularity of electromagnetic field around edges. Comparing with a conventional mode-matching method, the present method has two advantages. One is that it can avoid the usage of the dyadic Green's function, the other is that it can overcome the relative convergence problem. The consideration of the field singularity has greatly improved the convergence and the calculated accuracy of a solution. This analysis is rigorous and the computer cost is very low.
RIGOROUS AND FAST CONVERGENT ANALYSIS OF A RECTANGULAR WAVEGUIDE COUPLER SLOTTED IN COMMON WALL
2004-06-08
PIER
Vol. 46, 203-244, 2004
download: 188
Numerical and Experimental Validations of Iem for Bistatic Scattering from Natural and Manmade Rough Surfaces
Fifame Koudogbo , Paul Combes and Henri-Jose Mametsa
The Integral Equation Method (IEM) isapplied for about ten years to model the surface scattering phenomenon. Recently, Fung published in [1] an extra improved version of the IEM model. In thispap er, numerical and experimental validationsof the model are investigated. In backscattering, as in bistatic scattering, number of numerical validationsare made on a wide frequency band, by comparing IEM predictionswith a reference method results(Method of Moments). IEM results are also compared with those of some asymptotic models such as Small Perturbation Method (SPM) and Kirchhoff Model (KM) in the frequency domainswhere these latter are applicable. The improved model validation isac hieved by presenting confrontations of the simulation results with experimental data, some of them have been collected in appropriate papers, and the others come from experimentsw e conducted at the ElectroMagnetism and Radar Department (DEMR) of the Office National d'Etudes et de Recherches Aérospatiales (ONERA)-Toulouse (France).
NUMERICAL AND EXPERIMENTAL VALIDATIONS OF IEM FOR BISTATIC SCATTERING FROM NATURAL AND MANMADE ROUGH SURFACES
2004-06-08
PIER
Vol. 46, 77-104, 2004
download: 454
Contact Geometry in Electromagnetism
Matias Dahl
In the first part of this work we show that, by working in Fourier space, the Bohren decomposition and the Helmholtz's decomposition can be combined into one decomposition. This yields a completely mathematical decomposition, which decomposes an arbitrary vector field on ℜ3 into three components. A key property of the decomposition is that it commutes both with the curl operator and with the time derivative. We can therefore apply this decomposition to Maxwell's equations without assuming anything about the media. As a result, we show that Maxwell's equations split into three completely uncoupled sets of equations. Further, when a medium is introduced, these decomposed Maxwell's equations either remain uncoupled, or become coupled depending on the complexity of the medium. In the second part of this work, we give a short introduction to contact geometry and then study its relation to electromagnetism. By studying examples, we show that the decomposed fields in the decomposed Maxwell's equations always seem to induce contact structures. For instance, for a plane wave, the decomposed fields are the right and left hand circulary polarized components, and each of these induce their own contact structure. Moreover, we show that each contact structure induces its own Carnot-Carathéodory metric, and the path traversed by the circulary polarized waves seem to coincide with the geodesics of these metrics. This article is an abridged version of the author's master's thesis written under the instruction of Doctor Kirsi Peltonen and under the supervision of Professor Erkki Somersalo.
CONTACT GEOMETRY IN ELECTROMAGNETISM
2004-06-08
PIER
Vol. 46, 1-32, 2004
download: 200
Non-Relativistic Scattering in the Presence of Moving Objects: the Mie Problem for a Moving Sphere
Dan Censor
Recently non-relativistic boundary conditions based on the Lorentz force formulas have been introduced. It was shown that to the first order in the relative velocity v/c the results are in agreement with the exact relativistic formalism. Specific boundary value problems have been solved to get concrete results and demonstrate the feasibility of implementing the formalism. These included examples involving plane and cylindrical interfaces. Presently the velocity-dependent Mie problem, viz. scattering of a plane wave by a moving sphere, is investigated. The sphere is assumed to move in a material medium without mechanically affecting the medium. The analysis follows closely the solution for the cylindrical case, given before. The mathematics here (involving spherical vector waves and harmonics) is more complicated, and therefore sufficient detail and references are provided. The interesting feature emerging from the present analysis is that the velocity-dependent effects induce higher order multipoles, which are not present in the classical Mie solution for scattering by a sphere at rest. The formalism is sufficiently general to deal with arbitrary moving objects.