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Progress In Electromagnetics Research
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LOW-FREQUENCY SOLUTION FOR A PERFECTLY CONDUCTING SPHERE IN A CONDUCTIVE MEDIUM WITH DIPOLAR EXCITATION

By P. Vafeas, G. Perrusson, and D. Lesselier

Full Article PDF (199 KB)

Abstract:
This contribution concerns the interaction of an arbitrarily orientated, time-harmonic, magnetic dipole with a perfectly conducting sphere embedded in a homogeneous conductive medium. A rigorous low-frequency expansion of the electromagnetic field in positive integral powers (jk)n, k complex wavenumber of the exterior medium, is constructed. The first n = 0 vector coefficient (static or Rayleigh) of the magnetic field is already available, so emphasis is on the calculation of the next two nontrivial vector coefficients (at n = 2 and at n = 3) of the magnetic field. Those are found in closed form from exact solutions of coupled (at n = 2, to the one at n = 0) or uncoupled (at n = 3) vector Laplace equations. They are given in compact fashion, as infinite series expansions of vector spherical harmonics with scalar coefficients (for n = 2). The good accuracy of both in-phase (the real part) and quadrature (the imaginary part) vector components of the diffusive magnetic field are illustrated by numerical computations in a realistic case of mineral exploration of the Earth by inductive means. This canonical representation, not available yet in the literature to this time (beyond the static term), may apply to other practical cases than this one in geoelectromagnetics, whilst it adds useful reference results to the already ample library of scattering by simple shapes using analytical methods.

Citation:
P. Vafeas, G. Perrusson, and D. Lesselier, "Low-Frequency Solution for a Perfectly Conducting Sphere in a Conductive Medium with Dipolar Excitation," Progress In Electromagnetics Research, Vol. 49, 87-111, 2004.
doi:10.2528/PIER04021905
http://www.jpier.org/PIER/pier.php?paper=0402195

References:
1. Xiong, Z. and A. C. Tripp, "Electromagnetic scattering of large structures in layered earths using integral equations," Radio Science, Vol. 30, 921-929, 1995.
doi:10.1029/95RS00833

2. Oristaglio, M. L. and B. R. Spies (eds.), Three Dimensional Electromagnetics, SEG, Tulsa, 1999.

3. Kaufman, A. A. and G. V. Keller, Inductive Mining Prospecting, Elsevier Science, New York, 1985.

4. Bourgeois, B., K. Suignard, and G. Perrusson, "Electric and magnetic dipoles for geometric interpretation of three-component electromagnetic data in geophysics," Inverse Problems, Vol. 16, 1225-1262, 2000.
doi:10.1088/0266-5611/16/5/308

5. Dassios G. and R. E. Kleinman, Low Frequency Scattering, Low Frequency Scattering, Oxford University Press, Oxford, 2000.

6. Perrusson, G., D. Lesselier, M. Lambert, B. Bourgeois, A. Charalambopoulos, and G. Dassios, "Conductive masses in a half-space Earth in the diffusive regime: Fast hybrid modeling of a low-contrast ellipsoid," IEEE Trans. Geoscie. Remote Sensing, Vol. 38, 1585-1599, 2000.
doi:10.1109/36.851958

7. Habashy, T. M., R. W. Groom, and B. R. Spies, "Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering," J. Geophys. Res., Vol. 98, 1759-1775, 1993.

8. Charalambopoulos, A., G. Dassios, G. Perrusson, and D. Lesselier, "The localized nonlinear approximation in ellipsoidal geometry: a novel approach to the low frequency problem," Int. J. Engineer. Scie., Vol. 40, 67-91, 2002.
doi:10.1016/S0020-7225(01)00048-9

9. Hobson, E. W., The Theory of Spherical and Ellipsoidal Harmonics, Chelsea, New York, 1955.

10. Perrusson, G., D. Lesselier, P. Vafeas, G. Kamvyssas, and G. Dassios, "Low-frequency electromagnetic modeling and retrieval of simple orebodies in a conductive Earth," Progress in Analysis, Vol. 2, 1413-1422, 2003.

11. Ao, O. C., H. Braunisch, K. O'Neill, and J. A. Kong, "Quasimagnetostatic solution for a conducting and permeable spheroid with arbitrary excitation," IEEE Trans. Geoscie. Remote Sensing, Vol. 39, 2689-2701, 2001.
doi:10.1109/36.975003

12. Bowman, J. J., P. L. Uslenghi, and T. B. Senior (eds.), Electromagnetic and Acoustic Scattering by Simple Shapes, J. J. North Holland, Amsterdam, 1969.

13. Varadan, V. K. and V. V. Varadan (eds.), Acoustic, Electromagnetic and Elastic Wave Scattering. Low and High Frequency Asympotics, North Holland, Amsterdam, 1987.

14. Perrusson, G., P. Vafeas, and D. Lesselier, Low-frequency modeling of the interaction of magnetic dipoles and ellipsoidal bodies in a conductive medium, Proc. 2004 Int. URSI Symp. Electromagn. Theory, 2004.

15. Morse, P. M. and H. Feshbach, Methods of Theoretical Physics, Vol. I, II, McGraw-Hill, New York, 1953.

16. Tortel, H., "Electromagnetic imaging of a three-dimensional perfectly conducting object using a boundary integral formulation," Inverse Problems, Vol. 20, 385-398, 2004.
doi:10.1088/0266-5611/20/2/005

17. Dassios, G. and P. Vafeas, "Comparison of differential representations for radially symmetric Stokes flow," Abstract and Applied Analysis, 2004.


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