Generalization of the Second Order Vector Potential Formulation for Arbitrary Non-Orthogonal Curvilinear Coordinates Systems from the Covariant Form of Maxwell's Equations

Denis Prémel^{*}

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References

[1] C. V. Dodd and W. E. Deeds, “Analytical Solutions to Eddy Current Probe-Coil Problems,” Journal of Applied Physics, Vol. 39, No. 6, 1968, pp. 2829-2838.

[2] J. A. Tegopoulos and E. E. Kriezis, “Eddy Currents in Linear Conducting Media,” El-sevier, New York, 1985.

[3] J. R. Bowler, “Eddy Current Calculations Using Half- Space Green’s Functions,” Journal of Applied Physics, Vol. 61, No. 3, 1987, pp. 833-839.

[4] S. K. Burke, “Eddy-Current Induction in a Uniaxially Anisotropic Plate,” Journal of Applied Physics, Vol. 68, No. 1, 1990, pp. 3080-3090.

[5] J. R. Bowler, L. D. Sabbagh and H. A. Sab-bagh, “A Theoretical and Computational Model of Eddy Current Probes Incorporating Volume Integral and Conjuguate Gradient Methods,” IEEE Transactions on Magnetics, Vol. 25, No. 3, 1989, pp. 2650-2664.

[6] J. R. Bowler, S. A. Jenkins, L. D. Sabbagh and H. A. Sabbagh, “Eddy Current Probe Impedance due to a Volumetric Aw,” Journal of Applied Physics, Vol. 70, No. 3, 1991, pp. 1107-1114.

[7] S. M. Nair and J. H. Rose, “Electromagnetic Induction (Eddy Currents) in a Conducting Half-Space in the Absence and Presence of Inhomogeneities: A New Formalism,” Journal of Applied Physics, Vol. 68, No. 12, 1990, pp. 5995-6009.

[8] C. Reboud, G. Pichenot, D. Premel and R. Raillon, “2008 ECT Benchmark Results: Modeling with Civa of 3D Flaws Responses in Planar and Cylindrical Work Pieces,” Proceedings of the 35th Annual Review of Progress in Quantitative Nondestructive Evaluation, Chicago, 20-25 July 2008, pp. 1915-1921.

[9] Extende. http://www.extende.com

[10] D. Prémel (é not e), “Computation of a Quasi-Static Induced by Two Long Straight Parallel Wires in a Conductor with a Rough Surface,” Journal of Physics D: Applied Physics, Vol. 41, No. 24, 2008, 12 p.

[11] W. R. Smythe, “Static and Dynamic Electricity,” McGraw- Hill, New York, 1950.

[12] P. M. Morse and H. Feshbach, “Methods of Theoretical Physics,” McGraw-Hill, New York, 1953.

[13] L. P. Felsen and N. Marcuvitz, “Radiation and Scattering of Waves,” IEEE Press, Piscataway, 1994.

[14] P. Hammond, “Use of Potentials in Calculation of Electromagnetic. Physical Science, Measurement and Instrumentation, Management and Education—Reviews,” IEEE Proceedings A, Vol. 129, No. 2, 1982, pp. 106-112.

[15] T. Theodoulidis, “Analytical Modeling of Wobble in Eddy Current Tube Testing with Bobbin Coils,” Research in Nondestructive Evaluation, New York, Vol. 14, No. 2, 2002, pp. 111-126.

[16] S. K. Burke and T. P. Theodoulidis, “Impedance of a Horizontal Coil in a Borehole: A Model for Eddy-Current Bolthole Probes,” Journal of Physics D: Applied Physics, Vol. 37, No. 3, 2004, pp. 485-494.

[17] T. D. Tsiboukis, T. P. Theodoulidis, N. V. Kantartzis and E. E. Kriezis, “Analytical and Numerical Solution of the Eddy-Current Problem in Spherical Coordinates Based on the Second-Order Vector Potential Formulation,” IEEE Transactions on Magnetics, Vol. 33, No. 4, 1997, pp. 2461-2472.

[18] G. Mrozynski and E. Baum, “Analytical Determination of Eddy Currents in a Hollow Sphere Excited by an Arbitrary Dipole,” IEEE Transactions on Magnetics, Vol. 34, No. 6, 1998, pp. 3822-3829.

[19] T. D. Tsiboukis, T. P. Theodoulidis, N. V Kantartzis and E. E. Kriezis, “FDM-Based Second Order Potential Formulation for 3D Eddy Current Curvilinear Problems,” IEEE Transactions on Magnetics, Vol. 33, No. 2, 1997, pp. 1287-1290.

[20] E. J. Post, “Formal Structure of Electromagnetics: General Covariance and Electromagnetics. (Series in Physics),” North Holland Publishing Company, Amsterdam, 1962.

[21] L. B. Felsen and N. Marcuvitz, “Radiation and Scattering of Waves,” Prentice-Hall Englewood Clis, New Jersey, 1972.

[22] G. Granet, “Analysis of Diffraction by Surface-Relief Crossed Gratings with Use of the Chan-Dezon Method: Application to Multilayer Crossed Gratings,” Journal of the Optical Society of American A, Vol. 15, No. 5, 1998, pp. 1121-1131.

[23] K. A. Braham, R. Dusseaux and G. Granet, “Scattering of Electromagnetic Waves from Two-Dimensional Perfectly Conducting Random Rough Surfaces-Study with the Curvilinear Coordinate Method,” Waves in Random Media, Vol. 18, No. 2, 2008, pp. 255-274.