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Abstract

We study the scattering problem for a thin cylindrical target that is placed with arbitrary orientation in a rectangular TE₁₀ waveguide and subjected to an imposed electromagnetic field. The scattered far-field is expressed in terms of the scattered field inside the target and the far-field expansion of the dyadic Green's function for the waveguide. In order to capture features of interest in microwave heating applications, we allow the target material's electrical properties to be arbitrary functions of position along the thin cylindrical target's axis. Reflection and transmission coefficients for such a target, and an expression for the rate of deposition of electromagnetic energy within it are derived.

1. Lewin, L., Theory of Waveguides, J. Wiley and Sons, 1975.

2. Leviatan, Y. and G. S. Sheaffer, "Analysis of inductive dielectric posts in rectangular waveguide," IEEE Trans. Microwave Theory and Techniques, Vol. 35, No. 1, 48-59, 1987.
doi:10.1109/TMTT.1987.1133594

3. Gesche, R. and N. Lochel, "Scattering by a lossy dielectric cylinder in a rectangular waveguide," IEEE Trans. Microwave Theory and Techniques, Vol. 36, No. 1, 137-144, 1988.
doi:10.1109/22.3493

4. Siakavara, S. and J. N. Sahalos, "The discontinuity problem of a rectangular dielectric post in a rectangular waveguide," IEEE Trans. Microwave Theory and Techniques, Vol. 39, No. 9, 1617-1622, 1991.
doi:10.1109/22.83838

5. Abdulnour, J. and L. Marchildon, "Scattering by a dielectric obstacle in a rectangular waveguide," IEEE Trans. Microwave Theory and Techniques, Vol. 41, No. 11, 1988-1994, 1993.
doi:10.1109/22.273426

6. Chumachenko, V. P.S. I. Tarapov, and S. Eker, "Scattering by a lossy dielectric cylinder in a waveguide cross-junction," IEE Proc. Microw. Antennas Propag., Vol. 149, No. 4, 229-236, 2002.

7. Jones, D. S., Acoustic and Electromagnetic Waves, Oxford University Press, 1986.

8. Kevorkian, J. and J. D. Cole, Multiple Scale and Singular Perturbation Methods, Springer Verlag, 1996.

9. Westphal, W. B., "Dielectric constant and loss measurements in high-temperature materials," Laboratory for Insulation Research, 1963.

10. Kriegsmann, G. A., "Hot spot formation in microwave heated ceramic fibres," IMA Journal of Applied Mathematics, Vol. 59, 123-148, 1997.
doi:10.1093/imamat/59.2.123

11. Kriegsmann, G. A., "Pattern formation in microwave heated ceramics: cylinders and slabs," IMA Journal of Applied Mathematics, Vol. 66, No. 1, 1-32, 2001.
doi:10.1093/imamat/66.1.1

12. Stratton, J. A., Electromagnetic Theory, McGraw-Hill Book Company, 1941.

Dr. M. Booty

Dr. Gregory A. Kriegsmann