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.
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