We solve for the fields in a waveguide with finitely conducting walls by a singular perturbation technique. The method provides a systematic procedure for finding higher-order terms in the solution and also yields insight into the effects of conductivity on a waveguide whose cross section has degenerate eigenvalues. The problem is formulated in terms of the Hertz potential with the guide excited by an electric vector polarized longitudinally (TM case). Since the equations are similar for the case of the guide excited by a magnetic vector polarized longitudinally (TE case), the method developed may be easily extended to include that case.
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