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The fields radiated by an mode in an aperture of a corrugated pipe with quarter-wave teeth are derived by considering the pipe to be situated in an infinite perfectly conducting ground plane. Unlike the case for a smooth wall pipe, this model is reasonable since the corrugations force the edge taper in the plane of the pipe's aperture to be significantly increased from its smooth wall value of 4 dB. This considerably reduces the usual -plane edge diffraction effects (those in the plane are even less significant, being essentially the same as with no corrugations since the -plane taper is is infinite in either case). This model reveals that the -plane pattern of the pipe approaches the -plane pattern (with its wider main beam and lower sidelobes) and that the radiation is nearly linearly polarized only if the aperture is sufficiently large , where is the free-space wavelength and a is the radius of the aperture). This is in agreement with experimental results given. (Existing solutions of Minnet-Thomas and Clarricoats-Saha based on the Silver formulation predict beam symmetry and zero cross polarization despite aperture size.) The radiation characteristics: beam efficiency, aperture efficiency, gain, and cross-polarization ratio are computed for typical horn aperture sizes (i.e., horn diameters of about one to ten free-space wavelengths). Recognition of the fact that the main beam radiation can be described by the universal horn pattern of Kelleher facilitates reflector feed design procedure for arbitrary reflector edge illumination levels.