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The radiation field of a plasma-clad cylindrical antenna fed across an infinitesimal gap has been derived. The limitations on the validity of the far-field pattern have been stated. In the vicinity of the antenna, but in the region far from the gap, an expression is derived for the surface wave contribution which is the major source of field strength in this region. Analysis of the contour integration and discussion of the location of the various types of poles of the integrand on their appropriate Riemann sheets are presented. Numerical computations of far-field patterns and surface wave fields are presented graphically.