ABSTRACT
Analytic derivations of the rough tube mode exist for the azimuthally symmetric case, where the corrugations are irises, [6] and for a rectangular beam pipe with two opposite sides roughened by irises [7[. Provided the vacuum wavelength of the synchronous mode is large compared to the average distance between the corrugations the longitudinal electric field within each gap between adjacent irises can be assumed to be independent of the longitudinal coordinate [7] or equivalently the layer containing the corrugations can be replaced by an anisotropic dielectric [6]. The rough tube mode is then found by mode matching. Both approaches are not new. The first one was used to calculate wave propagation in corrugated waveguides. The latter averaging of material properties has been used e.g. for the analysis of waves incident upon laminated cores of transformers (see references given in [6, 7]).
