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The discrete longitudinal dielectric support bars for a TWT helical slow-wave structure of either of the circular and rectangular cross sections have been analyzed using the theoretical approach of smoothing out the supports azimuthally into a large number of dielectric tubes of their respective effective permittivity values. The number of such tubes is increased to a very large value in order to ensure converging results for better theoretical predictions. The method has been applied to study the dispersion characteristics of a helix in a metal envelope. The method has a special significance for better results for high-permittivity supports, large helix-to-envelope separation and high operating frequencies. The theoretical predictions are also compared with experimental values available elsewhere. The theoretical method suggested is general and is applicable to arbitrarily shaped support bars as well as to both glass/ceramic and metal envelopes.