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A special type of helical slow-wave structure encompassing a rectangular geometry is investigated in this paper, and the slow-wave characteristics are studied taking into account the anisotropically conducting helix. By using the electromagnetic integral equations at the boundaries, the dispersion equation and the interaction impedance of transverse antisymmetric modes in this structure are derived. Moreover, the obtained complex dispersion equation is numerically calculated. The calculation results by our theory agree well with the results obtained by the 3-D EM simulation software HFSS. The numerical results reveal that the phase velocity decreases and interaction impedance increases at higher frequencies by flattening (increasing the aspect ratio of) the rectangular helix structure. In addition, a comparison of slow-wave characteristics of this structure with a conventional round helix is made.