Focusing on traveling wave tube (TWT) applications, the interaction impedance between an electron beam and electromagnetic modes in three distinct, but related, corrugated waveguides that operate at millimeter waves is investigated together with the role of glide symmetry. Two waveguide structures have glide symmetry, and the irreducible Brillouin zone is related to half of the period, leading to a wide band linearity, i.e., nondispersive, property of the dispersion diagram. The investigation of the modes with longitudinal electric field that can be excited shows that the bottom-top glide symmetric corrugated waveguide has a wide band interaction impedance, hence it is a good candidate for millimeter wave TWT amplifiers.