This paper presents a new, “magnetic‐ring”, slow‐wave structure (SWS), which provides an excellent interaction with a cylindrical electron beam. Formed by a periodic row of rings made from material with a relatively high permeability, such a SWS produces aquasi‐E01wave, similar to that in the iris‐loaded waveguide. The deceleration is due to the rings’ permeability. The electric field is purely inductive, forming longitudinally oriented ellipses around the magnetic rings. The absence of an azimuthal component of electric field in the slow wave makes it possible to manufacture magnetic rings from non‐conducting materials, as well as from thin conducting layers, e.g. tape rings made from amorphous iron. A pipe, made from a non‐conductive material with finite permeability, also can replace a periodic row of magnetic rings. © 2003 American Institute of Physics