A relativistic field theory of a helix traveling wave tube (TWT) is described for the case in which a thin annular beam propagates through a sheath helix enclosed within a loss‐free wall. The theory is applied to the study of a TWT with an intense relativistic electron beam. The analysis implicitly includes beam space‐charge effects and is valid for arbitrary azimuthal mode number, and the coupled‐wave Pierce theory is recovered in thenear‐resonantlimit. The results indicate that impressive gains and efficiencies are possible in this regime. In addition, the interaction is relatively insensitive to the effects of a beam energy spread.