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A three-dimensional (3-D) nonlinear helix traveling-wave tube (TWT) analysis in the frequency domain is presented for a tape helix surrounded by a conducting wall. Dielectric- and vane-loading of the helix are included, as is circuit tapering and external focusing, by either a solenoid or a field produced by a periodic permanent magnet (PPM) stack. A complete tape helix dispersion equation is derived by an eigenvector analysis. The electromagnetic field is treated as a superposition of eigenvectors at different frequencies whose amplitudes and phases vary slowly in z. The nonlinear field equations are solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Beam space-charge waves are included using a superposition of solutions of the Helmholtz equation. The DC self-fields of the beam are also included. The three-dimensional simulation is compared with a previous 2.5 dimensional simulation using a sheath helix model, each of which is compared with a tube built at Northrop-Grumman Corp. The tape helix model is shown to be in substantially better agreement with the experiment than the sheath helix model.