Three-dimensional nonlinear theory of helix traveling-wave tubes

A three-dimensional (3-D) nonlinear helix traveling-wave tube (TWT) analysi s in the frequency domain is presented for a tape helix surrounded by a con ducting wall, Dielectric- and vane-loading of the helix are included, as is circuit tapering and external focusing, by either a solenoid or a field pr oduced by a periodic permanent magnet (PPM) stack. A complete tape helix di spersion equation is derived by an eigenvector analysis, The electromagneti c field is treated as a superposition of eigenvectors at different frequenc ies whose amplitudes and phases vary slowly in z. The nonlinear field equat ions are solved in conjunction with the three-dimensional Lorentz force equ ations for an ensemble of electrons. Beam space-charge waves are included u sing a superposition of solutions of the Helmholtz equation. The de self-fi elds of the beam are also included, The three-dimensional simulation is com pared 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.