Nonlinear theory of collective effects in helix traveling wave tubes

A time-dependent collective nonlinear analysis of a helix traveling wave tube including fluctuating (ac) space-charge effects is presented for a configuration where an electron beam propagates through a sheath helix surrounded by a conducting wall. The effects of dielectric and vane loading of the helix are included, as is efficiency enhancement by tapering the helix pitch, and external focusing by means of either a uniform solenoidal magnetic field or a periodic field produced by a periodic permanent magnet stack. Dielectric loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. Vane loading describes the insertion of an arbitrary number of vanes running the length of the helix. The electromagnetic field is represented as a superposition of azimuthally symmetric waves in a vacuum sheath helix. The propagation of each wave in vacuo, as well as the interaction of each wave with the electron beam, is included by allowing the amplit...