Nonlinear theory of collective effects in helix traveling wave tubes

Abstract

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 amplitudes of the waves to vary in z and t. The dynamical equation for the field is solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Collective effects from the fluctuating rf beam space-charge waves are also included in the analysis by means of a superposition of solutions of the Helmholtz equation. The simulation is compared with a linear theory of the interaction, and an example is described corresponding to a tube built at Northrop–Grumman Corp.