Nonlinear analysis of helix traveling wave tubes

A time-dependent nonlinear formulation of the interaction in the helix traveling wave tube is presented for a configuration in which an electron beam propagates through a sheath helix surrounded by a conducting wall. In order to describe both the variation in the wave dispersion and in the transverse inhomogeneity of the electromagnetic field with wave number, the field is represented as a superposition of waves in a vacuum sheath helix. An overall explicit sinusoidal variation of the form exp(ikz-iωt) is assumed (where ω denotes the angular frequency corresponding to the wave number k in the vacuum sheath helix), and the polarization and radial variation of each wave is determined by the boundary conditions in a vacuum sheath helix. Thus, while the field is three-dimensional in nature, it is azimuthally symmetric. 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. A dynamical equation for the field amplitudes is derived analogously to Poynting's equation, and solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Numerical examples are presented corresponding to both single- and multiwave interactions. copyright 1995 American Institute of Physics