A time-dependent nonlinear formulation of the interaction in the helix
traveling wave tube is presented for a configuration in which an elec
tron 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-i omega t) is assumed (where omega denotes the angular fr
equency 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 ampli
tudes is derived analogously to Poynting's equation, and solved in con
junction with the three-dimensional Lorentz force equations for an ens
emble of electrons. Numerical examples are presented corresponding to
both single- and multiwave interactions. (C) 1995 American Institute o
f Physics.