A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beam-wave interaction. The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix. Coupling impedance is introduced to the electromagnetic field equations' stimulating sources, which makes the theory easier and more flexible to realize. The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations. The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included. The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields, focusing fields and space-charge fields. The numerically simulated results of a tube are presented.