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.
A time-dependent theory for helix traveling wave tubes in beam-wave interaction is presented. The effect of wave on electrons is described by radio frequency (RF) field equations and space charge (SC) field equations, while the effect of electrons on waves is described by electron dynamic equations. The RF field equations are achieved from Ampere’s law and Faraday law, combined with sheath helix model RF field. The SC field equations are achieved from a space charge wave model. The electron dynamic equations are achieved by substituting the RF field equations and the SC field equations into the Lorenz force equation. Using coupling impedance to treat exciting sources of RF field equations, the RF and the SC field equations can be solved with the help of high frequency simulation software, such as HFSS or HFCS, which makes this time-dependent theory more flexible. The feasibility of this theory is proved by numerical simulation.
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