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This article contains analysis of properties discrete electron-wave interaction in resonance slow-wave system (SWS). Equations of interaction are written in matrix form. Eigenvalues of transfer matrix with electron beam define spread constant of four electron waves. Features of electron waves in SWS with «smooth» energy stream and in SWS with «winding» flow are examined. Simulation is performed and amplification of multisection TWT with passband and stopband sections of SWS is found. Field distribution along stopband section is found.

We present the mathematical models, computer code and numerical analysis for modeling linear operation regimes of broadband helix travelling­wave tube (TWT) with the inhomogeneous slow wave structure along the interaction space. One­dimensional model of the interaction of the forward and reflected electromagnetic waves with an electron beam in a inhomogeneous section of the slow wave structure was researched. The calculation method of the linear gain and self­excitation conditions of multisection TWT was suggested.

The role of the discrete description of electron-wave interaction in high-power traveling wave tubes is shown. Deals with the development of this trend on the basis of the theory of interaction of the difference equation excitation waveguides. The validity of the linear theory and developed a universal characteristic equation of electron waves, using the difference equation excitation waveguides in stopbands of slow-wave systems.