#### For citation:

Solncev V. A. By the theory of the electron waves and the discrete electron-wave interaction in the stopbands of the slow-wave systems. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2013, vol. 21, iss. 1, pp. 86-98. DOI: 10.18500/0869-6632-2013-21-1-86-98

# By the theory of the electron waves and the discrete electron-wave interaction in the stopbands of the slow-wave systems

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. Synchronous interaction of the electrons with the field stopband sections slow-wave systems characteristic equation reduces to biquadratic, analytical solutions which allow to analyze the properties of electron waves and amplification of the signal into the stopband section.

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