The fourth power algebraic characteristic equation is obtained for the wave number of the individual electron waves that exist in periodic slow-wave systems(SWS) with discrete electron-wave interaction. The study of properties of these waves and the solution of the corresponding boundary-value problem have been performed. It has allowed to find some properties of electron-wave interaction which are different or are identical to the SWS with discrete interactions or "smooth" SWS, for example helical SWS.
The model of the cell of slow-wave system of the type chained resonators with flyover channel filled with plasma was invented based upon the method of partial areas. The dispersion characteristics of this system were analyzed, and was shown that there is widening of passthrough line of this slow-wave system the same time the resistance of connection is getting bigger. This makes possible to explain some aspects of the work of plasmabeam TWT.