Electrodynamical properties of electron waves which can be excited in relativistic Cherenkov devices

The main goal of this paper is an investigation with the help of computer codes of a slow-wave system based on an effective mathematical methods of the linear theory of relativistic Cherenkov devices. The important features of the used theory is an electrodynamical description of electromagnetic fields realized by the incomplete Galerkin´s method in which projective system contains eigenfunctions of Dirichlet´s and Neumann´s problems for circular membrane. Coordinate system contains also additional basis functions that are orthogonal to projective basis functions and have amplitudes determined by boundary conditions. This method permits take into accounts exactly boundary conditions that prevent Gibbs phenomena and improve convergence of Galerkin´s rows