Resonator as high frequency electromagnetic field oscillation generator

The problem of finding the u(x-vector) field potential in a specific waveguide with generalized corrugated core geometry is considered. The perturbation is brought to the system by high energy electron beam, injected in a waveguide. It is shown that the Neumann spectral problem can be reduced to finding Green approximation solution, and how it can be solved by the discretization technique. Considered parameterization allow to optimize the u(x-vector) field for specific frequency tuning. This method can be used as plasma heating method for thermonuclear temperature control