Small signal theory of an open column grating with arbitrarily shaped groove

An open column grating with arbitrarily shaped groove is studied in this paper. The small signal analysis is carried out based on a model that an annular electron beam flies near the surface of the column grating. The dispersion equation is established for the slow wave in the way of self-consistent field theory. Through numerical solutions of the dispersion equation, the dispersion relation, frequency characteristic and the small signal gain for various shapes of groove are analyzed, as well as the dependences of the gain on the electron beam and grating parameters are investigated.