Linear analysis of electron dynamic for the slowly varied section waveguide resonator with the TM mode in a hybrid-magnicon

Based on the fundamental principles of a magnicon, we propose a hybrid-magnicon amplifier. It utilises an axially modulated annular electron beam, a vertical cylindrical waveguide opened driver cavity and a slowly varied section waveguide opened output cavity, all with TM-mode. A basic concept analysis of this new type of tube shows that it is possible to make a small power or MW pulsed tube with a suitable wide-band. For example, if operated at the third harmonic they can reach 8% bandwidth. This paper expounds the linear theory for the hybrid-magnicon using a simple new method which solves for the Dispersion Equation. It gives the Dispersion Equation for the self-consistent effect and the space charge effect of the slowly varied section waveguide rotating TM-mode opened resonator cavity. It also gives the interaction power between the wave and the electrons.