To the Stability Theory of Electron Beam Injected into Plane Diode

It was derived the dispersion equation on the base of analytical solution for the non-uniform hydrodynamic equation systems in the first approximation of the stability theory, relating the frequencies and increments (decrements) appearing electromagnetic oscillations with electron beam and plane diode parameters. The dispersion equation solution showed that into a diode, where the electron flow is passing, instability appears to be not described in literature earlier. This instability has place in decelerating flows, when in stationary state the diode potential minimum does not form. Physically, the instability is linear stage of phase transition from one-particle mode of moving to the mode with collective character.