Simplyfied Universal Analytical Model for Defining of Plasma Boundary Position in the Glow Discharge Electron Guns for Forming Conic Hollow Electron Beam

In the article the simplified analytical relations for estimation the plasma boundary position in the electrodes systems of high voltage glow discharge electron guns, formed the hollow conic electron beam, have been obtained. The distinguishing feature of proposed model is considering the main geometry parameters of simulated electrodes' system through the slope angle of anode surface. Analytical relation for defining position of plasma boundary relative to the cathode surface has been obtained by solving the cubic equation. The results of simulation for different slope angle of anode surface are presented and discussed.