Theoretical Estimates of Vacuum Conductivity of Nonlinear Channel of Short-Focus Electron Beam Transport

The paper presents analytical relationships obtained for calculating the vacuum conductivity of a nonlinear electron beam transport channel, the geometry of which is described by the power law dependence of the channel radius on the longitudinal coordinate. The dependences of the length of the transport channel on the pressure in the process chamber and also on the inlet and outlet radii of the channel are derived and analyzed. The obtained theoretical results are of practical importance for designing sputtering and welding electron beam equipment based on high-voltage glow discharge electron guns. The results of calculated data have been verified experimentally for a cylindrical transportation channel with an input diaphragm. To harmonize the theoretical and experimental data, a correction factor was introduced into the calculation formula to determine the length of the channel, and the value of this factor was adjusted based on the results of the experimental studies. The resulting relative difference between the calculated and experimental data does not exceed 15%. The calculated results obtained in this study can be used to optimize the geometry of the transport channel to achieve minimal losses of electron beam current in the channel.