Numerical algorithm for calculation of the vacuum conductivity of a non-linear channel for transporting a short-focus electron beam in the technological equipment

In the article, based on solving the equations of vacuum technology, an iterative algorithm for calculating vacuum conductivity and the geometric parameters of a curvilinear channel for transporting a short-focus electron beam is proposed and studied. For such a type of channel, the dependence of its radius on the longitudinal coordinate is described by a power function. The proposed algorithm is based on the numerical solution of a set of nonlinear equations using the Steffensen method. The results of the test calculations are presented. The provided tests confirm the stability of the proposed algorithm’s convergence for correct pressure and pumping speed values in electron-beam technological equipment. Such curved transport channels can be used in electron beam equipment based on high-voltage glow discharge electron guns intended for welding, melting metals, and the deposition of thin films. The criterion for the optimal geometry of a nonlinear channel is the minimum power loss of the electron beam during its transportation while ensuring the required pressure drop between the discharge and technological chambers.