Algorithm for Approximation of the Boundary Trajectory of an Electron Beam by Reference Points Using Root–Polynomial Functions

A new approach to approximation the boundary trajectories of short-focus electron beams, propagated in the soft vacuum, is given in the paper. The approach is based on using root-polynomial functions, which are generally describe the electron beam trajectories in specified physical conditions with very high accuracy. The distinguishing feature of proposed algorithm of approximation is fitting the root-polynomial curve by the different reference points of the beam boundary trajectory and choosing among its 2 curves, which give minimal error of approximation. After that the set of coefficients of root-polynomial function are calculated iteratively by using dichotomy method. Some examples of applying proposed algorithm for approximation the results of experimental measuring of boundary trajectories of electron beam in high voltage glow discharge electron gun are given in the paper. Obtained results of provided researches is necessary for preliminary estimation of focal parameters of electron beam, formed by high-voltage glow discharge electron guns.