Approximation of the Boundary Trajectory of a Short-Focus Electron Beam using Third-Order Root-Polynomial Functions and Recurrent Matrixes Approach

A new approach for approximating the ravine function, which corresponds to the boundary trajectory of a short-focus electron beam, propagated in ionized gas with compensation of the space charge of electrons, is proposed in the paper. The algorithm is based on applying root-polynomial functions and a recurrent matrix approach. The proposed algorithm of approximation is suitable for defining the boundary trajectories of electron beams, formed by high voltage glow discharge electron guns. Test numerical experiments of the approximation of the experimental data by using the third order root-polynomial functions are also considered.