Interpolation of the Boundary Trajectories of Electron Beams by the Roots from Polynomic Functions of Corresponded Order

Abstract

The roots from corresponded order polynomic functions is considered in the paper as the suitable method of interpolation for boundary trajectories of electron beams with high convergence angle, propagated in the ionized gas at the condition of compensation of owner space charge of beam electrons. Main distinguishing feature of propose interpolation functions is its linear behaver between the basic points of interpolation, and namely such behaver is usually generally corresponded to boundary trajectories of electron beams, propagated in ionized gas with compensation of electrons' space charge. For interpolation functions with polynomials from 2 to 5 orders the analytical relations for calculation the polynomial coefficients have been obtained. The results of interpolation are compared with numerical calculations for corresponded regimes of beam propagation and relative errors of interpolation have been estimated. The value of error for all regimes of beam propagation was smaller, than 8%.