CHOOSING THE METHOD OF INTERPOLATION OF THE BOUNDARY TRAJECTORIES OF SHORT-FOCUS ELECTRON BEAMS AND THEIR GUIDING IN THE IONIZED GAS

Abstract

Comparative analyze of the methods of interpolation of dependence of electron beam radius on position of cutting plane by the longitudinal coordinate with using three basic point have been provided in the article. It is shown, that main particularity of analytical functions, which are described such dependences, is that they have one global minimum, and outside the minimum region the character of such dependences is similar to linear. Two different approaches to interpolation of such dependences are considered. First method is based on the assumption, that in the region of beam focus the parabolical interpolation is used, and outside the focal region used the linear function. For describing of such dependences, the apparat of mathematical logic and arithmetic-logic expressions have been used. The main disadvantage of such describing of boundary trajectories of electron beams, propagated in the ionized gas, is that it is usually difficult to find the basic point, where the transfer from linear to parabolical dependence have to be realized. Another method of interpolation is based on the use of class of special functions, which are defined as the roots of n power from the polynomials of the same power. It is shown with using the method of computer simulation, that the behavior of such functions is generally corresponded to the ravine dependence, which described the trajectories of electron beams, propagated in the ionized gas. It is shown, that with using of such interpolation functions the difference between the simulation results, which are interpolated, and the values of interpolation function, always isn’t grater, than few percent, but in the most cases it consist the part of percent. Therefore, it is proved on the base of testing computer experiments, that using as the interpolation functions the roots of n power from the polynomial’s of the same power is the effective instrument for describing the boundary trajectories of short-focus electron beams in ionized gas. The obtained results are very important for the solution the practical task of defining the focal parameters of electron beams, generated by the electron sources, based on the high voltage glow discharge.