COMPORATIVE ANALIZE OF THE METODS OF INTERPOLATION AND APPROXIMATION OF THE BOUNDARY TRAJECTORY OF SHORT-FOCUS ELECTRON BEAM IN CONDITIONS OF ITS PROPAGATION IN THE IONIZED GAS

Abstract

Possibilities and particularities of using the functions, which are formed as the roots of corresponded power from the polynomials of same power, for interpolation and approximation of the boundary trajectory of electron beam during its propagation in the ionized gas in the conditions of compensation of the intrinsic space charge of electrons by the positive ions of residual gas, are considered in the article. It’s have been shown, that the nature of considered functional dependences is strongly corresponded to adequate describing of the boundary trajectories of electron beams for the defined physical conditions. The mathematical functions, which are set as the roots of corresponded power from the polynomials of same power, always have the one global minimum, and outside the minimum area its nature is mostly seems to linear. Namely such functions in the case of correct choosing of polynomial coefficients most accurately, as well as adequate, described the boundary trajectories of short-focus electron beams in the case of its guiding in the ionized gas. It is reasoned, that for finding the optimal values of polynomial coefficients during the solving the approximation task is suitable to use the symbolic processor and the library functions of the system of scientific and technical calculations MatLab. The test examples of such approximation are also considered. It is shown, that generally the error of approximation is smaller, than 10%.