Sistemnì Doslìdženâ ta Informacìjnì Tehnologìï (Dec 2024)

An advanced method of interpolation of short-focus electron beams boundary trajectories using higher-order root-polynomial functions and its comparative study

  • Igor Melnyk,
  • Alina Pochynok,
  • Mykhailo Skrypka

DOI
https://doi.org/10.20535/srit.2308-8893.2024.4.11
Journal volume & issue
no. 4
pp. 133 – 153

Abstract

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The comparison of three advanced novel methods for estimating the boundary trajectory of electron beams propagated in ionized gas, including lower-order interpolation, self-connected interpolation, and extrapolation, as well as higher-order interpolation, is considered and discussed in the article. All estimations of the corresponding errors have been provided relative to numerically solving the set of algebra-differential equations that describe the boundary trajectory of the electron beam. By providing analysis, it is shown and proven that lower-order interpolation usually gives the minimal value of average error, using the method of self-connected interpolation and extrapolation gives the minimal error for estimation of focal beam parameters, and higher-order interpolation is suitable to obtain a uniform error value over the entire interpolation interval. All results of error estimation were obtained using original computer software written in Python.

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