# USING OF MATRIX ALGORITHMS FOR CALCULATION OF TRAJECTORIES OF CHARGED PARTICLES AND FOR DEFINING PARAMETERS OF ELECTRON BEAM

I.V. Melnyk, A.V. Pochynok

Èlektron. model. 2020, 42(1):73-90
https://doi.org/10.15407/emodel.42.01.073

### ABSTRACT

In the article, on the background of analyzing the basic definitions of matrix programming theory and the arithmetic-logic relations, is shown, that the corresponded methods of matrix programming, based on the forming of recurrent matrices, can be effectively used for computer realization of complex algorithms with high level of difficulty. Such algorithms are widely used for solving the tasks of simulation of complex physical processes, taking place in powerful energetic and technological gas-discharge devices. The arithmetic-logic and recurrent matrices relations for calculation of potential distribution with using finite-difference method and for calculation of the charged particles trajectories with using four order Runge – Kutt method have been obtained. Also, with using of recurrent matrices relations, the algorithm for defining the position of electron beam focus during moving of the electrons’ in the ionized quasi-neutral medium have been written. Proposed analytical relations have been successfully used for simulation of electrodes’ systems of high voltage glow discharge technological electron sources. The results of calculation of electric field distribution in the simulated electrodes’ system and electron beam current density distribution at the beam focal plane are presented. Obtained analytical relations, based on the theory of mathematical logic and on the matrices analyze algorithm, is quite universal, and its can, without significant modification, be used for simulation other types of gas-discharge devices, including energetic and technological ones.

### KEYWORDS

recurrent matrixes, arithmetic-logic relation, vector-function, field problem, trajectory analyze, technological electron sources, high voltage glow discharge

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