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  5. VOL 42, NO 1 (2020)
  6. pp. 73-90

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

REFERENCES

  1. Melnyk, I.V., (2009), Systema naukovo-technichnyh rozrahunkiv MatLab ta ii vykorycnannya dlya rozvyazannya zadach iz elektroniky: navchalnyy posibnyk u dvoh tomah. Tom 2. Osnovy programuvannya ta rozvyazannya prukladnyh zadach [The System of Scientific and technical calculation MatLab and its using for solving the tasks if electronics: Tutorial Book in 2 volumes. Vol. 2. Fundamentals of Programming and Solving of Applied Tasks], University “Ukraine”, Kyiv, Ukraine.
  2. Melnyk, I.V., (2009), “Analyze of Using Matrix Macrooperation of MatLab System for Solving the Applied Tasks”, Elektronnoe Modelirovanie, Vol. 31, no 1, pp. 37-51.
  3. Melnyk, I.V. and Shinkarenko, N.V., (2011), “Analyze of Algorithmic Particularities of Calculated Matrixes for Solving the Programming Tasks by means of Matrix Macrooperation”, Elektronnoe Modelirovanie, Vol. 33, no 2, pp. 81-92.
  4. Plas, V.G. (2016), Python dlya slozhnyh zadach i mashinnoe obuchenie [Python for Complex Tasks and Computer Learning], Piter, St. Petersburg, Russia.
  5. Muller, A. and Van Rossum, G. (2017), Vvedenie v mashinnoe obuchenie s pomoschyu Python [Introducing to Computer Learning with Helping of Python], Izdatelskiy Dom “Williams”, Moscow, Russia.
  6. Melnyk, I.V. and Luntovskiy, A.O. (2016), “Analyze of Algorithmic Particularities of Calculated Matrixes for Solving the Programming Tasks by means of Matrix Macrooperation”, Elektronnoe Modelirovanie, Vol. 38, no 3, pp. 5-21.
    https://doi.org/10.15407/emodel.38.03.005
  7. Bronshtein, I.N. and Semendiaev, K.A. (1986), Spravochnik po matematike. Dlia inzhene­rov i uchaschihsya vtuzov [Reference Book on Mathematic. For Engineers and Students of Technical Institutions], Nauka, Moscow, Russia.
  8. Shiller, Z., Geizig, U. and Pantser, Z. (1980), Elektronno-luchevaia technologiya [Electron-Beam Technology], Energiya, Moscow, Russia.
  9. Molokovskiy, S.I. and Sushkov, A.D. (1991), Intensivnye elektronnye i ionnye puchki [Intensive Electron and Ion Beams], Energoatomizdat, Moscow, Russia.
  10. Siladii, M. (1990), Electronnaya i ionnaya optika [Electronic and Ion Optics], Mir, Moscow, Russia.
  11. Hocks, P. and Kasper, E. (1993), Osnovy elektronnoi optiki. Tom 1. Osnovy geometricheskoy optiki [Fundamentals of Electron Optics. Vol. 1. Fundamentals of Geometrical Optics], Mir, Moscow, Russia.
  12. Hocks, P. and Kasper, E. (1993), Osnovy elektronnoi optiki. Tom 2. Prikladnaia geometricheskaia optika [Fundamentals of Electron Optics. Vol. 2. Applied Geometrical Optics], Mir, Moscow, Russia.
  13. Hockney, R. and Eastwood, J. (1988), Computer Simulation Using Particles, London, CRC Press.
    https://doi.org/10.1201/9781439822050
  14. Zavialov, M.A., Kreyndel, Yu. E., Novikov, A.A. and Shanturin L.P. (1989), Plazmennye Protsessy v Technologicheskih Electronnyh Pushkah [Plasma Processec in Technological Electron Guns], Enegroatomizdat, Moscow, Russia.
  15. Illin, V.P. (1985), Chislennye Metody Resheniya Zadach Elektrofiziki [Numerical Methods for Solving Elektrophysic Problems], Nauka, Moskow, Russia.
  16. Mathius, D.G. and Fink, K.D., (2001), Chislennye metody. Ispolzovanie MATLAB [Numerical Methods. Using MATLAB], Izdatelskiy Dom “Williams”, Moscow, Russia.
  17. Samarskiy, A.A. and Gulin, A.V., (1989), Cyslennye metody. Uchebnoe posobie dlia vuzov [Numerical Methods. Tutorial Book for Students of Technical Institutions], Nauka, Moscow, Russia.
  18. Medvedev, A.V., Sveshnikov, V.M. and Turchanovskiy, P.Yu. (2014), “Parallelization of solving the boundary tasks on the quasistructure meshes with using of hybrid calculations CPU+GPU”, Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Vypusk: Informatsionnye tehnologii, Vol. 12, no 1, pp. 50-54.
  19. Vasiliev, F.P. (1988), Cyslennye metody resheniia ekstremalnyh zadach [Numerical Methods for Solving of Extremal Problems], Nauka, Moscow, Russia.
  20. Melnyk, I.V., (2005), “Numerical simulation of electric fields distribution and trajectories of charged particles at the high voltage glow discharge electron sources”, Izvestiya Vysshih uchebnyh zavedeniy. Radioelektronika, Vol. 58, no 6, pp. 61-71.

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