# Methods and algorithm for calculating the focal parameters of a hollow conical electron beam in high-voltage glow discharge electron guns with a focusing magnetic lens

## DOI:

https://doi.org/10.20535/SRIT.2308-8893.2021.3.02## Keywords:

high-voltage glow discharge, magnetic lens, hollow electron beam, electron drift model, minimax analysis, focal diameter of the electron beam, focal ring thickness## Abstract

The algorithm is considered for calculating the focal distance of a hollow conical electron beam generated by high-voltage glow discharge electron guns with magnetic focusing of the beam in the drift region, as well as a method for calculating the diameter of the focal ring and its thickness for such a beam. The proposed algorithm is based on the theory of electron drift in the field of a focusing magnetic lens and is designed using the methods of discrete mathematics and the minimax analysis. The obtained simulation results made it possible to establish the influence of the magnetic lens current on the focal diameter of a hollow conical electron beam and on its focal ring thickness. It is shown that the change in the focal parameters of a hollow conical electron beam can be effectively provided through the regulation of the magnetic lens current.

## References

A.A. Novikov, High Voltage Glow Discharge Electron Sources with Anode Plasma [in rus]. Moscow: Energoatomiadat, 1983, 96 p.

M.A. Zavialiv, Yu.E. Kreindel, A.A. Novikov, and L.P. Shanturin, Plasma Processes in technological Electron Guns [in rus]. Moscow: Atomiadat, 1989, 256 p.

S.V. Ladokhin et al., Electron Beam Melting in Foundry Production [in rus]. Kiev: Steel, 2007, 605 p.

P. Feinaeugle, G. Mattausch, S. Schmidt, and F.H. Roegner, “A new generation of plasma-based electron beam sources with high power density as a novel tool for high-rate PVD”, Society of Vacuum Coaters, 54-th Annual Technical Conference Proceedings, Chicago, 2011, pp. 202–209.

G. Mattausch et al.,“Gas discharge electron sources – proven and novel tools for thin-film technologies”, Elektrotechnica and Electronica (E+E), vol. 49, no. 5–6, pp. 183–195, 2014.

M.I. Grechanyuk, A.G. Melnyk, I.M. Grechanyuk, V.G. Melnyk, and D.V. Kovalchuk, “Modern electron beam technologies and equipment for melting and physical vapor deposition of different materials”, Elektrotechnica and Electronica (E+E),vol. 49, no. 5–6, pp. 115–121, 2014.

S. Denbnovetskiy et al., “Principles of operation of high voltage glow discharge electron guns and particularities of its technological application”, Proceedings of SPIE – The International Society of Optical Engineering, 2017, pp. 10445–10455.

I. Melnyk, S. Tyhai, and A. Pochynok, “Universal Complex Model for Estimation the Beam Current Density of High Voltage Glow Discharge Electron Guns”, Lecture Notes in Networks and Systems, 152, pp. 319–341, 2021. Available: https://www.springer.com/gp/book/9783030583583

I.V. Melnyk and A.V. Pochynok, “Algorithm for Calculating the Focal Parameters of Profile Electron Beams, Which Are Formed by Gas-Discharge Guns [in ukr]”, Systems Research and Information Technology, no. 2, pp. 7–17, 2019.

I.V. Melnyk and A.V. Pochynok, “System of Constructive Geometrical Parameters of The Model of Electronic Guns of High-Voltage Glow Discharge, Which Form Profile Electron Beams [in ukr]”, Systems Research and Information Technology, no. 1, pp. 50–65, 2019.

I.V. Melnyk and A.V. Pochynok, “Using Matrix Algorithms to Calculate the Trajectories of Charged Particles and Determine the Focal Parameters of the Electron Beam [in ukr]”, Electronic Modeling, vol. 42, no. 1, pp. 73–90, 2020.

I.V. Melnyk, MatLab as Scientific and Technical Calculation System and Its Use for Solving Problems in Electronics: a Textbook in 2 Volumes. Vol. 2. Fundamentals of Programming and Solving Applied Problems [in ukr]. Kyiv: University “Ukraine”, 2009, 327 p.

J.H. Mathews and K.D. Fink, Numerical Methods. Using Matlab; 3rd edition. Amazon, 1998.

I.V. Melnyk, Basics of Programming in Python. Volume 2. Developed Python Programming Language. Comprehensive Textbook on the Courses “Object-Oriented Programming” and “Computing Systems and Networks” for Undergraduate Students Studying In The Educational Program "Electronic Devices [in ukr]. Kyiv: “Kafedra”, 2020, 492 p.

S.I. Molokovsky and D.I. Sushkov, Intense Electron and Ion Beams [in rus]. Moscow: Energoatomizdat, 1991, 304 p.

M. Siladzy, Electronic and Ionic Optics [in rus]. Moscow: Mir, 1990, 640 p.

I. Melnyk, “Methodic of Simulation of Guiding of Short-Focus Electron Beam in the Equipotential Transporting Channel of High Voltage Glow Discharge Electron Guns”, Bulletin of the Taras Shevchenko National University of Kyiv. Radiophysics and Electronics, no. 1 (23), pp. 57–62, 2015.

J. Anderson, Discrete Mathematics and Combinatorics [in rus]. Moscow: Williams Publishing House, 2004, 960 p.

V.P. Vasiliev, Numerical Methods for Solving Extreme Problems: Textbook for Universities [in rus]. Moscow: “Nauka”, 1988, 552 p.

A.A. Samarskiy and A.V. Gulin, Numerical methods [in rus]. Moscow: “Nauka”, 1989, 432 p.

E. Kamke, Handbook of Ordinary Differential Equations [in rus]. Moscow: “Nauka”, 1976, 589 p.