Simulation of Focusing a Hollow Electron Beam by the Symmetric Magnetic Lens for Industrial Application in Additive Technologies
Abstract
The article studies the focusing features of a short-focus hollow electron beam formed from a wide surface of a cold cathode in high-voltage glow discharge electron guns using numerical simulation techniques. Such a type of electron beam is widely used today for producing new kinds of metals with unique properties by melting wire, which moves in a vertical direction through the ring-like beam focus. After that, the melted metal is crystallized on the horizontally moving substrate, which is located near the focus of the electron beam below. Such modern technology is considered three-dimensional printing of metal, or additive technologies. The original software created by the authors in the Python programming language has been used to obtain the corresponding simulation results. Analysis of the obtained numerical simulation results proved that with a small change in the beam trajectory divergence angle or the radius of the initial point on the cathode surface, the beam focus position, as a rule, does not change. Therefore, the annular focus of the beam is usually in a stable position on the longitudinal coordinate, and the thickness of the focal ring is always in the range of several millimeters. The corresponding theoretical results were compared with experimental data, and the difference between the theoretical and experimental results is in the range of 10-15% depending on the accelerating voltage and size of the cathode surface. High-voltage glow discharge electron guns with such parameters, by the thickness of the focal ring, can be successfully used in advanced industrial additive technologies for three-dimensional printing on metal surfaces by uniform heating along the perimeter of moving wires or rods with a variable diameter in the range of 0.5 – 10 mm.
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References
Wohlers Report 2023. Analysis. Trends. Forecasts. 3D Printing and Additive Manufacturing State of the Industry. ASTM International. (2023). https://wohlersassociates.com/product/wr2023/
An Additive Manufacturing Breakthrough: A How-to Guide for Scaling and Overcoming Key Challenges. White Paper. World Economic Forum, edited by F. Betti, C. Seidel, M. Meboldt, (2022). https://www3.weforum.org/docs/WEF_Additive_Manufacturing_Breakthrough_2022.pdf
A Guide to Additive Manufacturing, edited by D. Godec, J. Gonzalez-Gutierrez, A. Nordin, E. Pei, and J.U. Alcazar, (Springer, 2022). https://doi.org/10.1007/978-3-031-05863-9
M. Armstrong, H. Mehrabi, N. Naveed, Journal of Manufacturing Processes, 84, 1001 (2022). https://doi.org/10.1016/j.jmapro.2022.10.060
Identifying current and future application areas, existing industrial value chains and missing competences in the EU, in the area of additive manufacturing (3D-printing). European Commission. Final Report. Brussels, 15th of July, 2016. https://op.europa.eu/en/publication-detail/-/publication/b85f5e09-7e2b-11e6-b076-01aa75ed71a1/language-en
W. Frazier, Journal of Materials Engineering and Performance, 23(6), (2014). https://doi.org/10.1007/s11665-014-0958-z
Additive Manufacturing for the Aerospace Industry, edited by: F. Froes, and R. Boyer, (Elsevier, 2019). https://doi.org/10.1016/C2017-0-00712-7
K. Taminger, and R. Hafley, “Electron beam freeform fabrication: A rapid metal deposition process,” Proceedings of the 3rd Annual Automotive Composites Conference, (Troy, MI, USA, September, 9–10, 2003.
S. Stecker, K.W. Lachenberg, H. Wang and R.C. Salo, in: Proceedings of FABTECH and AWS Welding Show, (Atlanta, GA, USA, 2006). pp. 35–46.
Patent #8,344,281 B2, 2013. (USA).
F. Pixner, F. Warchomicka, P. Patrick, A. Steuwer, H. Colliander, R. Pederson, and N. Enzinger, Materials, 13, 3310 (2020). https://doi.org/10.3390/ma13153310
W.J. Sames, F.A. List, S. Pannala, R.R. Dehoff, and S.S. Babu, International Materials Reviews. 61, 5 (2016). https://doi.org/10.1080/09506608.2015.1116649
I. Melnyk, S. Tuhai, O. Kovalenko, M. Skrypka, and D. Kovalchuk, in: 2024 IEEE 7th International Conference on Smart Technologies in Power Engineering and Electronics (STEE), (Kyiv, Ukraine, 2024), pp. TT3.01.1-TT3.01.6. https://doi.org/10.1109/STEE63556.2024.10748050
I.V. Melnyk, S.B. Tugay, V.O. Kyryk, and I.S. Shved, System Research and Information Technologies, 2021(3), 17 (2021). https://doi.org/10.20535/SRIT.2308-8893.2021.3.02 (in Ukrainian)
H. Xu, X. Sang, B. Yang, Y. Peng, and J. Fan, Chinese journal of vacuum science and technology, 41(3), 284 (2021). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjvst.202005028?viewType=citedby-info
Chang Jiawei, Li Shengbo, Lin Zhishu, Bai Fengmin, Li Guozheng, and Bai Zongzheng, Chinese journal of vacuum science and technology, 44(5), (2024). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjvst.202401009
Gu Liang, Yang Jie, Zhao Hua, Tan Wei, and Li Jinrong, Chinese journal of vacuum science and technology, 44(2), 184 (2024). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjvst.202306003
Qui Yufan, Li Shengbo, Zheng Xinjian, Fu Shengping, and Bai Fengmin, Chinese journal of vacuum science and technology, 41(11), 1094 (2021). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjvst.202101027
Deng Chenhui, Wang Yan, Liu Junbiao, and Han Li, Chinese journal of vacuum science and technology, 40(9), 847 (2020). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjovst.2020.09.09
Wang Jian, Chinese journal of vacuum science and technology, 40(4), 381 (2020). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjovst.2020.04.17
Xiang Yidong, Zhao Ding, Xue Qianzhong, and Li Xiaofei, Chinese journal of vacuum science and technology, 40(3), 226 (2020). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjovst.2020.03.08
Wang Yan, Zhao Weixia, Deng Chenhui, Liu Junbiao, and Han Li, Chinese journal of vacuum science and technology, 40(1), 1 (2020). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjovst.2020.01.01
Gu Yunting, Lin Yanjian, Yan Baojun, Liu Shulin, Yang Yuzhen, Yu Yang, Wen Kaile, and Wang Yuman, Chinese journal of vacuum science and technology, 39(12), 1009 (2019). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjovst.2019.12.11
Huo Weijie, Hu Jing, Cao Xiaotong, Fu Yulei, and Zhao Wansheng, Chinese Journal of Vacuum Science and Technology, 39(8), 631 (2019). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjovst.2019.08.03
Fu Xuecheng, Wang Ying, Quan Xueling, Ju Minni, and Wang Fengdan, Chinese journal of vacuum science and technology, 39(5), 396 (2019). http://cjvst.cvs.org.cn/en/article/doi/10.13922/j.cnki.cjovst.2019.05.07
S.V. Denbnovetsky, I.V. Melnyk, V.G. Melnyk, B.A. Tugai, and S.B. Tuhai, in: 2016 International Conference Radio Electronics & Info Communications UkrMiCo, (Kyiv, Ukraine, 2016). pp. 1–4. https://ieeexplore.ieee.org/document/7739615
S.V. Denbnovetsky, I.V. Melnyk, V.G. Melnyk, B.A. Tugai, and S.B. Tuhai, in: 2017 IEEE 37th International Conference on Electronics and Nanotechnology ELNANO, (Kyiv, Ukraine, 2017). pp. 369-373. https://ieeexplore.ieee.org/document/7939781
S.V. Denbnovetsky, V.I. Melnik, I.V. Melnik, and B.A. Tugay, in: XVIII-th IEEE International Symposium on Discharges and Electrical Insulation in Vacuum, (ISDEIV, 1998, Eindhoven, The Netherland), vol. 2. pp. 637–640. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=738530
I.V. Melnik, and S.B. Tugay, Radioelectronics and Communications Systems, 55(11), (2012). https://doi.org/10.3103/S0735272712110064
I. Melnyk, S. Tuhai, M. Skrypka, T. Khyzhniak, and A. Pochynok, in: Information and Communication Technologies and Sustainable Development. ICT&SD 2022. Lecture Notes in Networks and Systems, edited by S. Dovgyi, O. Trofymchuk, V. Ustimenko, and L. Globa, vol. 809, (Springer, 2023). pp. 395–427. https://doi.org/10.1007/978-3-031-46880-3_24
I. Melnyk, A. Pochynok, and M. Skrypka, System Research and Information Technologies, 2024, #4. (2024). https://doi.org/10.20535/SRIT.2308-8893.2024.4.11 http://journal.iasa.kpi.ua/issue/view/18934/11880
I. Melnyk, A. Pochynok, M. Skrypka, System Research and Information Technologies, 2024(3), (2024). https://doi.org/10.20535/SRIT.2308-8893.2024.3.05
W. McKinney, Python for Data Analysis: Data Wrangling with Pandas, NumPy, and Jupyter, 3rd Edition, (O'Reilly Media, 2023).
F. Chollet, Deep Learning with Python. Second Edition. (Manning, 2022).
M. Lutz, Learning Python, Fifth Edition. (O'Reilly, 2013).
S. Schiller, U. Heisig, and S. Panzer, Electron Beam Technology, (New-York, John Wiley & Sons, 1995).
M. Szilagyi, Electron and Ion Optics, (Springer Science & Business Media, 2012).
E. Kasper, and P. Hawkes. Principles of Electron Optics: Applied Geometrical Optics. (Elsevier Science, 1989).
P. Grivet, P.W. Hawkes, and A. Septie, Electron Optics, (Elsevier, 2013).
Electron Beams, Lenses, and Optics, edited by A. B. El-Kareh, (Academic Press, 2012).
B.M. Smirnov, Theory of Gas Discharge Plasma, (Springer, 2015).
M.A. Lieberman, and A.J. Lichtenberg. Principles of Plasma Discharges for Materials Processing, (New York, Wiley Interscience, 1994).
Yu.P. Raizer, Gas Discharge Physics, (New York: Springer, 1991).
J.F. Epperson, An Introduction to Numerical Methods and Analysis, Revised Edition, (Wiley-Interscience, 2007).
M.K. Jain, S.R.K. Iengar, and R.K. Jain, Numerical Methods for Scientific & Engineering Computation. (New Age International Pvt. Ltd., 2010).
S.C. Chapra, and R.P. Canale, Numerical Methods for Engineers, 7th Edition, (McGraw Hill, 2014).
R.L. Burden, J.D. Faires, and A.M. Burden, Numerical Analysis, (Cengage Learning, 2015).
T. Sauer, Numerical Analysis, (Pearson, 2017).
R.W. Hamming, Numerical Methods for Scientists and Engineers, (Dover Publications, 1987).
E. Isaacson, and H.B. Keller, Analysis of Numerical Methods, (Dover Publications, 1994).
F.B. Hildebrand, Introduction to Numerical Analysis, (Dover Publications, 1987).
A. Greenbaum, and T.P. Chartier, Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms. (Princeton University Press, 2012).
A.J. Salgado, and S.M. Wise, Classical Numerical Analysis: A Comprehensive Course. (Cambridge University Press, 2023).
D.E. Stewart, Numerical Analysis: A Graduate Course, (Springer; 2022).
J.H. Mathews, and K.D. Fink, Numerical Methods. Using Matlab, third edition (Amazon, 1998).
V.G. Rudychev, M.O. Azarenkov, I.O. Girka, V.T. Lazurik, and Y.V. Rudychev, Radiation Physics and Chemistry, 206, 110815 (2023). https://doi.org/10.1016/j.radphyschem.2023.110815
V.G. Rudychev, V.T. Lazurik, and Y.V. Rudychev, Radiation Physics and Chemistry, 186, 109527 (2021). https://doi.org/10.1016/j.radphyschem.2021.109527
V. Lazurik, S. Sawan, V. Lazurik, and O. Zolotukhin, in: 4th International Maghreb Meeting of the Conference on Sciences and Techniques of Automatic Control and Computer Engineering Proceedings, (IEEE, Maghreb, 2024), pp. 649–653. https://doi.org/10.1109/MI-STA61267.2024.10599694
G. Lewin, Fundamentals of Vacuum Science and Technology. (McGraw-Hill, 1965).
J.M. Lafferty. Foundations of Vacuum Science and Technology. (John Wiley & Sons, 1998).
Copyright (c) 2025 Igor V. Melnyk, Serhii B. Tuhai, Mykhailo Yu. Skrypka, Mykola S. Surzhikov, Oleksandr M. Kovalenko, Dmytro V. Kovalchuk

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