Abstract
We study a model of the current distribution during heating of the surface of a tungsten sample under pulsed exposure to an electron beam. The model is based on solving the equations of electrodynamics and the two-phase Stefan problem for calculating the temperature in the sample region using a cylindrical coordinate system. The model parameters were taken from experiments at the “Beam of Electrons for Materials Test Applications” (BETA) stand created at the Budker Institute of Nuclear Physics. The particular case of axial symmetry is considered without taking the electromotive forces into account. The current is considered as a possible source of rotation of the substance which is observed in the experiment. The values of the current and the acceleration of matter at a surface temperature of over \(6000 \)K were obtained. The results of the simulation show that, to obtain an acceleration capable of initiating the experimentally observed rotation of the melt, it is necessary to take into account some alternative mechanisms of creating a current in the system with consideration of the evaporation of tungsten above the plate.
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REFERENCES
L. Vyacheslavov, A. Arakcheev, A. Burdakov, I. Kandaurov, A. Kasatov, V. Kurkuchekov, K. Mekler, V. Popov, A. Shoshin, D. Skovorodin, Yu. Trunev, and A. Vasilyev, “Novel Electron Beam Based Test Facility for Observation of Dynamics of Tungsten Erosion under Intense ELM-Like Heat Loads,” AIP Conference Proceedings 1771, 060004 (2016).
A. S. Arakcheev, D. E. Apushkinskaya, I. V. Kandaurov, A. A. Kasatov, V. V. Kurkuchekov, G. G. Lazareva, A. G. Maksimova, V. A. Popov, A. V. Snytnikov, Yu. A. Trunev, A. A. Vasilyev, and L. N. Vyacheslavov, “Two-Dimensional Numerical Simulation of Tungsten Melting under Pulsed Electron Beam,” Fusion Engineering and Design 132, 13–17 (2018).
G. G. Lazareva, A. S. Arakcheev, A. A. Vasilyev, and A. G. Maksimova, “Numerical Simulation of Tungsten Melting under Fusion Reactor-Relevant High-Power Pulsed Heating,” Smart Innovation, Systems and Technologies 133, 41–51 (2019).
G. G. Lazareva, A. S. Arakcheev, A. V. Burdakov, I. V. Kandaurov, A. A. Kasatov, V. V. Kurkuchekov, A. G. Maksimova, V. A. Popov, A. A. Shoshin, A. V. Snytnikov, A. V. Snytnikov, Yu. A. Trunev, A. A. Vasilyev, and L. N. Vyacheslavov, “Numerical Model of High-Power Transient Heating of Tungsten with Considering of Various Erosion Effects,” IOP Conf. Series: J. Phys.: Conf. Series 1103, 012001 (2018).
G. G. Lazareva, A. S. Arakcheev, I. V. Kandaurov, A. A. Kasatov, V. V. Kurkuchekov, A. G. Maksimova, V. A. Popov, A. V. Snytnikov, Yu. A. Trunev, A. A. Vasilyev, and L. N. Vyacheslavov, “Computational Experiment for Solution of the Stefan Problem with Nonlinear Coefficients,” AIP Conference Proceedings 2025, 080005 (2018).
P. Tolias, “Analytical Expressions for Thermophysical Properties of Solid and Liquid Tungsten Relevant for Fusion Applications,” Nuclear Materials and Energy 13, 42–57 (2017).
J. Jackson, Classical Electrodynamics (Wiley, New York, 1998; Mir, Moscow, 1965).
H. Buchholz, Calculation of Electric and Magnetic Fields (Izd. Inostr. Literatury, Moscow, 1961) [in Russian].
W. R. Smythe, Static and Dynamic Electricity (Edwards Brothers, Ann Arbor, Mich., 1936; Izd. Inostr. Literatury, Moscow, 1954).
N. N. Yanenko, Subincremental Method for Solution of Multidimensional Problems of Mathematical Physics (Nauka, Moscow, 1967) [in Russian].
V. P. Zagonov, “Mathematical Modeling of the Electromagnetic Effect of Pulsed Fields to Complex Technical Systems,” in Functioning and Development of Complex National Economic, Technical, Energy, Transport Systems, Communication Systems, and Communications (Znanie, Moscow, 1998), pp. 392–394.
M. E. Zhukovskii, “Self-Consistent Quasi-3D Model of Radiation Excitation of Electromagnetic Fields,” Mat. Modelir. 8 (4), 3–20 (1996).
A. A. Samarskii and E. S. Nikolaev, Methods of Solution of Grid Equations (Fizmatgiz, Moscow, 1978) [in Russian].
V. P. Il’in, Numerical Methods for Solution of Electrophysics Problems (Nauka, Moscow, 1985) [in Russian].
R. G. Strongin, V. P. Gergel’, V. A. Grishagin, and K. A. Barkalov, Parallel Computing in Problems of Global Optimization (Izd. Moskov. Gos. Univ., Moscow, 2013) [in Russian].
A. A. Vasilyev, A. S. Arakcheev, I. A. Bataev, V. A. Bataev, A. V. Burdakov, I. V. Kandaurov, A. A. Kasatov, V. V. Kurkuchekov, K. I. Mekler, V. A. Popov, A. A. Shoshin, D. I. Skovorodin, Yu. A. Trunev, and L. N. Vyacheslavov, “Observation of the Tungsten Surface Damage under ITER-Relevant Transient Heat Loads during and after Electron Beam Pulse,” AIP Conference Proceeding 1771, 060013 (2016).
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The authors were supported by the Russian Foundation for Basic Research (project no. 19–01–00422).
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Translated by L.B. Vertgeim
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Lazareva, G.G., Popov, V.A., Arakcheev, A.S. et al. Mathematical Simulation of the Distribution of the Electron Beam Current during Pulsed Heating of a Metal Target. J. Appl. Ind. Math. 15, 292–301 (2021). https://doi.org/10.1134/S1990478921020101
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DOI: https://doi.org/10.1134/S1990478921020101