Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2518410.22363/2658-4670-2020-28-4-398-405Research ArticleNumerical modeling of laser ablation of materialsAmirkhanovIlkizar V.<p>Candidate of Physical and Mathematical Sciences, Head of Sector “Scientific Division of Computational Physics”. Laboratory of Information Technologies</p>camir@jinr.ruSarkerNil R.<p>Candidate of Physical and Mathematical Sciences, Senior Researcher “Scientific Division of Computational Physics”. Laboratory of Information Technologies</p>sarker@jinr.ruSarkhadovIbrohim<p>Candidate of Physical and Mathematical Sciences, Senior Researcher “Scientific Division of Computational Physics”. Laboratory of Information Technologies</p>ibrohim@jinr.ruJoint Institute for Nuclear Research1512202028439840509122020Copyright © 2020, Amirkhanov I.V., Sarker N.R., Sarkhadov I.2020<p>In this paper, we report a numerical simulation of laser ablation of a material by ultrashort laser pulses. The thermal mechanism of laser ablation is described in terms of a one-dimensional nonstationary heat conduction equation in a coordinate system associated with a moving evaporation front. The laser action is taken into account through the functions of the source in the thermal conductivity equation that determine the coordinate and time dependence of the laser source. For a given dose of irradiation of the sample, the profiles of the sample temperature at different times, the dynamics of the displacement of the sample boundary due to evaporation, the velocity of this boundary, and the temperature of the sample at the moving boundary are obtained. The dependence of the maximum temperature on the sample surface and the thickness of the ablation layer on the radiation dose of the incident laser pulse is obtained. Numerical calculations were performed using the finite difference method. The obtained results agree with the results of other works obtained by their authors.</p>Numerical simulationablationpulsed lasersheat conduction equationчисленное моделированиеабляцияимпульсные лазерыуравнение теплопроводности<p>3. Introduction In recent years, pulsed laser ablation [1]-[3] (any process of laser-stimulated removal of matter, including the emission of electrons) of various materials has attracted more and more interest from the point of view of fundamental study of processes in matter under extreme conditions of ultrafast energy supply. This implies constructing a new physical theory describing strongly nonlinear effects. For a detailed analysis of the processes in the experiment, it is required to measure various characteristics of the ablation processes with picoand femtosecond time resolution, which in itself is a rather difficult task. Therefore, the problem of mathematical modeling of physical phenomena in this area becomes extremely urgent. To describe the dynamics of fast processes in a substance, the method of molecular dynamics (MD) can be used [4]. MD is quite effective for Amirkhanov I. V., Sarker N. R., Sarkhadov I., 2020 This work is licensed under a Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/4.0/ microscopic analysis of the mechanisms of melting and evaporation under overheating conditions both in the bulk of the target [5] and for a system with a free surface [6]. The emergence and propagation of pressure waves generated by laser radiation [7], [8], as well as the dynamics of laser ablation [9], is well modeled using MD. In this paper, we consider continuous methods (various modifications of the heat equation) for modeling the effect of laser radiation on matter. The evaporation process is mathematically described within the framework of the boundary value problem of thermal conductivity for a condensed medium in a coordinate system associated with a moving solid-vapor interface or a melt-vapor interface on which evaporation occurs. If we do not take into account the lateral removal of the laser radiation energy due to thermal conductivity, which is valid under the strict condition</p>[L. A. Zakharov and N. M. Bulgakov, “Numerical simulation of laser ablation of metals and polymers when exposed to pulses of infrared radiation: the effect of the initial temperature of the sample [Chislennoe modelirovanie lazernoj ablyacii metallov i polimerov pri vozdejstvii impul’sami infrakrasnogo izlucheniya: vliyanie nachal’noj temperatury obrazca],” Vestnik NGU. Seriya: Fizika, vol. 5, no. 1, pp. 39-47, 2010, in Russian.][S. I. Anisimov and B. S. Lukyanchuk, “Selected problems of laser ablation theory,” Phys. Usp., no. 45, pp. 293-324, 2002. DOI: 10.1070/ PU2002v045n03ABEH000966.][V. P. Veiko, M. N. Libenson, G. G. Chervyakov, and E. B. Yakovlev, Interaction of Laser Radiation with Matter. Power Optics [Vzaimodeistvie lazernogo izlucheniya s veshchestvom. Silovaya optika]. Moscow: Fizmatlit, 2008, in Russian.][M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids. Walton Street, Oxford OX2 6DP: Clarendon Press, 1991.][Z. H. Jin, P. Gumbsch, K. Lu, and E. Ma, “Melting mechanisms at the limit of superheating,” Physical Review Letters, vol. 87, no. 5, p. 055 703, Jul. 2001. DOI: 10.1103/PhysRevLett.87.055703.][F. F. Abraham and J. Q. Broughton, “Pulsed melting of silicon (111) and (100) surfaces simulated by molecular dynamics,” Physical Review Letters, vol. 56, no. 7, pp. 734-737, 1986. DOI: 10.1103/PhysRevLett.56.734.][L. V. Zhigilei and B. J. Garrison, “Pressure waves in microscopic simulations of laser ablation,” Materials Research Society Symposium - Proceedings, vol. 538, pp. 491-496, 1999.][J. I. Etcheverry and M. Mesaros, “Molecular dynamics simulation of the production of acoustic waves by pulsed laser irradiation,” Physical Review B, vol. 60, no. 13, pp. 9430-9434, 1999. DOI: 10.1103/PhysRevB. 60.9430.][L. V. Zhigilei and B. J. Garrison, “Microscopic mechanisms of laser ablation of organic solids in the thermal and stress confinement irradiation regimes,” Journal of Applied Physics, vol. 88, no. 3, pp. 1281-1298, 2000. DOI: 10.1063/1.373816.][I. V. Amirkhanov, N. R. Sarker, and I. Sarkhadov, “Numerical simulation of laser ablation of materials,” in Proceedings of the 10th International Conference “Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems” (ITTMM-2020), Moscow, in Russian, 2020, pp. 237-239.][I. V. Amirkhanov, E. V. Zemlyanaya, I. V. Puzynin, T. P. Puzynina, and I. Sarhadov, On the influence of the source shape in the model of phase transitions in metals irradiated with pulsed ion beams [O vliyanii formy istochnika v modeli fazovyh perekhodov v metallah, obluchaemyh impul’snymi puchkami ionov]. Dubna: JINR Communication P11-200278, 2002, p. 18, in Russian.][A. A. Samarskiy, The theory of difference schemes [Teoriya raznostnyh skhem], Russian. Moscow: Nauka, 1983, pp. 258-276, in Russian.]