A computational model for nanosecond pulse laser-plasma interactions. (English) Zbl 1453.76103

Summary: A multi-physics numerical model for laser-induced optical breakdown and laser-plasma interaction in a non-equilibrium gas is presented, accounting for: production of priming electrons via multi-photon ionization, energy absorption, cascade ionization, induced hydrodynamic response, and shock formation and propagation. The gas is governed by the Navier-Stokes equations, with non-equilibrium effects taken into account by means of a two-temperature model. The space-time dependence of the laser beam is modeled with a flux-tube formulation for the Radiative Transfer Equation. The flow governing equations are discretized in space using a second-order finite volume method. The semi-discrete equations are marched in time using an implicit-explicit (IMEX) dual time-stepping strategy, where diffusion and chemistry are solved implicitly, whereas convection is explicit. Application to a 20 ns long 50 mJ pulse laser-induced breakdown in quiescent \(O_2\) shows the advantages of this temporal discretization during and just after the laser pulse, while a less-expensive symmetric Strang splitting (with implicit chemistry) is sufficient for the post-breakdown gas dynamics after \(\simeq 0.1 \mu\) s. The integrated model is shown to reproduce key features of corresponding experiments.


76M12 Finite volume methods applied to problems in fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76N06 Compressible Navier-Stokes equations
82C40 Kinetic theory of gases in time-dependent statistical mechanics


Full Text: DOI


[1] Radziemski, L. J.; Cremers, D. A., Laser-Induced Plasmas and Applications (1989), Marcel Dekker Inc.: Marcel Dekker Inc. New York, NY
[2] Dumitrache, C.; van Odsol, R.; Limbach, C. M.; Yalin, A. P., Control of early flame kernel growth by multi-wavelength laser pulses for enhanced ignition, Sci. Rep., 7, Article 10239 pp. (2017)
[3] Tropina, A. A.; Miles, R. B.; Shneider, M. N., Mathematical model of dual-pulse laser ignition, J. Propuls. Power, 34, 408-414 (2018)
[4] Mahamud, R.; Tropina, A. A.; Shneider, M. N.; Miles, R. B., Dual-pulse laser ignition model, Phys. Fluids, 30, Article 106104 pp. (2018)
[5] Colonna, G.; Casavola, A.; Capitelli, M., Modelling of LIBS plasma expansion, Spectrochim. Acta, Part B, 56, 567-586 (2001)
[6] Capitelli, M.; Casavola, A.; Colonna, G.; De Giacomo, A., Laser-induced plasma expansion: theoretical and experimental aspects, Spectrochim. Acta, Part B, 59, 271-289 (2004)
[7] Casavola, A.; De Giacomo, A.; Dell’Aglio, M.; Taccogna, F.; Colonna, G.; De Pascale, O.; Longo, S., Experimental investigation and modelling of double pulse laser induced plasma spectroscopy under water, Spectrochim. Acta, Part B, 60, 975-985 (2005)
[8] Pietanza, L. D.; Colonna, G.; De Giacomo, A.; Capitelli, M., Kinetic processes for laser induced plasma diagnostic: a collisional-radiative model approach, Spectrochim. Acta, Part B, 65, 616-626 (2010)
[9] Cristoforetti, G.; Tognoni, E.; Gizzi, L. A., Thermodynamic equilibrium states in laser-induced plasmas: from the general case to laser-induced breakdown spectroscopy plasmas, Spectrochim. Acta, Part B, 90, 1-22 (2013)
[10] (Musazzi, S.; Umberto, P., Laser-Induced Breakdown Spectroscopy. Laser-Induced Breakdown Spectroscopy, Spinger Series in Optical Sciences (2014), Springer)
[11] Zhang, Y.; Jiang, X.; Wei, L.; Zhang, J.; Tang, C.; Huang, Z., Experimental and modeling study on auto-ignition characteristics of methane/hydrogen blends under engine relevant pressure, Int. J. Hydrog. Energy, 37, 19168-19176 (2012)
[12] Smirnov, N. N.; Betelin, V. B.; Shagaliev, R. M.; Nikitin, V. F.; Belyakov, I. M.; Deryuguin, Yu. N.; Aksenov, S. V.; Korchazhkin, D. A., Hydrogen fuel rocket engines simulations using LOGOS code, Int. J. Hydrog. Energy, 39, 10748-10756 (2014)
[13] Casavola, A.; Colonna, G.; De Giacomo, A.; De Pascale, O.; Capitelli, M., Experimental and theoretical investigation of laser-induced plasma of a titanium target, Appl. Opt., 42, 5963-5970 (2003)
[14] Kruer, W. L., The Physics of Laser Plasma Interactions, Frontiers in Physics (2003), Westview Press
[15] Maker, P. D.; Terhune, R. W.; Savage, C. M., Optical third harmonic generation, (Quantum Electronics: Proceedings of the 3rd International Congress (1964), Columbia Univ. Press: Columbia Univ. Press New York)
[16] Ostrovskaya, G. V.; Zaĭdel’, A. N., Laser spark in gases, Sov. Phys. Usp., 16, 834-855 (1975)
[17] Grey Morgan, C., Laser-induced breakdown of gases, Rep. Prog. Phys., 38, 621-665 (1975)
[18] Grey Morgan, C., Laser-induced breakdown phenomena, Sci. Prog., 65, 31-50 (1978)
[19] Raizer, Yu. P., Optical discharges, Sov. Phys. Usp., 23, 789-806 (1980)
[20] Raizer, Yu. P., Laser-Induced Discharge Phenomena, Studies in Soviet Science (1977), Springer-Verlag: Springer-Verlag New York
[21] Keldysh, L. V., Ionization in the field of a strong electromagnetic wave, Sov. Phys. JETP, 20, 1307-1314 (1965)
[22] Bebb, H. B.; Gold, A., Multiphoton ionization of hydrogen and rare-gas atoms, Phys. Rev., 143, 1-24 (1966)
[23] L’Huillier, A.; Mainfray, G.; Johnson, P. M., Multiphoton ionization versus dissociation of diatomic molecules irradiated by an intense 40 ps laser pulse, Chem. Phys. Lett., 103, 447-450 (1984)
[24] L’Huillier, A.; Jönsson, L.; Wendin, G., Multiphoton ionization of many-electron atoms, Int. J. Quant. Chem., 31, 833-840 (1987)
[25] Perry, M. D.; Landen, O. L.; Szöke, A.; Campbell, E. M., Multiphoton ionization of the noble gases by an intense 10^14-W/cm^2 dye laser, Phys. Rev. A, 37, 747-760 (1988)
[26] Mainfray, G.; Manus, G., Multiphoton ionization of atoms, Rep. Prog. Phys., 54, 1333-1372 (1991)
[27] Zel’dovich, Y. B.; Raizer, Yu. P., Cascade ionization of a gas by a light pulse, Sov. Phys. JETP, 20, 772 (1965)
[28] Zel’dovich, Y. B.; Raizer, Yu. P., Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (1967), Academic Press Inc: Academic Press Inc New York, NY
[29] Raizer, Yu. P., Heating of a gas by a powerful light pulse, Sov. Phys. JETP, 21, 1009-1017 (1965)
[30] De Michelis, C., Laser induced gas breakdown: a bibliographical review, IEEE J. Quantum Electron., 5, 188-202 (1969)
[31] Kandala, R. M.; Candler, G. V., Numerical studies of laser-induced energy deposition for supersonic flow control, AIAA J., 42, 2266-2275 (2004)
[32] Shneider, M. N.; Zheltikov, A. M.; Miles, R. B., Tailoring the air plasma with a double laser pulse, Phys. Plasmas, 18, Article 063509 pp. (2011)
[33] Ohnishi, N.; Tate, M.; Ogino, Y., Computational study of shock wave control by pulse energy deposition, Shock Waves, 22, 521-531 (2012)
[34] Dors, I. G.; Parigger, C. G., Computational fluid-dynamic model of laser-induced breakdown in air, Appl. Opt., 42, 5978-5985 (2003)
[35] Soubacq, S.; Pignolet, P.; Schall, E.; Batina, J., Investigation of a gas breakdown process in a laser-plasma experiment, J. Phys. D, Appl. Phys., 37, 2686-2702 (2004)
[36] Ghosh, S.; Mahesh, K., Numerical simulation of the fluid dynamic effects of laser energy deposition in air, J. Fluid Mech., 605, 329-354 (2008) · Zbl 1145.76040
[37] Sai Shiva, S.; Leela, Ch.; Prem Kiran, P.; Sijoy, C. D.; Ikkurthi, V. R.; Chaturvedi, S., Numerical investigation of nanosecond laser induced plasma and shock wave dynamics from air using 2D hydrodynamic code, Phys. Plasmas, 24, Article 083110 pp. (2017)
[38] Park, C., Nonequilibrium Hypersonic Aerothermodynamics (1990), Wiley: Wiley New York, NY
[39] Gnoffo, P. A.; Gupta, R. N.; Shinn, J. L., Conservation Equations and Physical Models for Hypersonic Air Flows in Thermal and Chemical Nonequilibrium (1989), NASA Technical Paper 2867
[40] Marcuse, D., Light Transmission Optics (1982), van Nostrand Reinhold Company
[41] Vincenti, W. J.; Kruger, C. H., Introduction to Physical Gasdynamics (1965), Wiley: Wiley New York, NY
[42] Gurvich, L. V., Thermodynamic Properties of Individual Substances (1994), CRC Press
[43] Edlén, B., Accurate semi-empirical formulae for the energy structure of Li I-like spectra, Phys. Scr., 19, 255-266 (1979)
[44] Kelly, R. L., Atomic and ionic spectrum lines below 2000 Angstroms. Hydrogen through Krypton, J. Phys. Chem. Ref. Data, 16, Supp. 1, 1-1678 (1987)
[45] Moore, C. E., Tables of Spectra of Hydrogen, Carbon, Nitrogen, and Oxygen Atoms and Ions, CRC Series in Evaluated Data in Atomic Physics (1993), CRC Press: CRC Press Boca Raton, FL
[46] Kramida, A.; Ralchenko, Yu.; Reader, J., NIST Atomic Spectra Database (ver. 5.5.6) (2018), National Institute of Standards and Technology: National Institute of Standards and Technology Gaithersburg, MD, 2018, September 17
[47] Panesi, M.; Magin, T. E.; Bourdon, A.; Bultel, A.; Chazot, O., Fire II flight experiment analysis by means of a collisional-radiative model, J. Thermophys. Heat Transf., 23, 236-248 (2009)
[48] Panesi, M.; Magin, T. E.; Bourdon, A.; Bultel, A.; Chazot, O., Electronic excitation of atoms and molecules for the FIRE II flight experiment, J. Thermophys. Heat Transf., 25, 361-374 (2011)
[49] Panesi, M.; Lani, A., Collisional radiative coarse-grain model for ionization in air, Phys. Fluids, 25, Article 057101 pp. (2013)
[50] Munafò, A.; Lani, A.; Bultel, A.; Panesi, M., Modeling of non-equilibrium phenomena in expanding flows by means of a collisional-radiative model, Phys. Plasmas, 20, Article 073501 pp. (2013)
[51] Ferziger, J. H.; Kaper, H. G., Mathematical Theory of Transport Processes in Gases (1972), North-Holland Pub. Co.
[52] Giovangigli, V., Multicomponent Flow Modeling (1999), Birkhäuser: Birkhäuser Berlin · Zbl 0956.76003
[53] Nagnibeda, E.; Kustova, E., Non-Equilibrium Reacting Gas Flows (2009), Springer: Springer Berlin · Zbl 1186.82003
[54] Capitelli, M.; Bruno, D.; Laricchiuta, A., Fundamental Aspects of Plasma Physics: Transport, Springer Series on Atomic, Optical, and Plasma Physics, vol. 74 (2013), Springer: Springer Heidelberg
[55] Bruno, D.; Catalfamo, C.; Capitelli and, O. D.M.; Colonna and, G.; Diomede, P.; Gorse, C.; Laricchiuta, A.; Longo, S.; Giordano, D.; Pirani, F., Transport properties of high-temperature Jupiter atmosphere components, Phys. Plasmas, 17, Article 112315 pp. (2010)
[56] Devoto, R. S., Transport properties of ionized monatomic gases, Phys. Fluids, 9, 1230-1240 (1966)
[57] Devoto, R. S., Transport coefficients of partially ionized Argon, Phys. Fluids, 10, 354-364 (1967)
[58] Curtiss, J. F.; Hirschfelder, J. O., Transport properties of multicomponent gas mixtures, J. Chem. Phys., 17, 550-555 (1949) · Zbl 0041.57704
[59] Gupta, R. N.; Lee, K.-P.; Thompson, R. A.; Yos, J. M., Calculations and curve fits of thermodynamic and transport properties for equilibrium air to 30000 K, NASA Ref. Publ., 1260 (1991)
[60] Park, C.; Jaffe, R. L.; Partridge, H., Chemical-kinetic parameters of hyperbolic earth entry, J. Thermophys. Heat Transf., 15, 76-90 (2001)
[61] Sutton, K.; Gnoffo, P. A., Multi-component diffusion with application to computational aerothermodynamics, (7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, Albuquerque, NM (1998)), AIAA Paper 1998-2575
[62] Oxenius, J., Kinetic Theory of Particles and Photons, Springer Series in Electronics and Photonics, vol. 20 (1986), Springer-Verlag: Springer-Verlag Berlin Heidelberg, Berlin
[63] Munafò, A.; Mansour, N. N.; Panesi, M., A reduced-order NLTE kinetic model for radiating plasmas of outer envelopes of stellar atmospheres, Astrophys. J., 838, 126 (2017)
[64] Park, C., Review of chemical-kinetic problems of future NASA missions, I: Earth entries, J. Thermophys. Heat Transf., 7, 385-398 (1993)
[65] Itikawa, Y., Cross sections for electron collisions with nitrogen molecules, J. Phys. Chem. Ref. Data, 35, 31-53 (2006)
[66] Itikawa, Y., Cross sections for electron collisions with oxygen molecules, J. Phys. Chem. Ref. Data, 38, 1-20 (2009)
[67] Lennon, M. A.; Bell, K. L.; Gilbody, H. B.; Hughes, J. G.; Kingston, A. E.; Murray, M. J.; Smith, F. J., Recommended data on the electron impact ionization of atoms and ions: fluorine to nickel, J. Phys. Chem. Ref. Data, 17, 1285-1363 (1988)
[68] Landau, L.; Teller, E., Theory of sound dispersion, Phys. Z. Sowjetunion, 10, 34-43 (1936), in German
[69] Millikan, R. C.; White, D. R., Systematics of vibrational relaxation, J. Chem. Phys., 39, 3209-3214 (1963)
[70] Petschek, H.; Byron, S., Approach to equilibrium ionization behind strong shock waves in argon, Ann. Phys., 1, 270-315 (1957)
[71] Candler, G. V.; MacCormack, R. W., Computation of weakly ionized hypersonic flows in thermochemical nonequilibrium, J. Thermophys. Heat Transf., 5, 266-273 (1991)
[72] Johnston, R. R., Free-free radiative transitions - a survey of theoretical results, J. Quant. Spectrosc. Radiat. Transf., 7, 815-835 (1967)
[73] Geltman, S., Free-free radiation in electron-neutral atom collisions, J. Quant. Spectrosc. Radiat. Transf., 13, 601-613 (1973)
[74] Pitchford, L. C.; Boeuf, J. P., SIGLO database (2018)
[75] Nishihara, M.; Freund, J. B.; Glumac, N. G.; Elliott, G. S., Influence of mode-beating pulse on laser-induced plasma, J. Phys. D, Appl. Phys., 51, Article 135601 pp. (2018)
[76] Hirsch, C., Numerical Computation of Internal and External Flows (1990), John Wiley & Sons: John Wiley & Sons New York, NY · Zbl 0742.76001
[77] Nompelis, I., Computational Study of Hypersonic Double-Cone Experiments for Code Validation (2004), University of Minnesota: University of Minnesota Minneapolis, MN, Ph.D. thesis
[78] Lani, A., An Object Oriented and High-Performance Platform for Areothermodynamics Simulations (2009), Univesité Libre de Bruxelles: Univesité Libre de Bruxelles Bruxelles, Belgium, Ph.D. thesis
[79] Liou, M. S., A sequel to AUSM: AUSM^+, J. Comput. Phys., 129, 364-382 (1996) · Zbl 0870.76049
[80] van Leer, B., Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method, J. Comput. Phys., 32, 101-136 (1979) · Zbl 1364.65223
[81] van Albada, G. D.; van Leer, B.; Roberts, W. W., A comparative study of computational methods in cosmic gasdynamics, Astron. Astrophys., 108, 76-84 (1982) · Zbl 0492.76117
[82] Blazek, J., Computational Fluid Dynamics: Principles and Applications (2006), Elsevier Science · Zbl 0995.76001
[83] Pulliam, T. H., Time accuracy and the use of implicit methods, (11th Computational Fluid Dynamics Conference. 11th Computational Fluid Dynamics Conference, Orlando, FL (1993)), AIAA Paper 1993-3360
[84] Hundsdorfer, W. H.; Verwer, J. G., Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Series in Computational Mathematics (2003), Springer · Zbl 1030.65100
[85] Wright, M. J.; Candler, G. V.; Boose, D., Data-parallel line relaxation for the Navier-Stokes equations, AIAA J., 36, 1603-1609 (1998)
[86] Balay, S.; Abhyankar, S.; Adams, M. F.; Brown, J.; Brune, P.; Buschelman, K.; Dalcin, L.; Eijkhout, V.; Gropp, W. D.; Kaushik, D.; Knepley, M. G.; May, D. A.; McInnes, L. C.; Rupp, K.; Smith, B. F.; Zampini, S.; Zhang, H.; Zhang, H., Petsc web page (2017)
[87] Balay, S.; Abhyankar, S.; Adams, M. F.; Brown, J.; Brune, P.; Buschelman, K.; Dalcin, L.; Eijkhout, V.; Gropp, W. D.; Kaushik, D.; Knepley, M. G.; May, D. A.; McInnes, L. C.; Rupp, K.; Sanan, P.; Smith, B. F.; Zampini, S.; Zhang, H.; Zhang, H. (2017), Argonne National Laboratory, PETSc Users Manual, Technical Report ANL-95/11 - Revision 3.8
[88] Balay, S.; Gropp, W. D.; McInnes, L. C.; Smith, B. F., Efficient management of parallelism in object oriented numerical software libraries, (Arge, E.; Bruaset, A. M.; Langtangen, H. P., Modern Software Tools in Scientific Computing (1997), Birkhäuser Press), 163-202 · Zbl 0882.65154
[89] Hindmarsh, A. C.; Brown, P. N.; Grant, K. E.; Lee, S. L.; Serban, R.; Shumaker, D. E.; Woodward, C. S., SUNDIALS: suite of nonlinear differential/algebraic equation solvers, ACM Trans. Math. Softw., 31, 363-396 (2005) · Zbl 1136.65329
[90] Strang, G., On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5, 506-517 (1968) · Zbl 0184.38503
[91] Gottlieb, S.; Shu, C.-W., Total variation diminishing Runge-Kutta schemes, Math. Comput., 67, 73-85 (1998) · Zbl 0897.65058
[92] Gottlieb, S.; Shu, C.-W.; Tadmor, E., Strong stability-preserving high-order time discretization methods, SIAM Rev., 43, 89-112 (2001) · Zbl 0967.65098
[93] Radhakrishnan, K.; Hindmarsh, A. C., Description and Use of Lsode, the Livermore Solver for Ordinary Differential Equations (1993), NASA Report 1327
[94] Thivet, F., Modeling of Hypersonic Flows in Thermal and Chemical Nonequilibrium (1992), Ecole Centrale Paris: Ecole Centrale Paris Châtenay-Malabry, France, in French
[95] Munafò, A.; Panesi, M.; Magin, T. E., Boltzmann rovibrational collisional coarse-grained model for internal energy excitation and dissociation in hypersonic flows, Phys. Rev. E, 89, Article 023001 pp. (2014)
[96] Alberti, A.; Munafò, A.; Koll, M.; Nishihara, M.; Pantano, C.; Freund, J. B.; Elliott, G. S.; Panesi, M., Laser-induced non-equilibrium plasma kernel dynamics, J. Phys. D, Appl. Phys., 53, Article 025201 pp. (2019)
[97] Thompson, K. W., Time dependent boundary conditions for hyperbolic systems, J. Comput. Phys., 68, 1-24 (1987) · Zbl 0619.76089
[98] Freund, J. B., Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound, AIAA J., 35, 740-742 (1997) · Zbl 0903.76081
[99] Jameson, A.; Yoon, S., Lower-upper implicit schemes with multiple grids for the Euler equations, AIAA J., 25, 929-935 (1987)
[100] Yoon, S.; Jameson, A., Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations, AIAA J., 26, 1025-2016 (1988)
[101] Werver, J. G., Explicit Runge-Kutta methods for parabolic partial differential equations, Appl. Numer. Math., 22, 359-379 (1996) · Zbl 0868.65064
[102] Werver, J. G.; Sommeijer, B. P., An implicit-explicit Runge-Kutta-Chebyshev scheme for diffusion-reaction equations, SIAM J. Sci. Comput., 25, 1824-1835 (2004) · Zbl 1061.65090
[103] Tsuda, N.; Yamada, J., Observation of forward breakdown mechanism in high-pressure argon plasma produced by irradiation by an excimer laser, J. Appl. Phys., 81, 582-596 (1997)
[104] Tsuda, N.; Yamada, J., Physical properties of dense plasma produced by XeCl excimer laser in high-pressure Argon gases, Jpn. J. Appl. Phys., 38, 3712-3715 (1999)
[105] Tsuda, N.; Yamada, J., Mechanism of forward development of a plasma produced by an excimer laser in high-pressure argon gases, J. Appl. Phys., 87, 2122-2126 (2000)
[106] Yan, H.; Adelgren, R.; Boguszko, M.; Elliott, G.; Knight, D., Laser energy deposition in quiescent air, AIAA J., 41, 1988-1995 (2003)
[107] Glumac, N.; Elliott, G.; Boguszko, M., Laser energy deposition in quiescent air, AIAA J., 43, 1984-1994 (2005)
[108] Abeele, D. V., An Efficient Computational Model for Inductively Coupled Air Plasma Flows Under Thermal and Chemical Non-Equilibrium (2000), Univesité Libre de Bruxelles: Univesité Libre de Bruxelles Bruxelles, Belgium, Ph.D. thesis
[109] Magin, T. E.; Degrez, G., Transport algorithms for partially ionized and unmagnetized plasmas, J. Comput. Phys., 198, 424-449 (2004) · Zbl 1116.76476
[110] Kihara, T.; Taylor, M. H.; Hirschfelder, J. O., Transport properties of gases assuming inverse power intermolecular potentials, Phys. Fluids, 3, 715-720 (1960) · Zbl 0113.46001
[111] Mason, E. A.; Munn, R. J.; Smith, F. J., Transport properties of ionized gases, Phys. Fluids, 10, 1827-1832 (1967)
[112] Devoto, R. S., Transport properties of ionized Argon, Phys. Fluids, 16, 616-623 (1973)
[113] Patankar, S., Numerical Heat Transfer and Fluid Flow, Hemisphere Series on Computational Methods in Mechanics and Thermal Science (1980), CRC Press
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.