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Modeling of the plasma produced by moderate energy laser beam interaction with metallic targets: Physics of the phenomena

Published online by Cambridge University Press:  15 June 2012

Isak I. Beilis
Isak I. Beilis*
Affiliation:
Electrical Discharge and Plasma Laboratory, School of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
*
Address correspondence and reprint requests to: Isak I. Beilis, Electrical Discharge and Plasma Laboratory, School of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, P. O. Box 39040, Tel Aviv 69978, Israel. E-mail: [email protected]
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Abstract

The physical phenomena of plasma plume generation and plasma expansion by target-laser interaction are considered for moderate laser power density. The kinetics of target vaporization, atom ionization, and plasma heating are described. The mechanism of electric sheath formation near the surface, electron emission from the target, and the electrical breakdown phenomena by laser irradiation are analyzed. The plasma expansion is described taking into account the near target plasma structure and the absorption of the laser radiation. The mechanisms accelerating the plasma and generating an electric field in it are discussed. The work reviews experiments and theoretical models and summarizes the results in order to understand the measurements and to discuss open questions. As example, the plasma parameters (electron temperature and density, degree of ionization, and plasma velocity) are calculated for an Ag target using the developed model that considers self-consistently the target heating, kinetics of target evaporation, plasma heating, and ion flux to the target. The calculated ion velocity in the expanding plasma jet is in accordance with the measurement. The ion energy linearly depends on the ion charge state, as observed experimentally.

Keywords

Electron emissionIon chargeLaser plasmaPlasma expansionSheathTarget ablation
Type
Research Article
Information
Laser and Particle Beams , Volume 30 , Issue 3 , September 2012 , pp. 341 - 356
Copyright
Copyright © Cambridge University Press 2012

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References

REFERENCES

Abdellatif, G. & Imam, H. (2002). A study of the laser plasma parameters at different laser wavelengths. Spectrochimica Acta B57, 1155.Google Scholar
Aden, M., Beyer, E. & Herziger, G. (1990). Laser-induced vaporization of metal as a Riemann problem. J. Phys. D: Appl. Phys. 23, 655.CrossRefGoogle Scholar
Aguilera, J.A., Bengoechea, J. & Arago., C. (2004). Spatial characterization of laser induced plasmas obtained in air and argon with different laser focusing distances. Spectrochimica Acta B59 461.Google Scholar
Anisimov, S.I., Bauerly, D. & Luk'yanchuk, B.S. (1993). Gas dynamics and film profiles in pulsed laser deposition of materials. Phys. Rev. B48, 12076–12081.CrossRefGoogle Scholar
Anisimov, S.I., Imas, Yu.A., Romanov, G.S. & Khodyko, Yu.V. (1971). Action of High-Power Radiation on Metals. Springfield, VA: National Technological Information Service.Google Scholar
Anisimov, S.I. (1968). Vaporization of metal absorbing laser radiation. Sov. Phys. JETP 37, 182–183.Google Scholar
Attwood, D.T., Sweeney, D.W., Auerbach, J.M. & Lee, P.H.Y. (1978). Interferometric confirmation of radiation-pressure effects in laser-plasma interactions. Phys. Rev. Lett. 40, 184.CrossRefGoogle Scholar
Beilis, I.I. (1974). Emission processes at the cathode of an electric arc. Sov. Phys. Tech. Phys. 19, 257.Google Scholar
Beilis, I.I. (1982). On the theory of the erosion processes in the cathode region of an arc discharge. Sov. Phys. Doklady 27, 150–152.Google Scholar
Beilis, I.I. (1985). Parameters of kinetic layer of arc discharge cathode region. IEEE Trans. Plasma Sci. PS-13, 288.CrossRefGoogle Scholar
Beilis, I.I. (1986). Cathode arc plasma flow in a Knudsen layer. High Temp. 24, 319.Google Scholar
Beilis, I.I. (1995). “Theoretical modelling of cathode spot phenomena.” In Handbook of Vacuum Arc Science and Technology (ed. Boxman, R.L.Martin, P.J.Sanders, D.M.). Park Ridge, N.J: Noyes Publishing, 208–256.Google Scholar
Beilis, I.I. (2001). State of the theory of vacuum arcs. IEEE Trans. Plasma Sci. 29, 657–670.CrossRefGoogle Scholar
Beilis, I.I. (2003). The vacuum arc cathode spot and plasma jet: Physical model and mathematical description. Plasma Phys. 43, 224–236.Google Scholar
Beilis, I.I. (2004). Nature of high-energy ions in the cathode plasma jet of a vacuum arc with high rate of current rise. Appl. Phys. Lett. 85, 2739.CrossRefGoogle Scholar
Beilis, I.I. (2006). Mechanism of laser plasma production and of plasma interaction with a target. Appl. Phys. Lett. 89, 091503.CrossRefGoogle Scholar
Beilis, I.I. (2007). Laser plasma generation and plasma interaction with ablative target. Laser Part. Beams 25, 53–63.CrossRefGoogle Scholar
Beilis, I.I. (2008). Metallic plasma production by laser ablation. Radi. Effects Defects Solids 163, 317.Google Scholar
Beilis, I.I., Keidar, M., Boxman, R.L. & Goldsmith, S. (1998). Theoretical study of plasma expansion in a magnetic field in a disk anode vacuum arc. J. Appl. Phys. 83, 709.CrossRefGoogle Scholar
Beilis, I.I. & Keidar, M. (1998). Sheath and presheath structure in the plasma wall-transition layer in an oblique magnetic field. Phys. Plasmas 5, 1545.CrossRefGoogle Scholar
Bhatnagar, P.L., Cross, E.P. & Krook, M. (1954). A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511.CrossRefGoogle Scholar
Bleiner, D., Bogaerts, A., Beiloni, F. & Nassisi, V. (2007). Laser-induced plasmas from the ablation of metallic targets: The problem of the onset temperature, and insights on the expansion dynamics. J. Appl. Phys. 101, 083301.CrossRefGoogle Scholar
Bogaerts, A., Chen, Z., Gijbels, R. & Vertes, A. (2003). Laser ablation for analytical sampling: What can we learn from modeling? Spectrochimica Acta. B58, 1867–1893.CrossRefGoogle Scholar
Bohm, D. (1949). Characteristics of Electrical Discharges in Magnetic Fields. New York: Mcgraw-Hill Book Company, Inc.Google Scholar
Caretto, G., Doria, D., Nassisi, V. & Siciliano, M.V. (2007). Photoemission studies from metal by UV lasers. J. Appl. Phys. 101, 073109.CrossRefGoogle Scholar
Caridi, F., Torrisi, L., Margarone, D., Picciotto, M., Mezzasalma, A.A. & Gammino, S. (2006). Energy distributions of particles ejected from laser generated pulsed plasmas. Czech. J. Phys. 56 B449–B455.CrossRefGoogle Scholar
Chang, J.J. & Warner, B.E. (1996). Laser-plasma interaction during visible-laser ablation of methods. Appl. Phys. Lett. 69, 22.Google Scholar
Chen, Z. & Bogaerts, A. (2005). Laser ablation of Cu and plume expansion into 1 atm ambient gas. J. Appl. Phys. 97, 063305.CrossRefGoogle Scholar
Chen, M., Liu, X., Yanga, X., Zhao, M., Sun, Y, Qi, H., Chenc, X. & Xu, X. (2008). The dimension of the core and the tail of the plasma produced by laser ablating SiC targets. Phys. Lett. A372, 5891.Google Scholar
Chen, M., Liu, X., Zhao, M., Chen, C. & Man, B. (2009a). Temporal and spatial evolution of Si atoms in plasmas produced by a nanosecond laser ablating silicon carbide crystals. Phys. Rev. E80, 016405.Google Scholar
Chen, M., Liu, X., Zhao, M. & Sun, Y. (2009b). Early-stage evolution of the plasma over KTiOPO4 samples generated by high-intensity laser radiations. Opt. Lett. 34, 2682.CrossRefGoogle ScholarPubMed
Corsi, M., Cristoforetti, G., Giuffrida, M., Hidalgo, M., Legnaioli, S., Palleschi, V., Salvetti, A., Tognoni, E. & Vallebona, C. (2004). Three-dimensional analysis of laser induced plasmas in single and double pulse configuration. Spectrochimica Acta Part B59, 723.Google Scholar
Cristoforetti, G., Lorenzetti, G., Benedetti, P.A., Tognoni, E., Legnaioli, S. & Palleschi, V. (2009). Effect of laser parameters on plasma shielding in single and double pulse configurations during the ablation of an aluminium target. J. Phys. D: Appl. Phys. 42, 225207.CrossRefGoogle Scholar
Davis, W.D. & Miller, C.H. (1969). Analysis of the electrode products emitted by dc arcs in a vacuum ambient. J. Appl. Phys. 40, 2212.CrossRefGoogle Scholar
Denavit, J. (1979). Collisionless plasma expansion into vacuum. Phys. Fluids B22, 1384.Google Scholar
Devies, J.R., Bell, A.R. & Tatarakis, M. (1999). Magnetic focusing and trapping of high-intensity laser-generated fast electrons at the rear of solid targets. Phys. Rev. E59, 6032.Google Scholar
Dubey, A.K. & Yadava, V. (2008). Laser beam machining—A review. Intern. J. Mach. Tools & Manufact. 48, 609.CrossRefGoogle Scholar
Dolan, W.W. & Dyke, W.P. (1954). Temperature and field emission of electrons from metals. Phys. Rev. 95, 327.CrossRefGoogle Scholar
Eliezer, S., Eliaz, N., Grossman, E., Fisher, D., Gouzman, I., Henis, Z., Pecker, S., Horovitz, Y., Fraenkel, M., Maman, S., Ezersky, V. & Eliezer, D. (2005). Nanoparticles and nanotubes induced by femtosecond lasers, Laser Part. Beams 23, 15–19.CrossRefGoogle Scholar
Eliezer, S. & Ludmirsky, A. (1983). Double layer formation in laser produced plasma. Laser Part. Beams 1, 251–269.CrossRefGoogle Scholar
Eliezer, S. & Hora, H. (1988). Double layers in laser produced plasma. Phys. Repts. 172, 339–406.CrossRefGoogle Scholar
Fernandez, J.C., Hegelich, B.M., Cobble, J.A., Flippo, K.A., Letzring, S.A., Johnson, R.P., Gautier, D.C., Shimada, T., Kyrala, G.A., Wang, Y., Wetteland, C.J. & Schreiber, J. (2005). Laser-ablation treatment of short-pulse laser targets: Toward an experimental program on energetic-ion interactions with dense plasmas. Laser Part. Beams 23, 267–273.CrossRefGoogle Scholar
Fisher, J. (1976). Distribution of pure vapor between two parallel plates under the influence of strong evaporation and condensation. Phys. Fluids 19, 1305.Google Scholar
Franghiadakis, Y., Fotakis, C. & Tzanetakis, P. (1999). Energy distribution of ions produced by excimer-laser ablation of solid and molten targets. Appl. Phys. A68, 391–397.CrossRefGoogle Scholar
Franklin, R.N. (2003). The plasma–sheath boundary region. J. Phys. D: Appl. Phys. 36, R309.CrossRefGoogle Scholar
Gamaly, E.G. (1993). The interaction of ultrashort, powerful laser pulses solid target: Ion expansion and acceleration with time-dependent ambipolar field. Phys. Fluids B5, 944.Google Scholar
Gamaly, E.G., Luther-Davies, B., Kolev, V.Z., Madsen, N.R., Duering, M. & Rode, A.V. (2005). Ablation of metals with picosecond laser pulses: Evidence of long-lived non-equilibrium surface states. Laser Part. Beams 23, 167–176.CrossRefGoogle Scholar
Gamaly, E.G.Rodea, A.V. & Luther-Davies, B. (1999). Ultrafast ablation with high-pulse-rate lasers. Part I: Theoretical considerations. J. Appl. Phys. 85, 4213–4221.CrossRefGoogle Scholar
Gamaly, E.G., Rode, A.V., Luther-Davies, B. & Tikhonchuk, V.T. (2002). Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics. Phys. Plasmas 9, 949.CrossRefGoogle Scholar
Gili, D.H. & Dougal, A.A. (1965). Breakdown minima due to electron-impact ionization in super-high-pressure gases irradiated by a focused giant-pulse laser. Phys. Rev. Lett. 15, 845.CrossRefGoogle Scholar
Gusarov, A.V., Gnedovets, A.G. & Smurov, I. (2000). Gas dynamics of laser ablation: Influence of ambient atmosphere. J. Appl. Phys. 88, 4352.CrossRefGoogle Scholar
Gusarov, V. & Aoki, K. (2005). Ionization degree for strong evaporation of metals. Phys. Plasmas 12, 083503.CrossRefGoogle Scholar
Hafez, M.A., Khedr, M.A., Elaksher, F.F. & Gamal, Y.E. (2003). Characteristics of Cu plasma produced by a laser interaction with a solid target. Plasma Sour. Sci. Technol. 12, 185.CrossRefGoogle Scholar
Hatchett, S.P., Brown, C.G., Cowan, T.E., et al. (2000). Electron, photon, and ion beams from the relativistic interaction of petawatt laser pulses with solid targets. Phys. Plasmas 7, 2076.CrossRefGoogle Scholar
Hegelich, M., Karsch, S., Pretzler, G., Habs, D., Witte, K., Guenther, W., Allen, M., Blazevic, A., Fuchs, J., Gauthier, J.C., Geissel, M., Audebert, P., Cowan, T. & Roth, M. (2002). MeV ion jets from short-pulse-laser interaction with thin foils. Phys. Rev. Lett. 89, 085002.CrossRefGoogle ScholarPubMed
Henc-Bartolic, V., Andreic, Z. & Kunze, H.J. (1994). Titanium plasma produced by a nitrogen laser. Phys. Scripta 50, 368.CrossRefGoogle Scholar
Henc-Bartolic, V., Boncina, T., Jakovljevic, S., Pipic, D. & Zupanic, F. (2008). The action of a laser on an aluminium target. Mater. Technol. 42, 111.Google Scholar
Hermann, J., Thomann, A.L., Leborgne, C. & Dubreuil, B. (1995). Pulsed diagnostics in pulsed laser TiN layer deposition. J. Appl. Phys. 77, 2928–2936.CrossRefGoogle Scholar
Hoffmann, D.H.H., Blazevic, A.P., Rosmej, N.O.Roth, M.Tahir, N.A., Tauschwitz, A., Udrea, S., Varentsov, D., Weyrich, K. & Maron, Y. (2005). Present and future prospective for high energy density physics with intense heavy ion and laser beams. Laser Part. Beams 23, 47–53.CrossRefGoogle Scholar
Hora, H. (1981). Physics of Laser Driven Plasmas. New York: John Wiley.Google Scholar
Itina, T.E., Hermann, J., Delaporte, Ph. & Sentis, M. (2002). Laser-generated plasma plume expansion: Combined continuous-microscopic modeling. Phys. Rev. E66, 066406.Google Scholar
Kasperczuk, A., Pisarczyk, T., Kalal, M., Martinkova, M., Ullschmied, J., Krousky, E., Masek, K., Pfeifer, M., Rohlena, K., Skala, J. & Pisarczyk, P. (2008). PALS laser energy transfer into solid targets and its dependence on the lens focal point position with respect to the target surface. Laser Part. Beams 26, 189–196.CrossRefGoogle Scholar
Keidar, M., Beilis, I.I., Boxman, R.L. & Goldsmith, S. (1996). 2-D expansion of the low density interelectrode vacuum arc plasma in an axial magnetic field. J. Phys. D: Appl. Phys. 29, 1973.CrossRefGoogle Scholar
Keidar, M., Boyd, I.D. & Beilis, I.I. (2001). On the model of Teflon ablation in an ablation-controlled discharge. J. Phys. D: Appl. Phys. 34, 1675.CrossRefGoogle Scholar
Keidar, M. & Beilis, I.I. (2005). Transition from plasma to space-charge sheath near the electrode in electrical discharges. IEEE Trans. Plasma Sci. 33, 1481.CrossRefGoogle Scholar
Knudsen, M. (1915). Die Maximale Verdampfungsgeschwindigkeit des Quecksilbers (The rate of mercury evaporation). Ann. Phys. Chem. 47, 697.Google Scholar
Langmuir, I. & Mackay, J.M.G. (1914). The vapor pressure of the metals platinum and molybdenum. Phys. Rev. 4 377.CrossRefGoogle Scholar
Langmuir, I. (1929). The interaction of electron and positive ion space charges in cathode sheaths. Phys. Rev. 33 954.CrossRefGoogle Scholar
Liseikina, T.V., Prellino, D., Cornolti, F. & Macchi, A. (2008). Ponderomotive acceleration of ions: Circular versus linear polarization. IEEE Trans. Plas. Sci. 36, 1866.CrossRefGoogle Scholar
Margarone, D., Torrisi, L., Borrielli, A. & Caridi, F. (2008). Silver plasma by pulsed laser ablation. Plasma Sour. Sci. Techol. 17, 035019.Google Scholar
Mazhukin, V.I., Nossov, V.V., Nickiforov, M.G. & Smurov, I. (2003). Optical breakdown in aluminum vapor induced by ultraviolet laser radiation. J. Appl. Phys. 93, 56.CrossRefGoogle Scholar
Miller, G.H., Moses, E.I. & Wuest, C.R. (2004). The National Ignition Facility: enabling fusion ignition for the 21st century. Nucl. Fusion 44, 228.CrossRefGoogle Scholar
Moscicki, T., Hoffman, J. & Szymanski, Z. (2006). Modelling of plasma plume induced during laser welding. J. Phys. D: Appl. Phys. 39, 685–692.CrossRefGoogle Scholar
Pearlman, J.S., Morse, B.L. (1978). Maximum expansion velocities laser plasmas. Phys. Rev. Lett. 40, 1652.CrossRefGoogle Scholar
Popov, S., Panchenko, A., Batrakov, A., Ljubchenko, F. & Mataibaev, V. (2011). Experimental Study of the Laser Ablation Plasma Flow from the Liquid Ga-In Target. IEEE Trans. Plasma Sci. 39, 1412.CrossRefGoogle Scholar
Pukhov, A. (2001). Three-dimensional simulations of ion acceleration from a foil irradiated by a short-pulse laser. Phys. Rev. Lett. 86, 3562.CrossRefGoogle ScholarPubMed
Raizer Yu, P. (1974). Laser Spark and Discharge Expansion. Moscow: Nauka.Google Scholar
Raizer Yu, P. (1965). Breakdown and heating of gases under the influence of a laser beam. Sov. Pys. Uspekhy 8, 650.Google Scholar
Raizer Yu, P. (1980). Optical discharges. Sov. Phys. Uspekhy 23, 789.Google Scholar
Rieger, G.W., Taschuk, M., Tsui, Y.Y. & Fedosejevs, R. (2003). Comparative study of laser-induced plasma emission from microjoule picosecond and nanosecond KrF-laser pulses. Spectrochim. Acta B58, 497.Google Scholar
Rosen, D.I., Mitteldorf, J., Kothandaraman, G., Pirri, A.N. & Pugh, E.R. (1982). Coupling of pulsed 0.35-µm laser radiation to aluminum alloys. J. Appl. Phys. 53, 3190.Google Scholar
Singh, R.K. & Narayan, J. (1990). Pulsed-laser evaporation technique for deposition of thin films: Physics and theoretical model. Phys. Rev. B41, 8843–8859.CrossRefGoogle Scholar
Schaumann, G., Schollmeier, M.S., Rodriguez-Prieto, G., Blazevic, A., Brambrink, E., Geissel, M., Korostiy, S., Pirzadeh, P., Roth, M., Rosmej, F.B., Faenov, A.Y., Pikuz, T.A., Tsigutkin, K., Maron, Y., Tahir, N.A. & Hoffmann, D.H.H. (2005). High energy heavy ion jets emerging from laser plasma generated by long pulse laser beams from the NHELIX laser system at GSI. Laser Part. Beams 23, 503.CrossRefGoogle Scholar
Schwarz-Selinger, T., Cahill, D.G., Chen, S.-C., Moon, S.-J. & Grigoropoulos, C.P. (2001). Micron-scale modifications of Si surface morphology by pulsed-laser texturing. Phys. Rev. B64, 155323.Google Scholar
Shoucri, M., Lavocat-Dubuis, , Matte, X.J-P. & Vidal, F. (2011). Numerical study of ion acceleration and plasma jet formation in the interaction of an intense laser beam normally incident on an overdense plasma. Laser Part. Beams 29, 315–332.CrossRefGoogle Scholar
Shukla, G. & Khare, A. (2010). Spectroscopic studies of laser ablated ZnO plasma and correlation with pulsed laser deposited ZnO thin film properties. Laser Part. Beams 28, 149–155.CrossRefGoogle Scholar
Steinke, S., Henig, A., Schnurer, M., Sokollik, T., Nickles, P.V., Jung, D., Kiefer, D., Horlein, R., Schreiber, J., Tajima, T., Yan, X.Q., Hegelich, M., Meyer-ter-Vehn, J., Sandner, W. & Habs, D. (2010). Efficient ion acceleration by collective laser-driven electron dynamics with ultra-thin foil targets. Laser Part. Beams 28, 215–221.CrossRefGoogle Scholar
Sun, Y., Chen, M., Li, Y., Qi, H., Zhao, M. & Liu, X. (2008). Analysis of plasma profile over KTiOAsO4 surface produced by 532 and 1064 nm laser radiations. J. Appl. Phys. 104, 123303.CrossRefGoogle Scholar
Torrisi, L., Ciavola, G., Gammino, S., Ando, L. & Barna, A. (2000). Metallic etching by high power Nd:yttrium–aluminum–garnet pulsed laser irradiation. Rev. Scientific Instrum. 71, 4330.CrossRefGoogle Scholar
Torrisi, L., Ando, L., Ciavola, G., Gammino, S. & Barna, A. (2001). Angular distribution of ejected atoms from Nd:YAG laser irradiating metals. Rev. Sci. Instrum. 72, 68.CrossRefGoogle Scholar
Torrisi, L., Gammino, S., Ando, L. & Laska, L. (2002). Tantalum ions produced by 1064 nm pulsed laser irradiation. J. Appl. Phys. 91, 4685.CrossRefGoogle Scholar
Torrisi, L. & Gammino, S. (2006). Method for the calculation of electrical field in laser-generated plasma for ion stream production. Rev. Sci. Instrum. 77, 03B707.CrossRefGoogle Scholar
Torrisi, L., Caridi, F., Margarone, D., Picciotto, A., Mangione, A. & Beltrano, J.J. (2006). Carbon-plasma produced in vacuum by 532 nm–3 ns laser pulses ablation. Appl. Surf. Sci. 252, 6383.CrossRefGoogle Scholar
Torrisi, L., Caridi, F., Margarone, D. & Borrielli, A. (2008a). Plasma-laser characterization by electrostatic mass quadrupole analyzer. Nucl. Instrum. Meth. Phys. Res. B266, 308.Google Scholar
Torrisi, L., Caridi, F., Margarone, D. & Borrielli, A. (2008b). Characterization of laser-generated silicon plasma. Appl. Surf. Sci. 254, 2090.CrossRefGoogle Scholar
Tajima, T. & Dawson, J.M. (1979). Laser electron accelerator. Phys. Rev. Lett. 43, 267.CrossRefGoogle Scholar
Tsue, Y.Y. & Redman, D.G. (2000). A laser ablation technique for improving the adhesion of laser-deposited diamond-like carbon coatings to metal substrates. Surf. Coat. Technol. 126 N2–3 96.Google Scholar
Wang, Hai-Xing, & Chen, Xi. (2003). Three-dimensional modelling of the laser-induced plasma plume characteristics in laser welding. J. Phys. D: Appl. Phys. 36, 628.CrossRefGoogle Scholar
Wickens, L.M., Allen, J.E. & Rumsby, P.T. (1978). Ion emission from laser-produced plasmas with two electron temperatures. Phys. Rev. Lett. 41, 243.CrossRefGoogle Scholar
Wilks, S.C., Langdon, A.B., Cowan, T.E., Roth, M., Singh, M., Hatchett, S., Key, M.H., Pennington, D., MacKinnon, A. & Snavely, R.A. (2001). Energetic proton generation in ultra-intense laser–solid interactions. Phys. Plasmas 8, 542.CrossRefGoogle Scholar
Zeldovich, Ya.B. & Raizer, Yu.P. (1966). Physics of shock waves and high-temperature hydrodynamic phenomena. New York: Academic Press.Google Scholar
Zheng, J.P., Huang, Z.Q., Shaw, D.T. & Kowk, H.C. (1989). Generation high-energy atomic beams laser. Appl. Phys. Lett. 54, 280–282.CrossRefGoogle Scholar
Zeng, X., Mao, X., Mao, S.S., Wen, Sy-Bor, Greif, R. & Russo, R.E. (2006). Laser-induced shockwave propagation from ablation in a cavity. Appl. Phys. Lett. 88, 061502.CrossRefGoogle Scholar