Abstract

The dynamics of the radiative plasma expansion into an ambient gas is considered. The model describes the evolution of the plasma emission spectrum and the dynamics of the resulting shock wave. The time frame for the applicability of the model is in the tens of nanoseconds after the laser pulse is terminated, until a few microseconds later when the plasma ceases to emit. It is assumed that local thermodynamic equilibrium is established and that the plume expands with spherical symmetry. The model outputs are spatial and temporal distributions of atoms, ions, and electron number densities, evolution of atom and ion line profiles, and the shock wave. The model should be applicable to spectroscopic analysis of the initial plasma state and plasma dynamics.

© 2006 Optical Society of America

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  1. J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
    [CrossRef]
  2. J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
    [CrossRef]
  3. S. Palanco, S. Conesa, and J. J. Laserna, " Analytical control of liquid steel in an induction melting furnace using a remote laser induced plasma spectrometer," J. Anal. At. Spectrom. 19, 462- 467 ( 2004).
    [CrossRef]
  4. A. K. Rai, F. -Y. Yueh, and J. P. Singh, " Laser-induced breakdown spectroscopy of molten aluminum alloy," Appl. Opt. 42, 2078- 2084 ( 2003).
    [CrossRef] [PubMed]
  5. K. Niemax and W. Sdorra, " Optical emission spectrometry and laser-induced fluorescence of laser-produced sample plumes," Appl. Opt. 29, 5000- 5006 ( 1990).
    [CrossRef] [PubMed]
  6. A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, " Laser ablation for analytical sampling: what we can learn from modeling?," Spectrochim. Acta Part B 58, 1867- 1893 ( 2003).
    [CrossRef]
  7. M. Capitelli, A Casavola, G. Colonna, and A. De Giakomo, " Laser-induced plasma expansion: theoretical and experimental aspects," Spectrochim. Acta Part B 59, 271- 289 ( 2004).
    [CrossRef]
  8. I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
    [CrossRef]
  9. T. E. Itina, J. Hermann, Ph. Delaporte, and M. Sentis, " Combined continuous-microscopic modeling of laser plume expansion," Appl. Surf. Sci. 208-209, 27- 32 ( 2003).
    [CrossRef]
  10. J. R. Ho, C. P. Grigoropoulos, and J. A. C. Humphrey, " Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum," J. Appl. Phys. 79, 7205- 7215 ( 1996).
    [CrossRef]
  11. V. I. Mazhukin, V. V. Nossov, M. G. Nickiforov, and I. Smurov, " Optical breakdown in aluminum vapor induced by ultraviolet laser radiation," J. Appl. Phys. 93, 56- 66 ( 2003).
    [CrossRef]
  12. V. I. Mazhukin, V. V. Nossov, G. Flamant, and I. Smurov, " Modeling of radiation transfer and emission spectra in laser-induced plasma of A1 vapor," J. Quant. Spectrosc. Radiat. Transfer 73, 451- 460 ( 2002).
    [CrossRef]
  13. L. V. Zhigilei, " Dynamics of the plume formation and parameters of the ejected clusters in short-pulse laser ablation," Appl. Phys. A 76, 339- 350 ( 2003).
    [CrossRef]
  14. M. I. Zeifman, B. J. Garrison, and L. V. Zhigilei, " Combined molecular dynamics--direct simulation Monte Carlo computational study of laser ablation plume evolution," J. Appl. Phys. 92, 2181- 2193 ( 2002).
    [CrossRef]
  15. N. Arnold, J. Gruber, and J. Heitz, " Spherical expansion of the vapor plume into ambient gas: an analytical model," Appl. Phys. A 69, (Suppl.) S87- S93 ( 1999).
  16. I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
    [CrossRef]
  17. I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
    [CrossRef]
  18. G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).
  19. Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, 1966), Vol. 1, p. 143.
  20. V. Kurdyumov, A. L. Sanchez, and A. Linan, " Heat propagation from a concentrated external energy source in a gas," J. Fluid Mech. 491, 379- 410 ( 2003).
    [CrossRef]
  21. H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
    [CrossRef]

2005 (1)

I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
[CrossRef]

2004 (4)

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

S. Palanco, S. Conesa, and J. J. Laserna, " Analytical control of liquid steel in an induction melting furnace using a remote laser induced plasma spectrometer," J. Anal. At. Spectrom. 19, 462- 467 ( 2004).
[CrossRef]

M. Capitelli, A Casavola, G. Colonna, and A. De Giakomo, " Laser-induced plasma expansion: theoretical and experimental aspects," Spectrochim. Acta Part B 59, 271- 289 ( 2004).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
[CrossRef]

2003 (6)

T. E. Itina, J. Hermann, Ph. Delaporte, and M. Sentis, " Combined continuous-microscopic modeling of laser plume expansion," Appl. Surf. Sci. 208-209, 27- 32 ( 2003).
[CrossRef]

A. K. Rai, F. -Y. Yueh, and J. P. Singh, " Laser-induced breakdown spectroscopy of molten aluminum alloy," Appl. Opt. 42, 2078- 2084 ( 2003).
[CrossRef] [PubMed]

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, " Laser ablation for analytical sampling: what we can learn from modeling?," Spectrochim. Acta Part B 58, 1867- 1893 ( 2003).
[CrossRef]

V. I. Mazhukin, V. V. Nossov, M. G. Nickiforov, and I. Smurov, " Optical breakdown in aluminum vapor induced by ultraviolet laser radiation," J. Appl. Phys. 93, 56- 66 ( 2003).
[CrossRef]

L. V. Zhigilei, " Dynamics of the plume formation and parameters of the ejected clusters in short-pulse laser ablation," Appl. Phys. A 76, 339- 350 ( 2003).
[CrossRef]

V. Kurdyumov, A. L. Sanchez, and A. Linan, " Heat propagation from a concentrated external energy source in a gas," J. Fluid Mech. 491, 379- 410 ( 2003).
[CrossRef]

2002 (2)

M. I. Zeifman, B. J. Garrison, and L. V. Zhigilei, " Combined molecular dynamics--direct simulation Monte Carlo computational study of laser ablation plume evolution," J. Appl. Phys. 92, 2181- 2193 ( 2002).
[CrossRef]

V. I. Mazhukin, V. V. Nossov, G. Flamant, and I. Smurov, " Modeling of radiation transfer and emission spectra in laser-induced plasma of A1 vapor," J. Quant. Spectrosc. Radiat. Transfer 73, 451- 460 ( 2002).
[CrossRef]

2001 (1)

I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
[CrossRef]

2000 (2)

J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
[CrossRef]

H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
[CrossRef]

1999 (1)

N. Arnold, J. Gruber, and J. Heitz, " Spherical expansion of the vapor plume into ambient gas: an analytical model," Appl. Phys. A 69, (Suppl.) S87- S93 ( 1999).

1996 (1)

J. R. Ho, C. P. Grigoropoulos, and J. A. C. Humphrey, " Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum," J. Appl. Phys. 79, 7205- 7215 ( 1996).
[CrossRef]

1990 (1)

1974 (1)

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

1966 (1)

Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, 1966), Vol. 1, p. 143.

Arnold, N.

N. Arnold, J. Gruber, and J. Heitz, " Spherical expansion of the vapor plume into ambient gas: an analytical model," Appl. Phys. A 69, (Suppl.) S87- S93 ( 1999).

Bogaerts, A.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, " Laser ablation for analytical sampling: what we can learn from modeling?," Spectrochim. Acta Part B 58, 1867- 1893 ( 2003).
[CrossRef]

Capitelli, M.

M. Capitelli, A Casavola, G. Colonna, and A. De Giakomo, " Laser-induced plasma expansion: theoretical and experimental aspects," Spectrochim. Acta Part B 59, 271- 289 ( 2004).
[CrossRef]

Casavola, A

M. Capitelli, A Casavola, G. Colonna, and A. De Giakomo, " Laser-induced plasma expansion: theoretical and experimental aspects," Spectrochim. Acta Part B 59, 271- 289 ( 2004).
[CrossRef]

Chen, Z.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, " Laser ablation for analytical sampling: what we can learn from modeling?," Spectrochim. Acta Part B 58, 1867- 1893 ( 2003).
[CrossRef]

Colonna, G.

M. Capitelli, A Casavola, G. Colonna, and A. De Giakomo, " Laser-induced plasma expansion: theoretical and experimental aspects," Spectrochim. Acta Part B 59, 271- 289 ( 2004).
[CrossRef]

Conesa, S.

S. Palanco, S. Conesa, and J. J. Laserna, " Analytical control of liquid steel in an induction melting furnace using a remote laser induced plasma spectrometer," J. Anal. At. Spectrom. 19, 462- 467 ( 2004).
[CrossRef]

Correll, T.

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

De Giakomo, A.

M. Capitelli, A Casavola, G. Colonna, and A. De Giakomo, " Laser-induced plasma expansion: theoretical and experimental aspects," Spectrochim. Acta Part B 59, 271- 289 ( 2004).
[CrossRef]

Delaporte, Ph.

T. E. Itina, J. Hermann, Ph. Delaporte, and M. Sentis, " Combined continuous-microscopic modeling of laser plume expansion," Appl. Surf. Sci. 208-209, 27- 32 ( 2003).
[CrossRef]

Flamant, G.

V. I. Mazhukin, V. V. Nossov, G. Flamant, and I. Smurov, " Modeling of radiation transfer and emission spectra in laser-induced plasma of A1 vapor," J. Quant. Spectrosc. Radiat. Transfer 73, 451- 460 ( 2002).
[CrossRef]

Garrison, B. J.

M. I. Zeifman, B. J. Garrison, and L. V. Zhigilei, " Combined molecular dynamics--direct simulation Monte Carlo computational study of laser ablation plume evolution," J. Appl. Phys. 92, 2181- 2193 ( 2002).
[CrossRef]

Gibb, E.

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

Gijbels, R.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, " Laser ablation for analytical sampling: what we can learn from modeling?," Spectrochim. Acta Part B 58, 1867- 1893 ( 2003).
[CrossRef]

Gornushkin, I. B.

I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
[CrossRef]

I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
[CrossRef]

Grigoropoulos, C. P.

J. R. Ho, C. P. Grigoropoulos, and J. A. C. Humphrey, " Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum," J. Appl. Phys. 79, 7205- 7215 ( 1996).
[CrossRef]

Gruber, J.

N. Arnold, J. Gruber, and J. Heitz, " Spherical expansion of the vapor plume into ambient gas: an analytical model," Appl. Phys. A 69, (Suppl.) S87- S93 ( 1999).

Heitz, J.

N. Arnold, J. Gruber, and J. Heitz, " Spherical expansion of the vapor plume into ambient gas: an analytical model," Appl. Phys. A 69, (Suppl.) S87- S93 ( 1999).

Hermann, J.

T. E. Itina, J. Hermann, Ph. Delaporte, and M. Sentis, " Combined continuous-microscopic modeling of laser plume expansion," Appl. Surf. Sci. 208-209, 27- 32 ( 2003).
[CrossRef]

Ho, J. R.

J. R. Ho, C. P. Grigoropoulos, and J. A. C. Humphrey, " Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum," J. Appl. Phys. 79, 7205- 7215 ( 1996).
[CrossRef]

Humphrey, J. A. C.

J. R. Ho, C. P. Grigoropoulos, and J. A. C. Humphrey, " Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum," J. Appl. Phys. 79, 7205- 7215 ( 1996).
[CrossRef]

Itina, T. E.

T. E. Itina, J. Hermann, Ph. Delaporte, and M. Sentis, " Combined continuous-microscopic modeling of laser plume expansion," Appl. Surf. Sci. 208-209, 27- 32 ( 2003).
[CrossRef]

Kazakov, A Ya.

I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
[CrossRef]

Kazakov, A. Ya.

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
[CrossRef]

Kurdyumov, V.

V. Kurdyumov, A. L. Sanchez, and A. Linan, " Heat propagation from a concentrated external energy source in a gas," J. Fluid Mech. 491, 379- 410 ( 2003).
[CrossRef]

Laserna, J. J.

S. Palanco, S. Conesa, and J. J. Laserna, " Analytical control of liquid steel in an induction melting furnace using a remote laser induced plasma spectrometer," J. Anal. At. Spectrom. 19, 462- 467 ( 2004).
[CrossRef]

Le, H. C.

H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
[CrossRef]

Linan, A.

V. Kurdyumov, A. L. Sanchez, and A. Linan, " Heat propagation from a concentrated external energy source in a gas," J. Fluid Mech. 491, 379- 410 ( 2003).
[CrossRef]

Marine, W.

H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
[CrossRef]

Matveev, O. I.

J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
[CrossRef]

Mazhukin, V. I.

V. I. Mazhukin, V. V. Nossov, M. G. Nickiforov, and I. Smurov, " Optical breakdown in aluminum vapor induced by ultraviolet laser radiation," J. Appl. Phys. 93, 56- 66 ( 2003).
[CrossRef]

V. I. Mazhukin, V. V. Nossov, G. Flamant, and I. Smurov, " Modeling of radiation transfer and emission spectra in laser-induced plasma of A1 vapor," J. Quant. Spectrosc. Radiat. Transfer 73, 451- 460 ( 2002).
[CrossRef]

Nickiforov, M. G.

V. I. Mazhukin, V. V. Nossov, M. G. Nickiforov, and I. Smurov, " Optical breakdown in aluminum vapor induced by ultraviolet laser radiation," J. Appl. Phys. 93, 56- 66 ( 2003).
[CrossRef]

Niemax, K.

Nossov, V. V.

V. I. Mazhukin, V. V. Nossov, M. G. Nickiforov, and I. Smurov, " Optical breakdown in aluminum vapor induced by ultraviolet laser radiation," J. Appl. Phys. 93, 56- 66 ( 2003).
[CrossRef]

V. I. Mazhukin, V. V. Nossov, G. Flamant, and I. Smurov, " Modeling of radiation transfer and emission spectra in laser-induced plasma of A1 vapor," J. Quant. Spectrosc. Radiat. Transfer 73, 451- 460 ( 2002).
[CrossRef]

Omenetto, N.

I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
[CrossRef]

I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
[CrossRef]

Palanco, S.

S. Palanco, S. Conesa, and J. J. Laserna, " Analytical control of liquid steel in an induction melting furnace using a remote laser induced plasma spectrometer," J. Anal. At. Spectrom. 19, 462- 467 ( 2004).
[CrossRef]

Pappas, D.

J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
[CrossRef]

Parisse, J. D.

H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
[CrossRef]

Rai, A. K.

Raizer, Yu. P.

Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, 1966), Vol. 1, p. 143.

Sanchez, A. L.

V. Kurdyumov, A. L. Sanchez, and A. Linan, " Heat propagation from a concentrated external energy source in a gas," J. Fluid Mech. 491, 379- 410 ( 2003).
[CrossRef]

Sdorra, W.

Sentis, M.

T. E. Itina, J. Hermann, Ph. Delaporte, and M. Sentis, " Combined continuous-microscopic modeling of laser plume expansion," Appl. Surf. Sci. 208-209, 27- 32 ( 2003).
[CrossRef]

Singh, J. P.

Smith, B. W.

I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
[CrossRef]

I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
[CrossRef]

Smurov, I.

V. I. Mazhukin, V. V. Nossov, M. G. Nickiforov, and I. Smurov, " Optical breakdown in aluminum vapor induced by ultraviolet laser radiation," J. Appl. Phys. 93, 56- 66 ( 2003).
[CrossRef]

V. I. Mazhukin, V. V. Nossov, G. Flamant, and I. Smurov, " Modeling of radiation transfer and emission spectra in laser-induced plasma of A1 vapor," J. Quant. Spectrosc. Radiat. Transfer 73, 451- 460 ( 2002).
[CrossRef]

Snetis, M.

H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
[CrossRef]

Stevenson, C. L.

I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
[CrossRef]

Vertes, A.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, " Laser ablation for analytical sampling: what we can learn from modeling?," Spectrochim. Acta Part B 58, 1867- 1893 ( 2003).
[CrossRef]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

Winefordner, J. D.

I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
[CrossRef]

I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
[CrossRef]

Yueh, F. -Y.

Zeifman, M. I.

M. I. Zeifman, B. J. Garrison, and L. V. Zhigilei, " Combined molecular dynamics--direct simulation Monte Carlo computational study of laser ablation plume evolution," J. Appl. Phys. 92, 2181- 2193 ( 2002).
[CrossRef]

Zeitoun, D. E.

H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
[CrossRef]

Zel'dovich, Ya. B.

Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, 1966), Vol. 1, p. 143.

Zhigilei, L. V.

L. V. Zhigilei, " Dynamics of the plume formation and parameters of the ejected clusters in short-pulse laser ablation," Appl. Phys. A 76, 339- 350 ( 2003).
[CrossRef]

M. I. Zeifman, B. J. Garrison, and L. V. Zhigilei, " Combined molecular dynamics--direct simulation Monte Carlo computational study of laser ablation plume evolution," J. Appl. Phys. 92, 2181- 2193 ( 2002).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. A (2)

L. V. Zhigilei, " Dynamics of the plume formation and parameters of the ejected clusters in short-pulse laser ablation," Appl. Phys. A 76, 339- 350 ( 2003).
[CrossRef]

N. Arnold, J. Gruber, and J. Heitz, " Spherical expansion of the vapor plume into ambient gas: an analytical model," Appl. Phys. A 69, (Suppl.) S87- S93 ( 1999).

Appl. Surf. Sci. (1)

T. E. Itina, J. Hermann, Ph. Delaporte, and M. Sentis, " Combined continuous-microscopic modeling of laser plume expansion," Appl. Surf. Sci. 208-209, 27- 32 ( 2003).
[CrossRef]

J. Anal. At. Spectrom. (3)

J. D. Winefordner, I. B. Gornushkin, D. Pappas, O. I. Matveev, and B. W. Smith, " Novel uses of lasers in atomic spectroscopy. Plenary lecture," J. Anal. At. Spectrom. 15, 1161- 1189 ( 2000).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, " Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star," J. Anal. At. Spectrom. 19, (advance article) ( 2004).
[CrossRef]

S. Palanco, S. Conesa, and J. J. Laserna, " Analytical control of liquid steel in an induction melting furnace using a remote laser induced plasma spectrometer," J. Anal. At. Spectrom. 19, 462- 467 ( 2004).
[CrossRef]

J. Appl. Phys. (3)

J. R. Ho, C. P. Grigoropoulos, and J. A. C. Humphrey, " Gas dynamics and radiation heat transfer in the vapor plume produced by pulsed laser irradiation of aluminum," J. Appl. Phys. 79, 7205- 7215 ( 1996).
[CrossRef]

V. I. Mazhukin, V. V. Nossov, M. G. Nickiforov, and I. Smurov, " Optical breakdown in aluminum vapor induced by ultraviolet laser radiation," J. Appl. Phys. 93, 56- 66 ( 2003).
[CrossRef]

M. I. Zeifman, B. J. Garrison, and L. V. Zhigilei, " Combined molecular dynamics--direct simulation Monte Carlo computational study of laser ablation plume evolution," J. Appl. Phys. 92, 2181- 2193 ( 2002).
[CrossRef]

J. Fluid Mech. (1)

V. Kurdyumov, A. L. Sanchez, and A. Linan, " Heat propagation from a concentrated external energy source in a gas," J. Fluid Mech. 491, 379- 410 ( 2003).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

V. I. Mazhukin, V. V. Nossov, G. Flamant, and I. Smurov, " Modeling of radiation transfer and emission spectra in laser-induced plasma of A1 vapor," J. Quant. Spectrosc. Radiat. Transfer 73, 451- 460 ( 2002).
[CrossRef]

Phys. Rev E (1)

H. C. Le, D. E. Zeitoun, J. D. Parisse, M. Snetis, and W. Marine, " Modeling of gas dynamics for a laser-generated plasma: propagation into low pressure gases," Phys. Rev E 62, 4152- 4161 ( 2000).
[CrossRef]

Spectrochim. Acta B (2)

I. B. Gornushkin, C. L. Stevenson, B. W. Smith, N. Omenetto, and J. D. Winefordner, " Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach," Spectrochim. Acta B 56, 1769- 1785 ( 2001).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Radiation dynamics of post-breakdown laser induced plasma," Spectrochim. Acta B , 59, 401- 418 ( 2004).
[CrossRef]

Spectrochim. Acta Part B (3)

I. B. Gornushkin, A Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, " Experimental verification of a radiative model of laser induced plasma expanding into vacuum," Spectrochim. Acta Part B 60, 215- 230 ( 2005).
[CrossRef]

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, " Laser ablation for analytical sampling: what we can learn from modeling?," Spectrochim. Acta Part B 58, 1867- 1893 ( 2003).
[CrossRef]

M. Capitelli, A Casavola, G. Colonna, and A. De Giakomo, " Laser-induced plasma expansion: theoretical and experimental aspects," Spectrochim. Acta Part B 59, 271- 289 ( 2004).
[CrossRef]

Other (2)

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, 1966), Vol. 1, p. 143.

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Figures (10)

Fig. 1
Fig. 1

Evolution of emission spectra as a function of Si number density. A, n Si = n C = 1 × 1018 cm−3; B, n Si = n C = 5 × 1018 cm−3; C, n Si = n C = 2.0 × 1019 cm−3. Fixed parameters: n Ar = 2.6 × 1019 cm−3; T 0 = 2.5 × 104 K.

Fig. 2
Fig. 2

Temporal and spatial distribution of the plasma temperature. A, n Si = n C = 1 × 1018 cm−3; B, n Si = n C = 5 × 1018 cm−3; C, n Si = n C = 2.0 × 1019 cm−3. Fixed parameters: nAr = 2.6 × 1019 cm−3, T 0 = 2.5 × 104 K. Different traces correspond to the first 20 time steps, Δtn , n = 1, … 20, scaled as Δtn = Δt 0⌊1 + η(1 + 4η) + η2 (1 + 14η) + η3 (1 + 24η)⌋, where η = n∕Ns and Ns is the total number of time steps (here, Ns = 800, Δt 0 = 4 × 10−10 s).

Fig. 3
Fig. 3

Temporal and spatial distribution of the electron density. A, n Si = n C = 1 × 1018 cm−3; B, n Si = n C = 5 × 1018 cm−3; C, n Si = n C = 2.0 × 1019 cm−3. Fixed parameters: n Ar = 2.6 × 1019 cm−3, T 0 = 2.5 × 104 K. The time scale is the same as in Fig. 2.

Fig. 4
Fig. 4

A, Temporal evolution of the shock-wave radius (in centimeters). B, Evolution of the plasma radius (in centimeters). C, Evolution of the shock-wave speed (centimeters per second). Traces 1, 2, and 3 correspond to Si (= C) number densities 1 × 1018, 5 ×1018, and 2 × 1019 cm−3, respectively; dotted line is the sound speed. Fixed parameters: n Ar = 2.6 × 1019 cm−3, T 0 = 2.5 × 104 K.

Fig. 5
Fig. 5

Temporal and spatial distribution of pressure (dyne cm−2) inside the plasma. A, n Si = n C = 1 × 1018 cm−3; B, n Si = n C = 5 × 1018 cm−3; C, n Si = n C = 2.0 × 1019 cm−3. Fixed parameters: n Ar = 2.6 × 1019 cm−3, T 0 = 2.5 × 104 K.

Fig. 6
Fig. 6

Evolution of emission spectra for different initial temperatures. A, T 0 = 2 × 104 K; B, T 0 = 2.5 × 104 K; C, T 0 = 3 × 104 K. Fixed parameters: n C = n Si = 0.5 × 1018 cm−3, n Ar = 2 × 1019 cm−3.

Fig. 7
Fig. 7

Propagation radii of a shock wave determined by the shadowgraph technique.

Fig. 8
Fig. 8

Spectra of SiC plasma in Ar recorded at different delay times.

Fig. 9
Fig. 9

Propagation radii of a shock wave calculated for n Si = n C = 2 × 1017 cm−3, T 0 = 2.5 × 104 K.

Fig. 10
Fig. 10

Evolution of emission spectra from SiC plasma calculated for n Si = n C = 2 × 1017 cm−3, T 0 = 2.5 × 104 K.

Equations (20)

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P ( r ) = exp [ σ r R sw n sw ( r ) d r ] ,
d N = 4 π R p     2 d R p n g exp [ σ n sw ( R sw R p ) ]
n amb t + 1 r 2 r [ r 2 ν ( r ) n amb ] = ν ( r ) ( k σ k n k ) n m .
n m t = D Δ n m ν ( r ) ( k σ k n k ) n m + 1 4 π R p     2 d N d t δ ( r R p ) ,
N g = 4 π 3 n g [ R sw 3 ( t ) R 0     3 ] .
N sw = 4 π 3 n sw [ R sw 3 ( t ) R p     3 ( t ) ] ,
N g N sw = 4 π n g R 0 R p s 2 exp [ σ n sw ( R sw s ) ] d s 4 π 3 n g I a ,
n sw = γ + 1 γ 1 [ 1 + 2 M 2 ( γ 1 ) ] 1 n g ,
M = R ˙ sw c g .
R sw 3 R 0     3 ( R sw 3 R p     3 ) γ + 1 γ 1 [ 1 + 2 M 2 ( γ 1 ) ] 1 = I a ,
ν sw = 2 R ˙ sw γ  +  1 ( 1 M 2 ) .
P sw = 4 π R p R sw ρ sw ν ( r ) r 2 d r ,
d P sw d t = 4 π ( p sw R p     2 p g R sw 2 ) ,
p sw = ( R sw R p ) 2 p g + 1 4 π R p     2 d P sw d t .
φ I ν r + 1 φ 2 r I ν φ + κ ν I ν = κ ν I ν b ,
t = 0:       T ( r , 0 ) = T 0 ( 1 k 1 r 2 ) ,
      g ( j ) ( r ) n ( j ) ( r , 0 ) = n 0 ( j ) ( 1 k 2 r 2 ) ,
      0.1   cm   R p ( 0 ) = R sw ( 0 ) 0.5   cm,
r = 0 :     u = 0 ,     u t = 0 ,
r = R sw :     p = p g .

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