Abstract

Aluminum spectra in the noble gases of helium and argon at initial delay times after plasma formation are numerically calculated. Temporal behavior of plasma emissions up to 200 ns after laser irradiation is investigated. Plasma parameters are computed by coupling the thermal model of laser ablation, hydrodynamic of plasma expansion, and Saha–Eggert equations. A spectrum is constructed from the superposition of 13 strong lines of aluminum and several strong lines of ambient gases. Spectral radiations are superimposed on a continuous emission composed of bremsstrahlung and recombination radiation. The self-absorption effect on plasma radiation at 1 atm gas pressure is studied. In this paper, a comparison between thin and thick aluminum radiation is done. Furthermore, the self-absorption coefficient of each strong line at laser energies of 0.5, 0.7, 0.9, and 1.1GW/cm2 is estimated. Results show that at specific laser energy, the self-absorption effect in argon is more significant than in helium. For most of the spectral lines in both noble gases, the self-absorption coefficient will diminish with the delay time. As indicated with passing time, the line widths of the self-absorbed lines will rise. More intense continuous emissions are observed at higher wavelengths, and these radiations will be increased with laser energy.

© 2013 Optical Society of America

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  22. H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
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  25. A. M. El Sherbini, A. A. S. Al Amer, A. T. Hassan, and T. M. El Sherbini, “Spectrometric measurement of plasma parameters utilizing the target ambient gas O I & N I atomic lines in LIBS experiment,” Opt. Photon. J. 2, 286–293 (2012).
  26. J. Aguilera, J. Bengoechea, and C. Aragón, “Curves of growth of spectral lines emitted by a laser-induced plasma: influence of the temporal evolution and spatial inhomogeneity of the plasma,” Spectrochim. Acta Part B 58, 221–237 (2003).
    [CrossRef]
  27. J. Aguiler and C. Aragón, “Characterization of laser-induced plasmas by emission spectroscopy with curve-of-growth measurements. Part I: temporal evolution of plasma parameters and self-absorption,” Spectrochim. Acta Part B 63, 784–792 (2008).
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  28. C. Aragon, J. Bengoechea, and J. A. Aguilera, “Influence of the optical depth on spectral line emission from laser-induced plasmas,” Spectrochim. Acta B 56, 619–628 (2001).
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  29. C. Aragon, F. Penalba, and J. Aguilera, “Curves of growth of neutral atom and ion lines emitted by a laser induced plasma,” Spectrochim. Acta Part B 60, 879–887 (2005).
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2013

F. Rezaei and S. H. Tavassoli, “Developing the model of laser ablation by considering the interplay between emission and expansion of aluminum plasma,” Phys. Plasmas 20, 013301 (2013).
[CrossRef]

2012

F. Rezaei and S. H. Tavassoli, “Numerical and experimental investigation of laser induced plasma spectrum of aluminum in the presence of a noble gas,” Spectrochim. Acta B 78, 29–36 (2012).
[CrossRef]

G. Colonna, L. Pietanza, and G. D’Ammando, “Self-consistent collisional-radiative model for hydrogen atoms: atom–atom interaction and radiation transport,” Chem. Phys. 398, 37–45 (2012).
[CrossRef]

A. M. El Sherbini, A. A. S. Al Amer, A. T. Hassan, and T. M. El Sherbini, “Spectrometric measurement of plasma parameters utilizing the target ambient gas O I & N I atomic lines in LIBS experiment,” Opt. Photon. J. 2, 286–293 (2012).

2010

G. D’Ammando, L. Pietanza, G. Colonna, S. Longo, and M. Capitelli, “Modelling spectral properties of nonequilibrium atomic hydrogen plasma,” Spectrochim. Acta Part B 65, 120–129 (2010).
[CrossRef]

S. Mehrabian, M. Aghaei, and S. H. Tavassoli, “Effect of background gas pressure and laser pulse intensity on laser induced plasma radiation of copper samples,” Phys. Plasmas 17, 043301 (2010).
[CrossRef]

G. D’Ammando, G. Colonna, L. D. Pietanza, and M. Capitelli, “Computation of thermodynamic plasma properties: a simplified approach,” Spectrochim. Acta Part B 65, 603–615 (2010).
[CrossRef]

J. B. Ahmed and J. Cowpe, “Experimental and theoretical investigation of a self-absorbed spectral line emitted from laser-induced plasmas,” Appl. Opt. 49, 3607–3612 (2010).
[CrossRef]

2009

A. Casavola, G. Colonna, and M. Capitelli,” Kinetic model of titanium laser induced plasma expansion in nitrogen environment,” Plasma Sources Sci. Technol. 18, 025027 (2009).
[CrossRef]

H. Y. Moon, K. H. Kathleen, N. Omenetto, B. W. Smith, and J. D. Winefordner, “On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 64, 702–713 (2009).

L. Sun and H. Yu, “Correction of self-absorption effect in calibration-free laser-induced breakdown spectroscopy by an internal reference method,” Talanta 79, 388–395 (2009).
[CrossRef]

2008

E. Ershov-Pavlov, K. Y. Katsalap, K. Stepanov, and Y. A. Stankevich, “Time-space distribution of laser-induced plasma parameters and its influence on emission spectra of the laser plumes,” Spectrochim. Acta Part B 63, 1024–1037 (2008).
[CrossRef]

M. Ribière, B. G. Chéron, and A. Bultel, “Self-absorbed lines analysis of a recombining laser induced aluminum plasma,” High Temp. Mater. Process. 12, 109–120 (2008).
[CrossRef]

A. Alonso-Medina, “Experimental determination of the Stark widths of Pb I spectral lines in a laser-induced plasma,” Spectrochim. Acta Part B. 63, 598–602 (2008).
[CrossRef]

M. Aghaei, S. Mehrabian, and S. H. Tavassoli, “Simulation of nanosecond pulsed laser ablation of copper samples: a focus on laser induced plasma radiation,” J. Appl. Phys. 104, 053303 (2008).
[CrossRef]

J. Aguiler and C. Aragón, “Characterization of laser-induced plasmas by emission spectroscopy with curve-of-growth measurements. Part I: temporal evolution of plasma parameters and self-absorption,” Spectrochim. Acta Part B 63, 784–792 (2008).
[CrossRef]

2007

E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
[CrossRef]

2006

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
[CrossRef]

A. Bogaerts, Z. Chen, and D. Bleiner, “Laser ablation of copper in different background gases: comparative study by numerical modeling and experiments,” J. Anal. At. Spectrom. 21, 384–395 (2006).
[CrossRef]

M. Elitzur and A. A. Ramos, “A new exact method for line radiative transfer,” Mon. Not. R. Astron. Soc. 365, 779 (2006).
[CrossRef]

B. Atalay, R. Aydin, A. Demir, N. Kenar, and E. Kacar, “Simulation of Ni-like and Co-like X-rays emitted from laser produced tin plasmas,” Czech. J. Phys. 56, B430–B435 (2006).
[CrossRef]

2005

Y. Ralchenko, “NIST atomic spectra database,” Memorie della Societa Astronomica Italiana Supplementi 8, 96 (2005).

A. V. Gusarov and I. Smurov, “Thermal model of nanosecond pulsed laser ablation: analysis of energy and mass transfer,” J. Appl. Phys. 97, 0143071 (2005).

C. Aragon, F. Penalba, and J. Aguilera, “Curves of growth of neutral atom and ion lines emitted by a laser induced plasma,” Spectrochim. Acta Part B 60, 879–887 (2005).
[CrossRef]

A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
[CrossRef]

2004

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

2003

A. Casavola, G. Colonna, and M. Capitelli, “Nonequilibrium conditions during a laser induced plasma expansion,” Appl. Surf. Sci. 208, 85–89 (2003).
[CrossRef]

A. Casavola, G. De. Colonna, A. Giacomo, and M. Capitelli, “Laser ablation of titanium metallic targets: comparison between theory and experiment,” J. Thermophys. Heat Transfer 17, 225–231 (2003).
[CrossRef]

A. R. Casavola, G. De. Colonna, A. De Giacomo, O. Pascale, and M. Capitelli, “Experimental and theoretical investigation of laser-induced plasma of a titanium target,” Appl. Opt. 42, 5963–5970 (2003).
[CrossRef]

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
[CrossRef]

J. Aguilera, J. Bengoechea, and C. Aragón, “Curves of growth of spectral lines emitted by a laser-induced plasma: influence of the temporal evolution and spatial inhomogeneity of the plasma,” Spectrochim. Acta Part B 58, 221–237 (2003).
[CrossRef]

O. Renner, J. Limpouch, E. Krousky, I. Uschmann, and E. Förster, “Spectroscopic characterization of plasma densities of laser-irradiated Al foils,” J. Quant. Spectrosc. Radiat. Transfer 81, 385–394 (2003).
[CrossRef]

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

2002

D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
[CrossRef]

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
[CrossRef]

2001

I. 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 Part B 56, 1769–1785 (2001).
[CrossRef]

V. Milosavljevic and G. Poparic, “Atomic spectral line free parameter deconvolution procedure,” Phys. Rev. E 63, 036404 (2001).
[CrossRef]

C. Aragon, J. Bengoechea, and J. A. Aguilera, “Influence of the optical depth on spectral line emission from laser-induced plasmas,” Spectrochim. Acta B 56, 619–628 (2001).
[CrossRef]

1999

I. B. Gornushkin, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Line broadening mechanisms in the low pressure laser-induced plasma,” Spectrochim. Acta Part B 54, 1207–1217 (1999).
[CrossRef]

C. Trassy and A. Tazeem, “Simulation of atomic and ionic absorption and emission spectra for thermal plasma diagnostics: application to a volatilization study in a plasma jet,” Spectrochim. Acta Part B 54, 581–602 (1999).
[CrossRef]

1995

D. Heading, J. Wark, G. Bennett, and R. Lee,” Simulations of spectra from dense aluminium plasmas,” J. Quant. Spectrosc. Radiat. Transfer. 54, 167–180 (1995).
[CrossRef]

1994

A. Vertes, R. Dreyfus, and D. Platt, “Modeling the thermal-to-plasma transitions for Cu photoablation,” IBM J. Res. Dev. 38, 3–10 (1994).
[CrossRef]

1971

R. O’Neill, “Algorithm AS 47: function minimization using a simplex procedure,” J. R. Soc. Stat. Ser. C 20, 338–345 (1971).

1948

R. D. Cowan and G. H. Dieke, “Self-absorption of spectrum lines,” Rev. Mod. Phys. 20, 418–455 (1948).
[CrossRef]

Adámek, P.

O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
[CrossRef]

Aghaei, M.

S. Mehrabian, M. Aghaei, and S. H. Tavassoli, “Effect of background gas pressure and laser pulse intensity on laser induced plasma radiation of copper samples,” Phys. Plasmas 17, 043301 (2010).
[CrossRef]

M. Aghaei, S. Mehrabian, and S. H. Tavassoli, “Simulation of nanosecond pulsed laser ablation of copper samples: a focus on laser induced plasma radiation,” J. Appl. Phys. 104, 053303 (2008).
[CrossRef]

Aguiler, J.

J. Aguiler and C. Aragón, “Characterization of laser-induced plasmas by emission spectroscopy with curve-of-growth measurements. Part I: temporal evolution of plasma parameters and self-absorption,” Spectrochim. Acta Part B 63, 784–792 (2008).
[CrossRef]

Aguilera, J.

C. Aragon, F. Penalba, and J. Aguilera, “Curves of growth of neutral atom and ion lines emitted by a laser induced plasma,” Spectrochim. Acta Part B 60, 879–887 (2005).
[CrossRef]

J. Aguilera, J. Bengoechea, and C. Aragón, “Curves of growth of spectral lines emitted by a laser-induced plasma: influence of the temporal evolution and spatial inhomogeneity of the plasma,” Spectrochim. Acta Part B 58, 221–237 (2003).
[CrossRef]

Aguilera, J. A.

C. Aragon, J. Bengoechea, and J. A. Aguilera, “Influence of the optical depth on spectral line emission from laser-induced plasmas,” Spectrochim. Acta B 56, 619–628 (2001).
[CrossRef]

Ahmed, J. B.

Al Amer, A. A. S.

A. M. El Sherbini, A. A. S. Al Amer, A. T. Hassan, and T. M. El Sherbini, “Spectrometric measurement of plasma parameters utilizing the target ambient gas O I & N I atomic lines in LIBS experiment,” Opt. Photon. J. 2, 286–293 (2012).

Alonso-Medina, A.

A. Alonso-Medina, “Experimental determination of the Stark widths of Pb I spectral lines in a laser-induced plasma,” Spectrochim. Acta Part B. 63, 598–602 (2008).
[CrossRef]

Amamou, H.

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
[CrossRef]

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
[CrossRef]

Angelo, P.

O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
[CrossRef]

Aragon, C.

C. Aragon, F. Penalba, and J. Aguilera, “Curves of growth of neutral atom and ion lines emitted by a laser induced plasma,” Spectrochim. Acta Part B 60, 879–887 (2005).
[CrossRef]

C. Aragon, J. Bengoechea, and J. A. Aguilera, “Influence of the optical depth on spectral line emission from laser-induced plasmas,” Spectrochim. Acta B 56, 619–628 (2001).
[CrossRef]

Aragón, C.

J. Aguiler and C. Aragón, “Characterization of laser-induced plasmas by emission spectroscopy with curve-of-growth measurements. Part I: temporal evolution of plasma parameters and self-absorption,” Spectrochim. Acta Part B 63, 784–792 (2008).
[CrossRef]

J. Aguilera, J. Bengoechea, and C. Aragón, “Curves of growth of spectral lines emitted by a laser-induced plasma: influence of the temporal evolution and spatial inhomogeneity of the plasma,” Spectrochim. Acta Part B 58, 221–237 (2003).
[CrossRef]

Atalay, B.

B. Atalay, R. Aydin, A. Demir, N. Kenar, and E. Kacar, “Simulation of Ni-like and Co-like X-rays emitted from laser produced tin plasmas,” Czech. J. Phys. 56, B430–B435 (2006).
[CrossRef]

Aydin, R.

B. Atalay, R. Aydin, A. Demir, N. Kenar, and E. Kacar, “Simulation of Ni-like and Co-like X-rays emitted from laser produced tin plasmas,” Czech. J. Phys. 56, B430–B435 (2006).
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J. Aguilera, J. Bengoechea, and C. Aragón, “Curves of growth of spectral lines emitted by a laser-induced plasma: influence of the temporal evolution and spatial inhomogeneity of the plasma,” Spectrochim. Acta Part B 58, 221–237 (2003).
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D. Heading, J. Wark, G. Bennett, and R. Lee,” Simulations of spectra from dense aluminium plasmas,” J. Quant. Spectrosc. Radiat. Transfer. 54, 167–180 (1995).
[CrossRef]

Bleiner, D.

A. Bogaerts, Z. Chen, and D. Bleiner, “Laser ablation of copper in different background gases: comparative study by numerical modeling and experiments,” J. Anal. At. Spectrom. 21, 384–395 (2006).
[CrossRef]

Bogaerts, A.

A. Bogaerts, Z. Chen, and D. Bleiner, “Laser ablation of copper in different background gases: comparative study by numerical modeling and experiments,” J. Anal. At. Spectrom. 21, 384–395 (2006).
[CrossRef]

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

Bois, A.

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
[CrossRef]

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
[CrossRef]

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F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

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F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

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D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
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G. D’Ammando, L. Pietanza, G. Colonna, S. Longo, and M. Capitelli, “Modelling spectral properties of nonequilibrium atomic hydrogen plasma,” Spectrochim. Acta Part B 65, 120–129 (2010).
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A. Casavola, G. Colonna, and M. Capitelli,” Kinetic model of titanium laser induced plasma expansion in nitrogen environment,” Plasma Sources Sci. Technol. 18, 025027 (2009).
[CrossRef]

M. Capitelli, A. Casavola, G. Colonna, and A. De Giacomo, “Laser-induced plasma expansion: theoretical and experimental aspects,” Spectrochim. Acta B 59, 271–289 (2004).
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A. Casavola, G. Colonna, and M. Capitelli, “Nonequilibrium conditions during a laser induced plasma expansion,” Appl. Surf. Sci. 208, 85–89 (2003).
[CrossRef]

A. R. Casavola, G. De. Colonna, A. De Giacomo, O. Pascale, and M. Capitelli, “Experimental and theoretical investigation of laser-induced plasma of a titanium target,” Appl. Opt. 42, 5963–5970 (2003).
[CrossRef]

Casavola, A.

A. Casavola, G. Colonna, and M. Capitelli,” Kinetic model of titanium laser induced plasma expansion in nitrogen environment,” Plasma Sources Sci. Technol. 18, 025027 (2009).
[CrossRef]

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

A. Casavola, G. De. Colonna, A. Giacomo, and M. Capitelli, “Laser ablation of titanium metallic targets: comparison between theory and experiment,” J. Thermophys. Heat Transfer 17, 225–231 (2003).
[CrossRef]

A. Casavola, G. Colonna, and M. Capitelli, “Nonequilibrium conditions during a laser induced plasma expansion,” Appl. Surf. Sci. 208, 85–89 (2003).
[CrossRef]

Casavola, A. R.

Chen, Z.

A. Bogaerts, Z. Chen, and D. Bleiner, “Laser ablation of copper in different background gases: comparative study by numerical modeling and experiments,” J. Anal. At. Spectrom. 21, 384–395 (2006).
[CrossRef]

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

Chéron, B. G.

M. Ribière, B. G. Chéron, and A. Bultel, “Self-absorbed lines analysis of a recombining laser induced aluminum plasma,” High Temp. Mater. Process. 12, 109–120 (2008).
[CrossRef]

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G. Colonna, L. Pietanza, and G. D’Ammando, “Self-consistent collisional-radiative model for hydrogen atoms: atom–atom interaction and radiation transport,” Chem. Phys. 398, 37–45 (2012).
[CrossRef]

G. D’Ammando, L. Pietanza, G. Colonna, S. Longo, and M. Capitelli, “Modelling spectral properties of nonequilibrium atomic hydrogen plasma,” Spectrochim. Acta Part B 65, 120–129 (2010).
[CrossRef]

G. D’Ammando, G. Colonna, L. D. Pietanza, and M. Capitelli, “Computation of thermodynamic plasma properties: a simplified approach,” Spectrochim. Acta Part B 65, 603–615 (2010).
[CrossRef]

A. Casavola, G. Colonna, and M. Capitelli,” Kinetic model of titanium laser induced plasma expansion in nitrogen environment,” Plasma Sources Sci. Technol. 18, 025027 (2009).
[CrossRef]

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

A. Casavola, G. Colonna, and M. Capitelli, “Nonequilibrium conditions during a laser induced plasma expansion,” Appl. Surf. Sci. 208, 85–89 (2003).
[CrossRef]

Colonna, G. De.

A. R. Casavola, G. De. Colonna, A. De Giacomo, O. Pascale, and M. Capitelli, “Experimental and theoretical investigation of laser-induced plasma of a titanium target,” Appl. Opt. 42, 5963–5970 (2003).
[CrossRef]

A. Casavola, G. De. Colonna, A. Giacomo, and M. Capitelli, “Laser ablation of titanium metallic targets: comparison between theory and experiment,” J. Thermophys. Heat Transfer 17, 225–231 (2003).
[CrossRef]

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D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
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E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
[CrossRef]

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
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A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
[CrossRef]

D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
[CrossRef]

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G. Colonna, L. Pietanza, and G. D’Ammando, “Self-consistent collisional-radiative model for hydrogen atoms: atom–atom interaction and radiation transport,” Chem. Phys. 398, 37–45 (2012).
[CrossRef]

G. D’Ammando, L. Pietanza, G. Colonna, S. Longo, and M. Capitelli, “Modelling spectral properties of nonequilibrium atomic hydrogen plasma,” Spectrochim. Acta Part B 65, 120–129 (2010).
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G. D’Ammando, G. Colonna, L. D. Pietanza, and M. Capitelli, “Computation of thermodynamic plasma properties: a simplified approach,” Spectrochim. Acta Part B 65, 603–615 (2010).
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M. Capitelli, A. Casavola, G. Colonna, and A. De Giacomo, “Laser-induced plasma expansion: theoretical and experimental aspects,” Spectrochim. Acta B 59, 271–289 (2004).
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A. R. Casavola, G. De. Colonna, A. De Giacomo, O. Pascale, and M. Capitelli, “Experimental and theoretical investigation of laser-induced plasma of a titanium target,” Appl. Opt. 42, 5963–5970 (2003).
[CrossRef]

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B. Atalay, R. Aydin, A. Demir, N. Kenar, and E. Kacar, “Simulation of Ni-like and Co-like X-rays emitted from laser produced tin plasmas,” Czech. J. Phys. 56, B430–B435 (2006).
[CrossRef]

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F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
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A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
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A. M. El Sherbini, A. A. S. Al Amer, A. T. Hassan, and T. M. El Sherbini, “Spectrometric measurement of plasma parameters utilizing the target ambient gas O I & N I atomic lines in LIBS experiment,” Opt. Photon. J. 2, 286–293 (2012).

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A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
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H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
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H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
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O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
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O. Renner, J. Limpouch, E. Krousky, I. Uschmann, and E. Förster, “Spectroscopic characterization of plasma densities of laser-irradiated Al foils,” J. Quant. Spectrosc. Radiat. Transfer 81, 385–394 (2003).
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A. Casavola, G. De. Colonna, A. Giacomo, and M. Capitelli, “Laser ablation of titanium metallic targets: comparison between theory and experiment,” J. Thermophys. Heat Transfer 17, 225–231 (2003).
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A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?” Spectrochim. Acta Part B 58, 1867–1893 (2003).
[CrossRef]

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E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
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I. 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 Part B 56, 1769–1785 (2001).
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I. B. Gornushkin, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Line broadening mechanisms in the low pressure laser-induced plasma,” Spectrochim. Acta Part B 54, 1207–1217 (1999).
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A. M. El Sherbini, A. A. S. Al Amer, A. T. Hassan, and T. M. El Sherbini, “Spectrometric measurement of plasma parameters utilizing the target ambient gas O I & N I atomic lines in LIBS experiment,” Opt. Photon. J. 2, 286–293 (2012).

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D. Heading, J. Wark, G. Bennett, and R. Lee,” Simulations of spectra from dense aluminium plasmas,” J. Quant. Spectrosc. Radiat. Transfer. 54, 167–180 (1995).
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A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
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B. Atalay, R. Aydin, A. Demir, N. Kenar, and E. Kacar, “Simulation of Ni-like and Co-like X-rays emitted from laser produced tin plasmas,” Czech. J. Phys. 56, B430–B435 (2006).
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H. Y. Moon, K. H. Kathleen, N. Omenetto, B. W. Smith, and J. D. Winefordner, “On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 64, 702–713 (2009).

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E. Ershov-Pavlov, K. Y. Katsalap, K. Stepanov, and Y. A. Stankevich, “Time-space distribution of laser-induced plasma parameters and its influence on emission spectra of the laser plumes,” Spectrochim. Acta Part B 63, 1024–1037 (2008).
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B. Atalay, R. Aydin, A. Demir, N. Kenar, and E. Kacar, “Simulation of Ni-like and Co-like X-rays emitted from laser produced tin plasmas,” Czech. J. Phys. 56, B430–B435 (2006).
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I. B. Gornushkin, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Line broadening mechanisms in the low pressure laser-induced plasma,” Spectrochim. Acta Part B 54, 1207–1217 (1999).
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O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
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O. Renner, J. Limpouch, E. Krousky, I. Uschmann, and E. Förster, “Spectroscopic characterization of plasma densities of laser-irradiated Al foils,” J. Quant. Spectrosc. Radiat. Transfer 81, 385–394 (2003).
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D. Heading, J. Wark, G. Bennett, and R. Lee,” Simulations of spectra from dense aluminium plasmas,” J. Quant. Spectrosc. Radiat. Transfer. 54, 167–180 (1995).
[CrossRef]

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E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
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F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
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A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
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D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
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O. Renner, J. Limpouch, E. Krousky, I. Uschmann, and E. Förster, “Spectroscopic characterization of plasma densities of laser-irradiated Al foils,” J. Quant. Spectrosc. Radiat. Transfer 81, 385–394 (2003).
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G. D’Ammando, L. Pietanza, G. Colonna, S. Longo, and M. Capitelli, “Modelling spectral properties of nonequilibrium atomic hydrogen plasma,” Spectrochim. Acta Part B 65, 120–129 (2010).
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H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
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H. Y. Moon, K. H. Kathleen, N. Omenetto, B. W. Smith, and J. D. Winefordner, “On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 64, 702–713 (2009).

Mueller, M.

E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
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H. Y. Moon, K. H. Kathleen, N. Omenetto, B. W. Smith, and J. D. Winefordner, “On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 64, 702–713 (2009).

I. 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 Part B 56, 1769–1785 (2001).
[CrossRef]

I. B. Gornushkin, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Line broadening mechanisms in the low pressure laser-induced plasma,” Spectrochim. Acta Part B 54, 1207–1217 (1999).
[CrossRef]

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E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
[CrossRef]

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
[CrossRef]

D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
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A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy (Cambridge University, 2006).

Panne, U.

E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
[CrossRef]

Pardini, L.

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
[CrossRef]

Pascale, O.

Penalba, F.

C. Aragon, F. Penalba, and J. Aguilera, “Curves of growth of neutral atom and ion lines emitted by a laser induced plasma,” Spectrochim. Acta Part B 60, 879–887 (2005).
[CrossRef]

Pietanza, L.

G. Colonna, L. Pietanza, and G. D’Ammando, “Self-consistent collisional-radiative model for hydrogen atoms: atom–atom interaction and radiation transport,” Chem. Phys. 398, 37–45 (2012).
[CrossRef]

G. D’Ammando, L. Pietanza, G. Colonna, S. Longo, and M. Capitelli, “Modelling spectral properties of nonequilibrium atomic hydrogen plasma,” Spectrochim. Acta Part B 65, 120–129 (2010).
[CrossRef]

Pietanza, L. D.

G. D’Ammando, G. Colonna, L. D. Pietanza, and M. Capitelli, “Computation of thermodynamic plasma properties: a simplified approach,” Spectrochim. Acta Part B 65, 603–615 (2010).
[CrossRef]

Platt, D.

A. Vertes, R. Dreyfus, and D. Platt, “Modeling the thermal-to-plasma transitions for Cu photoablation,” IBM J. Res. Dev. 38, 3–10 (1994).
[CrossRef]

Poparic, G.

V. Milosavljevic and G. Poparic, “Atomic spectral line free parameter deconvolution procedure,” Phys. Rev. E 63, 036404 (2001).
[CrossRef]

Ralchenko, Y.

Y. Ralchenko, “NIST atomic spectra database,” Memorie della Societa Astronomica Italiana Supplementi 8, 96 (2005).

Ramos, A. A.

M. Elitzur and A. A. Ramos, “A new exact method for line radiative transfer,” Mon. Not. R. Astron. Soc. 365, 779 (2006).
[CrossRef]

Redon, R.

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
[CrossRef]

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
[CrossRef]

Renner, O.

O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
[CrossRef]

O. Renner, J. Limpouch, E. Krousky, I. Uschmann, and E. Förster, “Spectroscopic characterization of plasma densities of laser-irradiated Al foils,” J. Quant. Spectrosc. Radiat. Transfer 81, 385–394 (2003).
[CrossRef]

Rezaei, F.

F. Rezaei and S. H. Tavassoli, “Developing the model of laser ablation by considering the interplay between emission and expansion of aluminum plasma,” Phys. Plasmas 20, 013301 (2013).
[CrossRef]

F. Rezaei and S. H. Tavassoli, “Numerical and experimental investigation of laser induced plasma spectrum of aluminum in the presence of a noble gas,” Spectrochim. Acta B 78, 29–36 (2012).
[CrossRef]

F. Rezaei, M. Sharafkhani, and S. H. Tavassoli, “Numerical investigation of spatially resolved laser induced breakdown spectroscopy,” in Proc. Conf. 6th Euro-Mediterranean Symposiumon LIBS, Turkey2011.

Ribière, M.

M. Ribière, B. G. Chéron, and A. Bultel, “Self-absorbed lines analysis of a recombining laser induced aluminum plasma,” High Temp. Mater. Process. 12, 109–120 (2008).
[CrossRef]

Ripert, M.

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
[CrossRef]

Rocco, H. O.

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

Rosmej, F.

O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
[CrossRef]

Rossetto, B.

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
[CrossRef]

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
[CrossRef]

Salvetti, A.

E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
[CrossRef]

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
[CrossRef]

D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
[CrossRef]

Schechter, I.

A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy (Cambridge University, 2006).

Schott, R.

O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
[CrossRef]

Sharafkhani, M.

F. Rezaei, M. Sharafkhani, and S. H. Tavassoli, “Numerical investigation of spatially resolved laser induced breakdown spectroscopy,” in Proc. Conf. 6th Euro-Mediterranean Symposiumon LIBS, Turkey2011.

Silfvast, W. T.

W. T. Silfvast, Laser Fundamentals (Cambridge University, 1996) p. 105.

Singh, J. P.

J. P. Singh and S. N. Thakur, Laser-Induced Breakdown Spectroscopy (Elsevier, 2007), p. 424.

Smith, B. W.

H. Y. Moon, K. H. Kathleen, N. Omenetto, B. W. Smith, and J. D. Winefordner, “On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 64, 702–713 (2009).

I. 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 Part B 56, 1769–1785 (2001).
[CrossRef]

I. B. Gornushkin, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Line broadening mechanisms in the low pressure laser-induced plasma,” Spectrochim. Acta Part B 54, 1207–1217 (1999).
[CrossRef]

Smurov, I.

A. V. Gusarov and I. Smurov, “Thermal model of nanosecond pulsed laser ablation: analysis of energy and mass transfer,” J. Appl. Phys. 97, 0143071 (2005).

Sobral, H.

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

Stankevich, Y. A.

E. Ershov-Pavlov, K. Y. Katsalap, K. Stepanov, and Y. A. Stankevich, “Time-space distribution of laser-induced plasma parameters and its influence on emission spectra of the laser plumes,” Spectrochim. Acta Part B 63, 1024–1037 (2008).
[CrossRef]

Stepanov, K.

E. Ershov-Pavlov, K. Y. Katsalap, K. Stepanov, and Y. A. Stankevich, “Time-space distribution of laser-induced plasma parameters and its influence on emission spectra of the laser plumes,” Spectrochim. Acta Part B 63, 1024–1037 (2008).
[CrossRef]

Stevenson, C. L.

I. 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 Part B 56, 1769–1785 (2001).
[CrossRef]

Sun, L.

L. Sun and H. Yu, “Correction of self-absorption effect in calibration-free laser-induced breakdown spectroscopy by an internal reference method,” Talanta 79, 388–395 (2009).
[CrossRef]

Tavassoli, S. H.

F. Rezaei and S. H. Tavassoli, “Developing the model of laser ablation by considering the interplay between emission and expansion of aluminum plasma,” Phys. Plasmas 20, 013301 (2013).
[CrossRef]

F. Rezaei and S. H. Tavassoli, “Numerical and experimental investigation of laser induced plasma spectrum of aluminum in the presence of a noble gas,” Spectrochim. Acta B 78, 29–36 (2012).
[CrossRef]

S. Mehrabian, M. Aghaei, and S. H. Tavassoli, “Effect of background gas pressure and laser pulse intensity on laser induced plasma radiation of copper samples,” Phys. Plasmas 17, 043301 (2010).
[CrossRef]

M. Aghaei, S. Mehrabian, and S. H. Tavassoli, “Simulation of nanosecond pulsed laser ablation of copper samples: a focus on laser induced plasma radiation,” J. Appl. Phys. 104, 053303 (2008).
[CrossRef]

F. Rezaei, M. Sharafkhani, and S. H. Tavassoli, “Numerical investigation of spatially resolved laser induced breakdown spectroscopy,” in Proc. Conf. 6th Euro-Mediterranean Symposiumon LIBS, Turkey2011.

Tazeem, A.

C. Trassy and A. Tazeem, “Simulation of atomic and ionic absorption and emission spectra for thermal plasma diagnostics: application to a volatilization study in a plasma jet,” Spectrochim. Acta Part B 54, 581–602 (1999).
[CrossRef]

Thakur, S. N.

J. P. Singh and S. N. Thakur, Laser-Induced Breakdown Spectroscopy (Elsevier, 2007), p. 424.

Tognoni, E.

E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
[CrossRef]

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
[CrossRef]

D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
[CrossRef]

Trassy, C.

C. Trassy and A. Tazeem, “Simulation of atomic and ionic absorption and emission spectra for thermal plasma diagnostics: application to a volatilization study in a plasma jet,” Spectrochim. Acta Part B 54, 581–602 (1999).
[CrossRef]

Uschmann, I.

O. Renner, J. Limpouch, E. Krousky, I. Uschmann, and E. Förster, “Spectroscopic characterization of plasma densities of laser-irradiated Al foils,” J. Quant. Spectrosc. Radiat. Transfer 81, 385–394 (2003).
[CrossRef]

Vertes, A.

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

A. Vertes, R. Dreyfus, and D. Platt, “Modeling the thermal-to-plasma transitions for Cu photoablation,” IBM J. Res. Dev. 38, 3–10 (1994).
[CrossRef]

Wark, J.

D. Heading, J. Wark, G. Bennett, and R. Lee,” Simulations of spectra from dense aluminium plasmas,” J. Quant. Spectrosc. Radiat. Transfer. 54, 167–180 (1995).
[CrossRef]

Winefordner, J. D.

H. Y. Moon, K. H. Kathleen, N. Omenetto, B. W. Smith, and J. D. Winefordner, “On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 64, 702–713 (2009).

I. 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 Part B 56, 1769–1785 (2001).
[CrossRef]

I. B. Gornushkin, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Line broadening mechanisms in the low pressure laser-induced plasma,” Spectrochim. Acta Part B 54, 1207–1217 (1999).
[CrossRef]

Yu, H.

L. Sun and H. Yu, “Correction of self-absorption effect in calibration-free laser-induced breakdown spectroscopy by an internal reference method,” Talanta 79, 388–395 (2009).
[CrossRef]

Appl. Opt.

Appl. Surf. Sci.

A. Casavola, G. Colonna, and M. Capitelli, “Nonequilibrium conditions during a laser induced plasma expansion,” Appl. Surf. Sci. 208, 85–89 (2003).
[CrossRef]

Chem. Phys.

G. Colonna, L. Pietanza, and G. D’Ammando, “Self-consistent collisional-radiative model for hydrogen atoms: atom–atom interaction and radiation transport,” Chem. Phys. 398, 37–45 (2012).
[CrossRef]

Czech. J. Phys.

B. Atalay, R. Aydin, A. Demir, N. Kenar, and E. Kacar, “Simulation of Ni-like and Co-like X-rays emitted from laser produced tin plasmas,” Czech. J. Phys. 56, B430–B435 (2006).
[CrossRef]

High Temp. Mater. Process.

M. Ribière, B. G. Chéron, and A. Bultel, “Self-absorbed lines analysis of a recombining laser induced aluminum plasma,” High Temp. Mater. Process. 12, 109–120 (2008).
[CrossRef]

IBM J. Res. Dev.

A. Vertes, R. Dreyfus, and D. Platt, “Modeling the thermal-to-plasma transitions for Cu photoablation,” IBM J. Res. Dev. 38, 3–10 (1994).
[CrossRef]

J. Anal. At. Spectrom.

A. Bogaerts, Z. Chen, and D. Bleiner, “Laser ablation of copper in different background gases: comparative study by numerical modeling and experiments,” J. Anal. At. Spectrom. 21, 384–395 (2006).
[CrossRef]

J. Appl. Phys.

A. V. Gusarov and I. Smurov, “Thermal model of nanosecond pulsed laser ablation: analysis of energy and mass transfer,” J. Appl. Phys. 97, 0143071 (2005).

M. Aghaei, S. Mehrabian, and S. H. Tavassoli, “Simulation of nanosecond pulsed laser ablation of copper samples: a focus on laser induced plasma radiation,” J. Appl. Phys. 104, 053303 (2008).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

O. Renner, J. Limpouch, E. Krousky, I. Uschmann, and E. Förster, “Spectroscopic characterization of plasma densities of laser-irradiated Al foils,” J. Quant. Spectrosc. Radiat. Transfer 81, 385–394 (2003).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer.

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and P. Matheron, “Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma,” J. Quant. Spectrosc. Radiat. Transfer. 75, 747–763 (2002).
[CrossRef]

H. Amamou, A. Bois, B. Ferhat, R. Redon, B. Rossetto, and M. Ripert, “Correction of the self-absorption for reversed spectral lines: application to two resonance lines of neutral aluminium,” J. Quant. Spectrosc. Radiat. Transfer. 77, 365–372 (2003).
[CrossRef]

D. Heading, J. Wark, G. Bennett, and R. Lee,” Simulations of spectra from dense aluminium plasmas,” J. Quant. Spectrosc. Radiat. Transfer. 54, 167–180 (1995).
[CrossRef]

O. Renner, P. Adámek, P. Angelo, E. Dalimier, E. Förster, E. Krousky, F. Rosmej, and R. Schott, “Spectral line decomposition and frequency shifts in Al Heα group emission from laser-produced plasma,” J. Quant. Spectrosc. Radiat. Transfer. 99, 523–536 (2006).
[CrossRef]

J. R. Soc. Stat. Ser. C

R. O’Neill, “Algorithm AS 47: function minimization using a simplex procedure,” J. R. Soc. Stat. Ser. C 20, 338–345 (1971).

J. Thermophys. Heat Transfer

A. Casavola, G. De. Colonna, A. Giacomo, and M. Capitelli, “Laser ablation of titanium metallic targets: comparison between theory and experiment,” J. Thermophys. Heat Transfer 17, 225–231 (2003).
[CrossRef]

Memorie della Societa Astronomica Italiana Supplementi

Y. Ralchenko, “NIST atomic spectra database,” Memorie della Societa Astronomica Italiana Supplementi 8, 96 (2005).

Mon. Not. R. Astron. Soc.

M. Elitzur and A. A. Ramos, “A new exact method for line radiative transfer,” Mon. Not. R. Astron. Soc. 365, 779 (2006).
[CrossRef]

Opt. Photon. J.

A. M. El Sherbini, A. A. S. Al Amer, A. T. Hassan, and T. M. El Sherbini, “Spectrometric measurement of plasma parameters utilizing the target ambient gas O I & N I atomic lines in LIBS experiment,” Opt. Photon. J. 2, 286–293 (2012).

Phys. Plasmas

S. Mehrabian, M. Aghaei, and S. H. Tavassoli, “Effect of background gas pressure and laser pulse intensity on laser induced plasma radiation of copper samples,” Phys. Plasmas 17, 043301 (2010).
[CrossRef]

F. Rezaei and S. H. Tavassoli, “Developing the model of laser ablation by considering the interplay between emission and expansion of aluminum plasma,” Phys. Plasmas 20, 013301 (2013).
[CrossRef]

Phys. Rev. E

V. Milosavljevic and G. Poparic, “Atomic spectral line free parameter deconvolution procedure,” Phys. Rev. E 63, 036404 (2001).
[CrossRef]

Plasma Sources Sci. Technol.

A. Casavola, G. Colonna, and M. Capitelli,” Kinetic model of titanium laser induced plasma expansion in nitrogen environment,” Plasma Sources Sci. Technol. 18, 025027 (2009).
[CrossRef]

Rev. Mod. Phys.

R. D. Cowan and G. H. Dieke, “Self-absorption of spectrum lines,” Rev. Mod. Phys. 20, 418–455 (1948).
[CrossRef]

Spectrochim. Acta B

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

F. Rezaei and S. H. Tavassoli, “Numerical and experimental investigation of laser induced plasma spectrum of aluminum in the presence of a noble gas,” Spectrochim. Acta B 78, 29–36 (2012).
[CrossRef]

C. Aragon, J. Bengoechea, and J. A. Aguilera, “Influence of the optical depth on spectral line emission from laser-induced plasmas,” Spectrochim. Acta B 56, 619–628 (2001).
[CrossRef]

Spectrochim. Acta Part B

C. Aragon, F. Penalba, and J. Aguilera, “Curves of growth of neutral atom and ion lines emitted by a laser induced plasma,” Spectrochim. Acta Part B 60, 879–887 (2005).
[CrossRef]

J. Aguilera, J. Bengoechea, and C. Aragón, “Curves of growth of spectral lines emitted by a laser-induced plasma: influence of the temporal evolution and spatial inhomogeneity of the plasma,” Spectrochim. Acta Part B 58, 221–237 (2003).
[CrossRef]

J. Aguiler and C. Aragón, “Characterization of laser-induced plasmas by emission spectroscopy with curve-of-growth measurements. Part I: temporal evolution of plasma parameters and self-absorption,” Spectrochim. Acta Part B 63, 784–792 (2008).
[CrossRef]

E. Tognoni, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, M. Mueller, U. Panne, and I. Gornushkin, “A numerical study of expected accuracy and precision in calibration-free laser-induced breakdown spectroscopy in the assumption of ideal analytical plasma,” Spectrochim. Acta Part B 62, 1287–1302 (2007).
[CrossRef]

C. Trassy and A. Tazeem, “Simulation of atomic and ionic absorption and emission spectra for thermal plasma diagnostics: application to a volatilization study in a plasma jet,” Spectrochim. Acta Part B 54, 581–602 (1999).
[CrossRef]

G. D’Ammando, L. Pietanza, G. Colonna, S. Longo, and M. Capitelli, “Modelling spectral properties of nonequilibrium atomic hydrogen plasma,” Spectrochim. Acta Part B 65, 120–129 (2010).
[CrossRef]

E. Ershov-Pavlov, K. Y. Katsalap, K. Stepanov, and Y. A. Stankevich, “Time-space distribution of laser-induced plasma parameters and its influence on emission spectra of the laser plumes,” Spectrochim. Acta Part B 63, 1024–1037 (2008).
[CrossRef]

D. Bulajic, M. Corsi, G. Cristoforetti, S. Legnaioli, V. Palleschi, A. Salvetti, and E. Tognoni, “A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 57, 339–353 (2002).
[CrossRef]

I. 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 Part B 56, 1769–1785 (2001).
[CrossRef]

H. Y. Moon, K. H. Kathleen, N. Omenetto, B. W. Smith, and J. D. Winefordner, “On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 64, 702–713 (2009).

F. Bredice, F. O. Borges, H. Sobral, M. Di Villagran-Muniz, H. O. Rocco, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption of manganese emission lines in laser induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 61, 1294–1303 (2006).
[CrossRef]

A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy, G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini, A. Salvetti, and E. Tognoni, “Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta Part B 60, 1573–1579 (2005).
[CrossRef]

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

G. D’Ammando, G. Colonna, L. D. Pietanza, and M. Capitelli, “Computation of thermodynamic plasma properties: a simplified approach,” Spectrochim. Acta Part B 65, 603–615 (2010).
[CrossRef]

I. B. Gornushkin, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Line broadening mechanisms in the low pressure laser-induced plasma,” Spectrochim. Acta Part B 54, 1207–1217 (1999).
[CrossRef]

Spectrochim. Acta Part B.

A. Alonso-Medina, “Experimental determination of the Stark widths of Pb I spectral lines in a laser-induced plasma,” Spectrochim. Acta Part B. 63, 598–602 (2008).
[CrossRef]

Talanta

L. Sun and H. Yu, “Correction of self-absorption effect in calibration-free laser-induced breakdown spectroscopy by an internal reference method,” Talanta 79, 388–395 (2009).
[CrossRef]

Other

W. Lochte-Holtgreven, Plasma Diagnostics (Wiley Interscience, 1968).

A. N. Cox, Allen’s Astrophysical Quantities (Springer, 1999).

D. Diver, A Plasma Formulary for Physics, Technology, and Astrophysics (Wiley-VCH, 2011).

J. P. Singh and S. N. Thakur, Laser-Induced Breakdown Spectroscopy (Elsevier, 2007), p. 424.

A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy (Cambridge University, 2006).

W. T. Silfvast, Laser Fundamentals (Cambridge University, 1996) p. 105.

F. Rezaei, M. Sharafkhani, and S. H. Tavassoli, “Numerical investigation of spatially resolved laser induced breakdown spectroscopy,” in Proc. Conf. 6th Euro-Mediterranean Symposiumon LIBS, Turkey2011.

H. R. Griem, Plasma Spectroscopy (McGraw-Hill, 1964).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of plasma expansion in one dimension.

Fig. 2.
Fig. 2.

Time and space dependence of plasma temperature in ambient gases of (a) and (b) helium and (c) and (d) argon, at laser intensities of 0.7 and 0.9GW/cm2.

Fig. 3.
Fig. 3.

Temporal distribution of aluminum spectrum at different delay times of t1=30, t2=50, t3=100, t4=150, and t5=200ns in (a) and (b) helium and (c) and (d) argon, and at laser energies of 0.7 and 0.9GW/cm2.

Fig. 4.
Fig. 4.

Comparison between aluminum radiations in two conditions of thin and thick plasma, in (a) helium and (b) argon gases, at laser energy of 0.7GW/cm2, and at a delay time of 100 ns in a logarithmic scale.

Fig. 5.
Fig. 5.

Self-absorption coefficient variation of spectral lines of 308.22, 309.27, 394.40, and 396.15 nm with delay time, in (a) and (b) helium and (c) and (d) argon noble gases and at laser irradiances of 0.7 and 0.9GW/cm2.

Fig. 6.
Fig. 6.

Self-reversal behavior of the lines of 394.40 and 396.15 nm, at different laser energies of 0.5, 0.7, 0.9, and 1.1GW/cm2 in (a) helium and (b) argon gas.

Fig. 7.
Fig. 7.

Self-absorption emission of the lines of 308.22, 309.27, 396.15, 281.62, and 394.40 nm as a function of laser energy in (a) helium and (b) argon gases at delay time of 150 ns.

Fig. 8.
Fig. 8.

Continuous emission variation of aluminum as a function of laser energy in (a) helium and (b) argon at a delay time of 100 ns.

Tables (3)

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Table 1. Spectral Lines Parameters Including Wavelength, Transition Probability, Lower and Upper Energy Levels, and Degeneracy of Upper Level [37]

Tables Icon

Table 2. Some Self-Absorption Coefficients for Different Spectral Lines at Several Delay Times in Helium Gas at 1.1GW/cm2

Tables Icon

Table 3. Self-Absorption Parameters of Some Spectral Lines at Different Delay Times in Argon Ambient Gas at 1.1GW/cm2

Equations (22)

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SA=I(λj)I0(λj),
t(Uint+12ρv2)+x[(Uint+12ρv2)v+Pv](αIB+αPI)I+Erad+x(q)=0.
Erad=Espec+Ebrems+Erecom.
Uint=32(nAl+ngas+ne)kBT+IPAlnAl++(IPAl+IPAl+)nAl+++IPgasngas+Eexc.
Eexc=nAlEex,Al(1xAl+xAl++)+nAlEex,Al+xAl++ngasEex,gas(1xgas+)+ngasEex,gas+xgas+,
εspecj(ν)=NuAuljhνjLj(ν,νj,γulj),
Nu=NtotgueEujkBTZ,
Lj(ν,νj,γulj)=(γulj4π2)(ννj)2+(γulj4π)2.
γulj=2π(c/λj2)Δλstarkj.
Δλstark=2ωnenref,
Inonselfabsorb(ν)=k=1ksj=1Nsεspecj(ν).
I(1)=εspec(1)=j=1NsNu(1)AuljhνjLj(1)(ν,νj,γulj).
I(2)=j=1NsNu(2)AuljhνjLj(2)(ν,νj,γulj)+εspec(1)ek(2)dx=εspec(2)+I(1)ek(2)dx.
I(n)=j=1NsNu(n)AuljhνjLj(n)(ν,νj,γulj)+I(n1)ek(n)dx=εspec(n)+I(n1)ek(n)dx.
k(n)=hνjc(BulNlBluNu)Lj(n)(ν,νj,γulj).
Aul=glguBlu8πhν3c3,guBul=glBlu.
k(n)=guAulNtotλ28πZeElkBT(1ehνkBT)Lj(n)(ν,νj,γulj).
Iselfabsorb=ε(250)+I(249)ek(250)dx.
Ibrems(ν)=ptothkBTehνkBT.
ptot=mnmzm2nee624π2ε03c3mekBTme,
Irecom=ptothkBTehvkBTeχmTχmTξn3.
Itot(v,t,x)=Ibrems(v,t,x)+Irecom(v,t,x)+Ispectral(v,t,x).

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