Abstract

Computer simulation and experimental study of a pulsed electrical-discharge DF laser pumped by the SF6-D2 non-chain reaction are presented. The computer model encompassing 28 reactions is based on laser rate equations theory, and applied to approximately describe the chemical processes of non-chain DF laser. A comprehensive study of the dependence of number density on time for all particles in the gain area is conducted by numerical calculation adopting Runge-Kutta method. The output performance of non-chain pulsed DF laser as a function of the output mirror reflectivity and the mixture ratio are analyzed. The calculation results are compared with experimental data, showing good agreement with each other. Both the theoretical analysis and experimental results present that the laser output performance can be improved by optimizing the mixture ratio and output mirror reflectivity. The optimum values of mixture ratio and output mirror reflectivity are respectively 10:1 and 30%. The single pulse energy of 4.95J, pulse duration of 148.8ns and peak power of 33.27 MW are achieved under the optimum conditions.

©2012 Optical Society of America

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References

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  1. G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE 5414, 41–51 (2004).
    [Crossref]
  2. B. Bravy, G. Vasiliev, V. Agroskin, and V. Papin, “Recognition of Composition and of Microphysical Characteristics of Aerosol Clouds in Multifrequency Sounding with DF Laser Based Lidar System,” Proc. SPIE 4882, 394–399 (2003).
    [Crossref]
  3. A. J. Beaulieu, J. A. Nilson, and K. O. Tan, “A practical DF laser for ranging applications,” in Proceedings of Laser Rader Technology and Applications, (Quebec, Canada, 1986), 8–13.
  4. V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
    [Crossref]
  5. S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
    [Crossref]
  6. G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE 5414, 1–25 (2004).
    [Crossref]
  7. F. Bachmann, “High Power Laser Sources for Industry and their Applications,” Proc. SPIE 6735, 1–13 (2007).
  8. V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE 6101, 1–9 (2006).
  9. A. A. Belevtsev, S. Yu. Kazantsev, I. G. Kononov, and K. N. Firsov, “Detachment instability of self-sustained volume discharge in active media of non-chain HF (DF) lasers,” Quantum Electron. 40(6), 484–489 (2010).
    [Crossref]
  10. V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
    [Crossref]
  11. R. W. Gross and J. F. Bott, Handbook of Chemical Lasers (John Wiley & Sons Ltd., 1976), Chap. 8.
  12. A. N. Panchenko, V. M. Orlovskii, V. F. Tarasenko, and E. H. Baksht, “Efficient operation modes of a non-chain HF laser pumped by self-sustained discharge,” Proc. SPIE 5137, 303–310 (2003).
    [Crossref]
  13. D. S. Perry and J. C. Polanyi, “Energy distribution among reaction products, IX. F+H2, HF, and D,” J. Chem. Phys. 57(4), 1574–1586 (1972).
    [Crossref]
  14. K. L. Kompa, Chemical Lasers (Springer-Verlag, 1973).
  15. E. Arunan, D. W. Setser, and J. F. Ogilvie, “Vibration-rotational Einstein coefficients for HF /DF and HCI/DCI,” J. Chem. Phys. 97(3), 1734–1741 (1992).
    [Crossref]

2010 (2)

A. A. Belevtsev, S. Yu. Kazantsev, I. G. Kononov, and K. N. Firsov, “Detachment instability of self-sustained volume discharge in active media of non-chain HF (DF) lasers,” Quantum Electron. 40(6), 484–489 (2010).
[Crossref]

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

2007 (1)

F. Bachmann, “High Power Laser Sources for Industry and their Applications,” Proc. SPIE 6735, 1–13 (2007).

2006 (1)

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE 6101, 1–9 (2006).

2004 (2)

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE 5414, 1–25 (2004).
[Crossref]

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE 5414, 41–51 (2004).
[Crossref]

2003 (2)

B. Bravy, G. Vasiliev, V. Agroskin, and V. Papin, “Recognition of Composition and of Microphysical Characteristics of Aerosol Clouds in Multifrequency Sounding with DF Laser Based Lidar System,” Proc. SPIE 4882, 394–399 (2003).
[Crossref]

A. N. Panchenko, V. M. Orlovskii, V. F. Tarasenko, and E. H. Baksht, “Efficient operation modes of a non-chain HF laser pumped by self-sustained discharge,” Proc. SPIE 5137, 303–310 (2003).
[Crossref]

2001 (1)

V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
[Crossref]

1998 (1)

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

1992 (1)

E. Arunan, D. W. Setser, and J. F. Ogilvie, “Vibration-rotational Einstein coefficients for HF /DF and HCI/DCI,” J. Chem. Phys. 97(3), 1734–1741 (1992).
[Crossref]

1972 (1)

D. S. Perry and J. C. Polanyi, “Energy distribution among reaction products, IX. F+H2, HF, and D,” J. Chem. Phys. 57(4), 1574–1586 (1972).
[Crossref]

Agroskin, V.

B. Bravy, G. Vasiliev, V. Agroskin, and V. Papin, “Recognition of Composition and of Microphysical Characteristics of Aerosol Clouds in Multifrequency Sounding with DF Laser Based Lidar System,” Proc. SPIE 4882, 394–399 (2003).
[Crossref]

Arunan, E.

E. Arunan, D. W. Setser, and J. F. Ogilvie, “Vibration-rotational Einstein coefficients for HF /DF and HCI/DCI,” J. Chem. Phys. 97(3), 1734–1741 (1992).
[Crossref]

Bachmann, F.

F. Bachmann, “High Power Laser Sources for Industry and their Applications,” Proc. SPIE 6735, 1–13 (2007).

Baksht, E. H.

A. N. Panchenko, V. M. Orlovskii, V. F. Tarasenko, and E. H. Baksht, “Efficient operation modes of a non-chain HF laser pumped by self-sustained discharge,” Proc. SPIE 5137, 303–310 (2003).
[Crossref]

Belevtsev, A. A.

A. A. Belevtsev, S. Yu. Kazantsev, I. G. Kononov, and K. N. Firsov, “Detachment instability of self-sustained volume discharge in active media of non-chain HF (DF) lasers,” Quantum Electron. 40(6), 484–489 (2010).
[Crossref]

Bravy, B.

B. Bravy, G. Vasiliev, V. Agroskin, and V. Papin, “Recognition of Composition and of Microphysical Characteristics of Aerosol Clouds in Multifrequency Sounding with DF Laser Based Lidar System,” Proc. SPIE 4882, 394–399 (2003).
[Crossref]

Bulaev, V. D.

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

Elutin, A. S.

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

Firsov, K. N.

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

A. A. Belevtsev, S. Yu. Kazantsev, I. G. Kononov, and K. N. Firsov, “Detachment instability of self-sustained volume discharge in active media of non-chain HF (DF) lasers,” Quantum Electron. 40(6), 484–489 (2010).
[Crossref]

Frolov, Y. N.

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

Frolov, Yu. N.

V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
[Crossref]

Goda, M.

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE 5414, 1–25 (2004).
[Crossref]

Graves, B. R.

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE 5414, 41–51 (2004).
[Crossref]

Gusev, V. S.

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

Kazantsev, S. Yu.

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

A. A. Belevtsev, S. Yu. Kazantsev, I. G. Kononov, and K. N. Firsov, “Detachment instability of self-sustained volume discharge in active media of non-chain HF (DF) lasers,” Quantum Electron. 40(6), 484–489 (2010).
[Crossref]

Kononov, I. G.

A. A. Belevtsev, S. Yu. Kazantsev, I. G. Kononov, and K. N. Firsov, “Detachment instability of self-sustained volume discharge in active media of non-chain HF (DF) lasers,” Quantum Electron. 40(6), 484–489 (2010).
[Crossref]

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

Kudryashov, E. A.

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

Lazarenko, V. I.

V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
[Crossref]

Lysenko, S. L.

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

Marciniak, M. A.

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE 5414, 1–25 (2004).
[Crossref]

Morozov, Yu. B.

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

Ogilvie, J. F.

E. Arunan, D. W. Setser, and J. F. Ogilvie, “Vibration-rotational Einstein coefficients for HF /DF and HCI/DCI,” J. Chem. Phys. 97(3), 1734–1741 (1992).
[Crossref]

Orlovskii, V. M.

A. N. Panchenko, V. M. Orlovskii, V. F. Tarasenko, and E. H. Baksht, “Efficient operation modes of a non-chain HF laser pumped by self-sustained discharge,” Proc. SPIE 5137, 303–310 (2003).
[Crossref]

Panchenko, A. N.

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE 6101, 1–9 (2006).

A. N. Panchenko, V. M. Orlovskii, V. F. Tarasenko, and E. H. Baksht, “Efficient operation modes of a non-chain HF laser pumped by self-sustained discharge,” Proc. SPIE 5137, 303–310 (2003).
[Crossref]

Papin, V.

B. Bravy, G. Vasiliev, V. Agroskin, and V. Papin, “Recognition of Composition and of Microphysical Characteristics of Aerosol Clouds in Multifrequency Sounding with DF Laser Based Lidar System,” Proc. SPIE 4882, 394–399 (2003).
[Crossref]

Patterson, S. P.

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE 5414, 41–51 (2004).
[Crossref]

Pegoev, I. N.

V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
[Crossref]

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

Perram, G. P.

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE 5414, 1–25 (2004).
[Crossref]

Perry, D. S.

D. S. Perry and J. C. Polanyi, “Energy distribution among reaction products, IX. F+H2, HF, and D,” J. Chem. Phys. 57(4), 1574–1586 (1972).
[Crossref]

Polanyi, J. C.

D. S. Perry and J. C. Polanyi, “Energy distribution among reaction products, IX. F+H2, HF, and D,” J. Chem. Phys. 57(4), 1574–1586 (1972).
[Crossref]

Poznyshev, A. N.

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

Setser, D. W.

E. Arunan, D. W. Setser, and J. F. Ogilvie, “Vibration-rotational Einstein coefficients for HF /DF and HCI/DCI,” J. Chem. Phys. 97(3), 1734–1741 (1992).
[Crossref]

Sinkov, S. N.

V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
[Crossref]

Sin'kov, S. N.

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

Tarasenko, V. F.

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE 6101, 1–9 (2006).

A. N. Panchenko, V. M. Orlovskii, V. F. Tarasenko, and E. H. Baksht, “Efficient operation modes of a non-chain HF laser pumped by self-sustained discharge,” Proc. SPIE 5137, 303–310 (2003).
[Crossref]

Vasiliev, G.

B. Bravy, G. Vasiliev, V. Agroskin, and V. Papin, “Recognition of Composition and of Microphysical Characteristics of Aerosol Clouds in Multifrequency Sounding with DF Laser Based Lidar System,” Proc. SPIE 4882, 394–399 (2003).
[Crossref]

Velikanov, S. D.

V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
[Crossref]

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

Wank, R. H.

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE 5414, 41–51 (2004).
[Crossref]

Wilson, G.

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE 5414, 41–51 (2004).
[Crossref]

J. Chem. Phys. (2)

D. S. Perry and J. C. Polanyi, “Energy distribution among reaction products, IX. F+H2, HF, and D,” J. Chem. Phys. 57(4), 1574–1586 (1972).
[Crossref]

E. Arunan, D. W. Setser, and J. F. Ogilvie, “Vibration-rotational Einstein coefficients for HF /DF and HCI/DCI,” J. Chem. Phys. 97(3), 1734–1741 (1992).
[Crossref]

Proc. SPIE (8)

A. N. Panchenko, V. M. Orlovskii, V. F. Tarasenko, and E. H. Baksht, “Efficient operation modes of a non-chain HF laser pumped by self-sustained discharge,” Proc. SPIE 5137, 303–310 (2003).
[Crossref]

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE 5414, 41–51 (2004).
[Crossref]

B. Bravy, G. Vasiliev, V. Agroskin, and V. Papin, “Recognition of Composition and of Microphysical Characteristics of Aerosol Clouds in Multifrequency Sounding with DF Laser Based Lidar System,” Proc. SPIE 4882, 394–399 (2003).
[Crossref]

V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO2 remote sensing in the atmosphere,” Proc. SPIE 4168, 232–235 (2001).
[Crossref]

S. D. Velikanov, A. S. Elutin, E. A. Kudryashov, I. N. Pegoev, S. N. Sin'kov, and Y. N. Frolov, “DF laser application for hydrocarbon control in the atmosphere,” Proc. SPIE 3493, 231–236 (1998).
[Crossref]

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE 5414, 1–25 (2004).
[Crossref]

F. Bachmann, “High Power Laser Sources for Industry and their Applications,” Proc. SPIE 6735, 1–13 (2007).

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE 6101, 1–9 (2006).

Quantum Electron. (2)

A. A. Belevtsev, S. Yu. Kazantsev, I. G. Kononov, and K. N. Firsov, “Detachment instability of self-sustained volume discharge in active media of non-chain HF (DF) lasers,” Quantum Electron. 40(6), 484–489 (2010).
[Crossref]

V. D. Bulaev, V. S. Gusev, S. Yu. Kazantsev, I. G. Kononov, S. L. Lysenko, Yu. B. Morozov, A. N. Poznyshev, and K. N. Firsov, “High-power repetitively pulsed electric-discharge HF laser,” Quantum Electron. 40(7), 615–618 (2010).
[Crossref]

Other (3)

R. W. Gross and J. F. Bott, Handbook of Chemical Lasers (John Wiley & Sons Ltd., 1976), Chap. 8.

A. J. Beaulieu, J. A. Nilson, and K. O. Tan, “A practical DF laser for ranging applications,” in Proceedings of Laser Rader Technology and Applications, (Quebec, Canada, 1986), 8–13.

K. L. Kompa, Chemical Lasers (Springer-Verlag, 1973).

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Figures (10)

Fig. 1
Fig. 1 Number density versus time for SF6, F, D2 and D.

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Fig. 2
Fig. 2 Populations of the vibrational levels as a function of time after onset of electrical discharge.

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Fig. 3
Fig. 3 Photon number density of the vibrational levels as a function of time

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Fig. 4
Fig. 4 Dependences of the photon number density on time for different density of D2

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Fig. 5
Fig. 5 Dependence of photon number density on time

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Fig. 6
Fig. 6 Dependences of the output laser power on time for different output mirror reflectivity

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Fig. 7
Fig. 7 Optical experimental setup: (1) main electrodes; (2) preionization pins; (3) rear mirror; (4) output mirror; (5) beam-splitting mirror; (6) laser energy meter; (7) attenuators; (8) HgCdTe detector; (9) oscilloscope.

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Fig. 8
Fig. 8 Fitting curves of calculated and experimental laser pulse energy versus the density of D2

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Fig. 9
Fig. 9 Fitting curves of calculated and experimental laser pulse energy versus output mirror reflectivity

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Fig. 10
Fig. 10 Laser pulse shape (a) experimental result (b) calculated result

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Equations (24)

Equations on this page are rendered with MathJax. Learn more.

SF 6 + e → SF 5 + F + e
SF 6 + e → SF 5 + + F + 2e
SF 6 + e → SF 4 +2F+ e
F+ D 2 →DF ( v ) +D  (v=0,1,2,3,4)
DF ( v ) + DF → DF ( v−1 ) + DF
DF ( v ) + D 2 → DF ( v−1 ) + D 2
DF ( v ) + D → DF ( v−1 ) + D
DF ( v ) + F → DF ( v−1 ) + F  (v=1,2,3,4)
DF ( v ) + hυ → DF ( v−1 ) + 2hυ  (v=1,2,3,4)
d[ SF 6 ] dt =− k e n e [ SF 6 ]
d[F] dt = k e n e [ SF 6 ]−k[ D 2 ][ F ]
d[D 2 ] dt =−k[ D 2 ][ F ]
d[D] dt =k[ D 2 ][ F ]
d[ DF( 4 ) ] dt = k 4 [ D 2 ][ F ]− σ 4 c( [ DF( 4 ) ]−[ DF( 3 ) ] ) q 4 − ∑ i k 4i [ DF( 4 ) ] [ M i ]
d[ DF( 3 ) ] dt = k 3 [ D 2 ][ F ]+ σ 4 c( [ DF( 4 ) ]−[ DF( 3 ) ] ) q 4 + ∑ i k 4i [ DF( 4 ) ] [ M i ] − σ 3 c( [ DF( 3 ) ]−[ DF( 2 ) ] ) q 3 − ∑ i k 3i [ DF( 3 ) ] [ M i ]
d[ DF( 2 ) ] dt = k 2 [ D 2 ][ F ]+ σ 3 c( [ DF( 3 ) ]−[ DF( 2 ) ] ) q 3 + ∑ i k 3i [ DF( 3 ) ] [ M i ] − σ 2 c( [ DF( 2 ) ]−[ DF( 1 ) ] ) q 2 − ∑ i k 2i [ DF( 2 ) ] [ M i ]
d[ DF( 1 ) ] dt = k 1 [ D 2 ][ F ]+ σ 2 c( [ DF( 2 ) ]−[ DF( 1 ) ] ) q 2 + ∑ i k 2i [ DF( 2 ) ] [ M i ] − σ 1 c( [ DF( 1 ) ]−[ DF( 0 ) ] ) q 1 − ∑ i k 1i [ DF( 1 ) ] [ M i ]
d[ DF( 0 ) ] dt = k 0 [ D 2 ][ F ]+ σ 1 c( [ DF( 1 ) ]−[ DF( 0 ) ] ) q 1 + ∑ i k 1i [ DF( 1 ) ] [ M i ]
d q v dt = A v,v−1 [ DF( v ) ]+ σ v c( [ DF( v ) ]−[ DF( v−1 ) ] ) q v + clnR 2L q v
n e ( t )= N 0 sin(πt/T)rect(t/T−0.5)
q= ∑ v=1 v=4 q v
P out =− S 2 hvqclnR
E=hv ∬ clnR 2L qdVdt ​
n(0)= p⋅ N A / ( R⋅T )

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