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.

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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. SPIE5414, 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. SPIE4882, 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. SPIE4168, 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. SPIE3493, 231–236 (1998).
    [CrossRef]
  6. G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE5414, 1–25 (2004).
    [CrossRef]
  7. F. Bachmann, “High Power Laser Sources for Industry and their Applications,” Proc. SPIE6735, 1–13 (2007).
  8. V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE6101, 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. SPIE5137, 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. SPIE6735, 1–13 (2007).

2006 (1)

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE6101, 1–9 (2006).

2004 (2)

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE5414, 1–25 (2004).
[CrossRef]

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE5414, 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. SPIE4882, 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. SPIE5137, 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. SPIE4168, 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. SPIE3493, 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. SPIE4882, 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. SPIE6735, 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. SPIE5137, 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. SPIE4882, 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. SPIE3493, 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. SPIE3493, 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. SPIE4168, 232–235 (2001).
[CrossRef]

Goda, M.

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE5414, 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. SPIE5414, 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. SPIE3493, 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. SPIE4168, 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. SPIE5414, 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. SPIE5137, 303–310 (2003).
[CrossRef]

Panchenko, A. N.

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE6101, 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. SPIE5137, 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. SPIE4882, 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. SPIE5414, 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. SPIE4168, 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. SPIE3493, 231–236 (1998).
[CrossRef]

Perram, G. P.

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE5414, 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. SPIE4168, 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. SPIE3493, 231–236 (1998).
[CrossRef]

Tarasenko, V. F.

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE6101, 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. SPIE5137, 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. SPIE4882, 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. SPIE4168, 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. SPIE3493, 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. SPIE5414, 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. SPIE5414, 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. SPIE5137, 303–310 (2003).
[CrossRef]

G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE5414, 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. SPIE4882, 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. SPIE4168, 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. SPIE3493, 231–236 (1998).
[CrossRef]

G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE5414, 1–25 (2004).
[CrossRef]

F. Bachmann, “High Power Laser Sources for Industry and their Applications,” Proc. SPIE6735, 1–13 (2007).

V. F. Tarasenko and A. N. Panchenko, “Efficient discharge-pumped non-chain HF and DF lasers,” Proc. SPIE6101, 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.

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

Photon number density of the vibrational levels as a function of time

Fig. 4
Fig. 4

Dependences of the photon number density on time for different density of D2

Fig. 5
Fig. 5

Dependence of photon number density on time

Fig. 6
Fig. 6

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

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.

Fig. 8
Fig. 8

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

Fig. 9
Fig. 9

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

Fig. 10
Fig. 10

Laser pulse shape (a) experimental result (b) calculated result

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 ( v1 ) + DF
DF ( v ) + D 2 DF ( v1 ) + D 2
DF ( v ) + D DF ( v1 ) + D
DF ( v ) + F DF ( v1 ) + F  (v=1,2,3,4)
DF ( v ) + hυ DF ( v1 ) + 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,v1 [ DF( v ) ]+ σ v c( [ DF( v ) ][ DF( v1 ) ] ) q v + clnR 2L q v
n e ( t )= N 0 sin(πt/T)rect(t/T0.5)
q= v=1 v=4 q v
P out = S 2 hvqclnR
E=hv clnR 2L qdVdt
n(0)= p N A / ( RT )

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