## Computer modeling and experimental study of non-chain pulsed electric-discharge DF laser |

Optics Express, Vol. 20, Issue 27, pp. 28912-28922 (2012)

http://dx.doi.org/10.1364/OE.20.028912

Acrobat PDF (1382 KB)

### Abstract

Computer simulation and experimental study of a pulsed electrical-discharge DF laser pumped by the SF_{6}-D_{2} 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 OSA

## 1. Introduction

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}+ D

_{2}, which has the risk of premature ignition and explosion. On the contrary non-chain pulsed DF laser has no risk of corrosion and explosion. Besides, it has other advantages, such as compact structure, easy operation, good beam quality, high peak power, high energy, etc. Non-chain DF laser becomes more attractive due to all these advantages [8–10

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]

_{6}and D

_{2}, the reactions contained in this model are as follows:

_{2}and the production rate of F; the de-excitation rate mainly depends on relaxation effects of ground state DF, D

_{2}, D and F on the excited DF through collision processes. Accordingly, the ratio of SF

_{6}-D

_{2}mixture should be properly selected for optimizing the output performance of DF laser.

_{6}-D

_{2}electric-discharge chemical laser.

## 2. Computer model

_{6}by electrons collision; 3) F atoms form instantaneously after electrical discharge and distribute homogeneously in the gain area; 4) The gas temperature in the stimulated radiation transition process keeps unchanged.

*k*

_{e}is the rate constant for dissociation of F from SF

_{6}by electrons collision,

*k*

_{e}= 0.15 × 10

^{−7}cm

^{3}/s [12

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]

*k*is the total reaction rate constant of the reaction F + D

_{2}→DF + D,

*k*

_{v}is the individual vibrational rate constants, and

*k*=

*k*

_{0}+

*k*

_{1}+

*k*

_{2}+

*k*

_{3}+

*k*

_{4}.

*M*

_{i}(i = 1, 2, 3, 4) is the number density of particle

*i*which is effective in relaxation of excited DF. These de-excitation particles in turn are ground state DF, D

_{2}, D and F.

*k*

_{vi}is the relaxation rate constant for vibrational level v caused by species

*i*. The formation and de-excitation rate constants for DF are calculated by the formula given by Perry and Polanyi [13

13. D. S. Perry and J. C. Polanyi, “Energy distribution among reaction products, IX. F+H_{2}, HF, and D,” J. Chem. Phys. **57**(4), 1574–1586 (1972). [CrossRef]

*σ*

_{v}is the cross-section for stimulated emission of vibrational level v, the value of

*σ*

_{v}is 10

^{−18}~10

^{−16}cm

^{2}[14].

*A*

_{v,v-1}is the spontaneous emission coefficient of vibrational level v, and

*A*

_{4,3}= 155.1 s

^{−1},

*A*

_{3,2}= 131.5 s

^{−1},

*A*

_{2,1}= 98.1 s

^{−1},

*A*

_{1,0}= 54.5 s

^{−1}[15

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]

*n*

_{e}is the number density of electrons per unit volume, which is given by a approximation formula:

*N*

_{0}is chosen as 4.864 × 10

^{12},

*T*is the duration of current pulse.

*q*

_{v}is the photon number density from stimulated transitions v→v-1, so the total photon number density can be read as:The laser output power can be expressed as:The single pulse laser energy can be expressed as:Where

*h*is the Plank’s constant,

*v*is the center frequency of DF laser,

*c*is the speed of light,

*R*is the reflectivity of output mirror,

*L*is the length of laser cavity,

*S*and

*V*are respectively the gain cross section and gain volume. Supposing the initial pressures of working mixture SF

_{6}and D

_{2}are

*p*

_{1},

*p*

_{2}, and then the initial number density can be calculated by the formula:Where

*N*

_{A}is the Avogadro’s number,

*R*is the Gas constant, and

*T*is the temperature of the reacting mixture with the value of 300K.The initial number density of other dependent variables is zero. With the above rate constants and initial values, the model can be solved numerically using the Runge-Kutta method.

## 3. Numerical calculations and discussion

_{6}and D

_{2}respectively are 10000Pa, 1000Pa, whose initial number density calculated by Eq. (15) are 2.4143 × 10

^{18}cm

^{−3}and 2.4143 × 10

^{17}cm

^{−3}. Figure 1 shows the time histories of the number density of SF

_{6}, F, D

_{2}and D when the reflectivity of output mirror is 30%.

_{6}and D

_{2}decrease rapidly over time and reach a particular value finally. While the density of F increases sharply to a peak value and then decreases to zero. Besides, the density of D experiences a rapid growth and a slow growth and finally tends to a constant value, which has no decrease in the whole process. These can be explained as follows: (1) during the entire process the reactants only are consumed and have no generation, so their densities decrease gradually. (2) A large number of energetic electrons rapidly generate in the gain region after onset of electric discharge, which make the SF

_{6}dissociate to F by impacting. The generation rate of F is larger than the reaction consumption rate, so the density of F rises rapidly. While with the continuing of electric discharge, the density of F grows slowly as the number density of high energy electrons decreases. The density of F tends to zero ultimately due to reaction consumption and the termination of electric discharge. (3) D atoms have a sustained generation from the chemical reaction and no consumption, so its number density increases continuously till the end of chemical reactions.

_{6}-D

_{2}mixture is one of the important factors that affect the output performance of DF laser, so it is necessary to investigate the dependence of photon number density on the mixture ratio. Keeping the partial pressure of SF

_{6}as 10kPa, the theoretical calculations were carried out with the mixture ratio varying among 4:1, 6:1, 8:1, 10:1, 12:1 and 15:1. Figure 4 presents the calculated results.

_{6}and the same reflectivity of output mirror, the photon number density increases rapidly with the increase of the density of D

_{2}first; when the density of D

_{2}is 2.4143 × 10

^{17}cm

^{−3}, at which the mixture ratio is SF

_{6}: D

_{2}= 10:1, the photon number density reaches the maximum; later it decreases with the increase of D

_{2}. The density of F produced by dissociating of SF

_{6}is constant at the same discharge conditions when the density of SF

_{6}is invariable. When the density of D

_{2}is small, there is not enough D

_{2}to react with F which results in generation of a few excited DF, besides the excess F atoms have de-excitation effect on excited DF, and thus the inverted population density of DF is small, which causes the lower photon number density. As the density of D

_{2}increases, the density of excited DF increases and the number of residual F decreases owing to chemical reaction with D

_{2}, so the de-excitation effect of F gets weaken and the number of F and D

_{2}is gradually matching. When the number density of D

_{2}increases to 2.4143 × 10

^{17}cm

^{−3}(SF

_{6}: D

_{2}= 10:1), the number density of photons in the cavity reaches maximum value. However with the further increase of D

_{2}, the density of F is a restrictive condition gradually, and the de-excitation effects of D

_{2}and D on excited DF also increase, which in turn lead the decline of the inverted population density.

_{6}: D

_{2}= 10:1).The calculated results are shown in Figs. 5 and 6 .The reflectivity of output mirror are 10%, 20%, 30%, 40%, 50%, and 60%.

## 4. Experiments

### 4.1 Experimental setup

_{1}= 99% and a CaF

_{2}plane output mirror R

_{2}. The length of the cavity was 220cm.

### 4.2 Experimental results and discussion

_{6}was invariable with the value of 2.4143 × 10

^{18}cm

^{−3}, the discharge voltage was 39kV, and the reflectivity of the output mirror was 30%. Under these conditions, the output laser energy versus the ratio of SF

_{6}-D

_{2}mixture was studied. The mixture ratio used in the experiment were 4:1, 6:1, 8:1, 10:1, 12:1 and 15:1 individually. The fitting curves of the calculated and experimental laser energy versus mixture ratio are shown in Fig. 8 . As can be seen, the fitting curves of the experimental results and the theoretical calculations are in good agreement. The output energy first increases and then reduces with the increasing of the density of D

_{2}. When the number density of D

_{2}was 2.4143 × 10

^{17}cm

^{−3}(SF

_{6}: D

_{2}= 10:1) the pulse energy reached the maximum value. The theoretical calculations and the experiment results both show that there exists an optimum mixture ratio at which the output energy of DF laser reaches its maximum. The experimental laser energy is about 3% higher than the laser energy attained from theoretical calculation at each mixture ratio. The main reasons are as follows: (1) the rate coefficients of several reactions may be imprecise; (2) the electrons density in the gain area is presented by an approximate formula, which couldn’t precisely describe the variation of electrons density under the experimental conditions. In order to close to the experimental results, the theoretical calculations of the single pulse energy should be multiplied by a proper correction factor. The revised calculation model can correctly describe the dynamics of non-chain pulsed DF laser.

_{6}: D

_{2}= 10:1), and the discharge voltage remained 39kV. The reflectivity of the CaF

_{2}output mirrors are 10%, 20%, 30%, 40%, 50%, 60%, respectively. Figure 9 presents the fitting curves of the calculated and experimental laser energy versus the reflectivity of the output mirror. In contrast to the two fitting curves, a conclusion can be drawn that the experiment results agree well with theoretical calculations by computer model. Just as shown in Fig. 9, when the reflectivity of the output mirror is 30%, the non-chain pulsed DF laser attains the maximum output laser energy. Non-chain pulsed laser has the optimal reflectivity of output mirror to realize the maximum output laser energy.

_{6}: D

_{2}= 10:1 and R

_{2}= 30%. Figure 10(a) shows the measured laser pulse shape of DF laser, the pulse duration of which is 148.8 ns. The corresponding output laser energy is 4.95J, so the peak power is 33.27MW. Figure 10(b) is the theoretical calculation of the output power versus time. The calculated pulse width is118ns and the pulse peak power is 40.82MW. Figure 10 shows that the measured results of peak power and pulse shape of DF laser are in agreement with the theoretical calculations by computer model.

## 5. Conclusions

_{6}-D

_{2}mixture and on the reflectivity of output mirror. Both the calculation and experiment present that the optimal value of mixture ratio and output reflectivity is respectively 10:1 and 30% in our works.

## Acknowledgments

## References and links

1. | G. Wilson, B. R. Graves, S. P. Patterson, and R. H. Wank, “Deuterium fluoride laser technology and demonstrators,” Proc. SPIE |

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 |

3. | A. J. Beaulieu, J. A. Nilson, and K. O. Tan, “A practical DF laser for ranging applications,” |

4. | V. I. Lazarenko, S. D. Velikanov, I. N. Pegoev, S. N. Sinkov, and Yu. N. Frolov, “Analysis of DF laser applicability to SO |

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 |

6. | G. P. Perram, M. A. Marciniak, and M. Goda, “High energy laser weapons: technology overview,” Proc. SPIE |

7. | F. Bachmann, “High Power Laser Sources for Industry and their Applications,” Proc. SPIE |

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

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. |

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. |

11. | R. W. Gross and J. F. Bott, |

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 |

13. | D. S. Perry and J. C. Polanyi, “Energy distribution among reaction products, IX. F+H |

14. | K. L. Kompa, |

15. | E. Arunan, D. W. Setser, and J. F. Ogilvie, “Vibration-rotational Einstein coefficients for HF /DF and HCI/DCI,” J. Chem. Phys. |

**OCIS Codes**

(140.0140) Lasers and laser optics : Lasers and laser optics

(140.1550) Lasers and laser optics : Chemical lasers

(140.3430) Lasers and laser optics : Laser theory

(140.3538) Lasers and laser optics : Lasers, pulsed

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: October 9, 2012

Revised Manuscript: November 19, 2012

Manuscript Accepted: November 21, 2012

Published: December 12, 2012

**Citation**

Peng Ruan, Jijiang Xie, Laiming Zhang, Jin Guo, Jingjiang Xie, Guilong Yang, Dianjun Li, Qikun Pan, Gaijuan Tan, Fanjiang Meng, and Shiming Li, "Computer modeling and experimental study of non-chain pulsed electric-discharge DF laser," Opt. Express **20**, 28912-28922 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28912

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### References

- 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]
- 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.
- 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).
- 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]
- R. W. Gross and J. F. Bott, Handbook of Chemical Lasers (John Wiley & Sons Ltd., 1976), Chap. 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]
- 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]
- K. L. Kompa, Chemical Lasers (Springer-Verlag, 1973).
- 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]

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