Detailed characteristics of a pulsed H<sub>2</sub> +
F<sub>2</sub> laser. 2: Theory

Paul E. Sojka; Ronald L. Kerber

doi:10.1364/AO.25.000076

Applied Optics
Vol. 25,
Issue 1,
pp. 76-85
(1986)
•https://doi.org/10.1364/AO.25.000076

Detailed characteristics of a pulsed H₂ + F₂ laser. 2: Theory

Paul E. Sojka and Ronald L. Kerber

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Paul E. Sojka and Ronald L. Kerber, "Detailed characteristics of a pulsed H₂ + F₂ laser. 2: Theory," Appl. Opt. 25, 76-85 (1986)

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Abstract

A theoretical investigation of a pulsed, flash photolytically initiated, HF laser pumped by the H₂ + F₂ chain reaction is presented. The results of computer simulations of the laser kinetic mechanisms are compared to small signal gain, total pulse energy, and time-resolved spectral measurements. These comparisons show that a model assuming vibrational-to-translational (V–T) energy transfer as the dominant HF deactivation channel more closely predicts gain and spectroscopic durations, initiation, peak and termination times, plus peak gain magnitudes and total pulse energies than a similar model assuming vibrational-to-rotational (V–R) energy transfer as the dominant deactivation channel. This is contrary to the current understanding of HF kinetic mechanisms. It is concluded that the current understanding of these mechanisms is not sufficient to quantitatively predict either the time-resolved spectra or gain of the H₂ + F₂ laser. Model results also indicate that rotational relaxation is fast compared to other deactivation processes, but slow compared to stimulated emission. Finally, the model gives an estimated lower bound for the experimental [F]/[F₂] ratio of 0.0025%.

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Reaction number		Rate coefficient units of cm, mole, s, cal	M, υ,A,g(υ)
(1a)	$H_{2} (0) + M_{1} = 2 H + M_{1}$	$K_{- 1 a} = 6.2 \times 10^{17} T^{- 0.95}$	$M_{1} = all species except H and H_{2}$
(1b)	$H_{2} (0) + H_{2} = 2 H + H_{2}$	$K_{- 1 b} = 9.4 \times 10^{16} T^{- 0.61}$
(1c)	$H_{2} (0) + H = 2 H + H$	$K_{- 1 c} = 1.2 \times 10^{14} T^{0.5}$
(2)	$F_{2} + M_{2} = 2 F + M_{2}$	$\begin{array}{l} {K_{2}}^{M} & = 5.0 \times 10^{13} A_{M} \\ exp (- 35, 100 / RT) \times 10^{- (E_{0} - E_{υ})} \end{array}$	$\begin{array}{l} A_{F} & = 10, A_{F_{2}} = 2.7, A_{He} = 2, \\ A_{2} = 1, all others \end{array}$
(3)	$HF (υ) + M_{3} = H + F + M_{3}$	$\begin{array}{l} K_{3} (υ) & = \frac{1.2 A_{M}}{n + 1} \times 10^{19} T^{- 1} \\ exp (- 135, 100 / RT) \end{array}$	$\begin{array}{l} A_{F} & = A_{H} = A_{HF} = 5, A_{3} = 1, all \\ others : υ = 0 \dots n \end{array}$
(4a)	$F + H_{2} (0) = HF (υ) + H$	$\begin{array}{l} K_{4} & = g (υ) \times 4.9 \times 10^{11} T^{0.8} \\ exp (- 600 / RT) \end{array}$	$\begin{array}{l} υ & = 1, 2, 3; g (1) = 0.17 \\ g (2) = 0.55, g (3) = 0.28; \\ g (υ) = 0, υ > 3 \end{array}$
(4b-1)	$HF (4) + H = H_{2} (υ^{'}) + F$	$K_{- 4} (υ = 4) = 6.0 \times 10^{11} T^{0.5}$
(4b-2)	$HF (5) + H = H_{2} (υ^{'}) + F$	$K_{- 4} (υ = 5) = 8.8 \times 10^{11} T^{0.5}$
(4b-3)	$HF (6) + H = H_{2} ((υ^{'}) + F$	$K_{- 4} (υ = 6) = 1.6 \times 10^{12} T^{0.5}$
(5)	$H + F_{2} = HF (υ) + F$	$\begin{array}{l} K_{g} & = g (υ) \times 3.0 \times 10^{9} T^{1.3} \\ exp (- 950 / RT) \end{array}$	$\begin{array}{l} g (υ) & = 0, υ - 0, 1, 2, 3; \\ g (3) = 0.08, g (4) = 0.13, \\ g (5) = 0.35, g (6) = 0.44, \\ g (υ) = 0, υ > 6 \end{array}$
(6a)^b	$HF (υ) + HF = HF (υ^{'}) + HF$	$\begin{array}{l} K_{6 a} & = 1.1 \times 10^{10} υ^{3.5} T^{0.5} \\ exp (1030 / RT) \end{array}$	$υ^{'} = υ - 1$
(6b)	$HF (υ) + H_{2} = HF (υ^{'}) + H_{2}$	$K_{6_{b υ}} = 6.0 \times 10^{7} υ T$	$υ^{'} = υ - 1$
(6c)	$HF (υ) + H = HF (υ^{'}) + H$	$\begin{array}{l} K_{6_{c (υ, υ^{'})}} & = g (υ, υ^{'}) \times 1.5 \times 10^{12} \\ exp (- 700 / RT) \end{array}$	$\begin{array}{l} g (1, 0) & = 1, g (2, 1) = g (2, 0) = 1.8, \\ g (υ, υ - 1) = 360, υ = 3, \dots, 6, \\ g (υ, υ - n) = 1.8, υ E 3, \dots, 6, \\ n = 2 \dots υ \end{array}$
(6d)	$HF (υ) + F = HF (υ^{'}) + F$	$K_{6_{d υ}} = 1.6 \times 10^{13} υ exp (- 2700 / RT)$	$υ^{'} = υ - 1$
(6e)	$HF (υ) + M_{6} = HF (υ^{'}) + M_{6}$	$K_{6_{e υ}} = 7.7 \times - 10^{- 7} υ T^{5} A_{M}$	$A_{F_{2}} = A_{Ar} = 1.0, A_{He} = 2.0$
(7)	$HF (υ) + HF (υ^{'}) = HF (υ + 1) + HF (υ^{'} - 1)$	$K_{7} (υ, 1; υ + 1, 0) = 3.6 \times 10^{15} υ^{- 1} T^{- 1}$	$υ = 1, υ^{'} = 1$
(7)	$HF (υ) + HF (υ^{'}) = HF (υ + 1) + HF (υ^{'} - 1)$	$K_{7} (υ, υ^{'}, υ + 1, υ^{'} - 1) = 3 \times 10^{15} υ^{- 1} T^{- 1}$	$υ = 2, \dots, 7, υ^{'} = 1, \dots 6$
(8a)	$H_{2} (υ) + M_{8} = H_{2} (υ - 1) + M_{8}$	$K_{8 a} = 2.5 \times 10^{- 4} υ T^{4.3} A_{M_{8}}$	$\begin{array}{l} A_{H_{2}} & = 4, A_{8} = 1 all others \\ υ = 1, 2 \end{array}$
(8b)	$H_{2} (υ) + H = H_{2} (υ - 1) + H$	$K_{8 b} = 2 \times 10^{13} exp (- 2720 / RT)$	$υ = 1, 2$
(9)	$HF (υ - n) + H_{2} (υ^{'} + n) = HF (υ) + H_{2} (υ^{'})$	$K_{9} = 8 \times 10^{11} υ$	$υ = 1 \dots 6; n = 1, \dots, υ$
(10a)	$HF (0, 10) + HF (υ, J) = HF (0, 10 - Δ J) + HF (υ, J)$	$\begin{array}{l} K_{10 a} & = 1.023 \times 10^{16} T^{- 0.805} \\ exp (- 2569 / RT) \end{array}$
(10b)	$HF (1, 10) + HF (υ, J) HF (1, 10 - Δ J) + HF (υ, J)$	$\begin{array}{l} K_{10 b} & = 3.38 \times 10^{16} T^{- 0.893} \\ exp (- 2436 / RT) \end{array}$

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Applied Optics