Effect of cavity transients and rotational relaxation on the performance of pulsed HF chemical lasers: a theoretical investigation

J. J. T. Hough; R. L. Kerber

doi:10.1364/AO.14.002960

Applied Optics
Vol. 14,
Issue 12,
pp. 2960-2970
(1975)
•https://doi.org/10.1364/AO.14.002960

Effect of cavity transients and rotational relaxation on the performance of pulsed HF chemical lasers: a theoretical investigation

J. J. T. Hough and R. L. Kerber

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J. J. T. Hough and R. L. Kerber, "Effect of cavity transients and rotational relaxation on the performance of pulsed HF chemical lasers: a theoretical investigation," Appl. Opt. 14, 2960-2970 (1975)

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Abstract

Two rate-equation models of a pulsed HF laser are presented. Calculations with these models reveal the time evolution of the gain and intensity of lasing on all lines in vibrational–rotational bands studied and the time histories of concentrations of the chemical species. The present formulation permits an accurate assessment of the effect of vibrational relaxation and rotational relaxation. The model predictions are compared with earlier models to illustrate their unique features. Multiline lasing on vibrational–rotational bands is predicted; however, the general trends of J shifting are similar to those of earlier models. It is found that lasing does not begin when the medium gain reaches threshold, but intensity increases sharply after the gain is far above threshold. The gain subsequently drops rapidly and oscillates near the threshold value. The effect of rotational relaxation on laser performance is shown for multiline laser operation, and the enhancing effect of cascading is clearly revealed. The present models are found to predict output and performance consistent with experiment.

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Rate	Energy, J/cc							Time, μsec

	E₁₀	E₂₁	E₃₂	E₄₃	E₅₄	E₆₅	E	t₁	t_½
	Constant-gain model
Standard	0.0208	0.0337	0.0195	0.0115	0.0109	0.0048	0.101	4.1	1.0
High VV HF	0.0151	0.0400	0.0235	0.0123	0.0112	0.0049	0.107	4.0	1.0
	Present model
Standard	0.0184	0.0310	0.0164	0.0092	0.0095	0.0041	0.089	3.2	1.0
High VV HF	0.0131	0.0373	0.0212	0.0102	0.0095	0.0041	0.096	3.0	1.0
Gas kinetic VV HF	0.0044	0.0272	0.0334	0.0266	0.0136	0.0054	0.110	3.2	1.1

Reaction No.	Reaction	Rate coefficient, cc/mol-sec	M, υ
1a^b	F + H₂(0) = HF(1) + H	k_1a = 2.6 × 10^13−1.6/θ
1b	F + H₂(0) = HF(2) + H	k_1b = 8.8 × 10^13−1.6/θ
1c	F + H₂(0) = HF(3) + H	k_1c = 4.4 × 10^13−1.6/θ
1d	F + H₂(0) = HF(4) + H	k_−1d = 7.4 × 10^12−0.50/θ
1e	F + H₂(0) = HF(5) + H	k_−1e = 1.1 × 10^13−0.51/θ
1f	F + H₂(0) = HF(6) + H	k_−1f = 1.9 × 10^13−0.56/θ
2a	H + F₂ = HF(0) + F	k_2a = 1.1 × 10^12−2.4/θ
2b	H + F₂ = HF(1) + F	k_2b = 2.5 × 10^12−2.4/θ
2c	H + F₂ = HF(2) + F	k_2c = 3.5 × 10^12−2.4/θ
2d	H + F₂ = HF(3) + F	k_2d = 3.6 × 10^12−2.4/θ
2e	H + F₂ = HF(4) + F	k_2e = 1.6 × 10^13−2.4/θ
2f	H + F₂ = HF(5) + F	k_2f = 3.6 × 10^13−2.4/θ
2g	H + F₂ = HF(6) + F	k_2g = 4.8 × 10^13−2.4/θ
2h	H + F₂ = HF(7) + F	k₂_h = 5.5 × 10^12−2.4/θ
2i	H + F₂ = HF(8) + F	k₂_i = 2.5 × 10^12−2.4/θ
3a_υ^c	HF(υ) + M₁ = HF(υ − 1) + M₁	k₃_{a_υ} = υ(10^14.0T^−0.8 + 10^0.4T^3.5)	M₁ = HF, υ = 1⋯8
3b₁	HF(1) + M₂ = HF(0) + M₂	k₃_b₁ = 1.5 × 10^10−1.1/^θT	M₂ = F
3b₂	HF(2) + M₂ = HF(1) + M₂	k₃_b₂ = 1.5 × 10^10−0.5/^θT
3b_υ	HF(υ) + M₂ = HF(υ − 1) + M₂	k₃_{b_υ} = 1.5 × 10¹⁰T	υ = 3⋯8
3c_υ	HF(υ) + M₄ = HF(υ − 1) + M₄	k₃_{c_υ} = υ (8 × 10⁻⁴T⁴)	M₄ = Ar, F₂, SF₆, υ = 1⋯8
3d_υ	HF(υ) + M₅ = HF(υ − 1) + M₅	k₃_{d_υ} = υ(8.7 × 10⁻⁷T⁵)	M₅ = He, υ = 1⋯8
3e_υ	HF(υ) + M₆ = HF(υ′) + M₆	k₃_{e_υ} = 1.8 × 10^13−0.7/θ	M₆ = H, υ = 1⋯8, υ′ < υ
3f_υ	HF(υ) + M₇ = HF(υ − 1) + M₇	k₃_{f_υ} = υ(1 × 10⁵T²)	M₇ = H₂, υ = 1⋯8
4a	HF(υ) + HF(υ) = HF(υ − 1) + HF(υ + 1)	k_4a = 1.5 × 10¹²T^1/2	υ = 1⋯7
4b	HF(υ) + HF(υ + 1) = HF(υ − 1) + HF(υ + 2)	k_4b = 0.5k_4a	υ = 1⋯6
4c	HF(υ) + HF(υ + 2) = HF(υ − 1) + HF(υ + 3)	k_4c = 0.25k_4a	υ = 1⋯5
4d	HF(υ) + HF(υ + 3) = HF(υ − 1) + HF(υ + 4)	k_4d = 0.125k_4a	υ = 1⋯4
5a	HF(0) + H₂(1) = HF(1) + H₂(0)	k_5a = 9 × 10¹¹
5b	HF(1) + H₂(1) = HF(2) + H₂(0)	k_5b = 2.9 × 10¹²
5c	HF(2) + H₂(1) = HF(3) + H₂(0)	k_5c = 9 × 10¹²
5d	HF(3) + H₂(1) = HF(4) + H₂(0)	k_5d = 2 × 10¹³
5e	HF(0) + H₂(2) = HF(1) + H₂(1)	k_5e = k_5a
5f	HF(1) + H,(2) = HF(2) + H₂(1)	k_5f = k_5b
6a_υ	H₂(υ) + M₈ = H₂(υ − 1) + M₈	k₆_{a_υ} = υ(2.5 × 10⁻⁴)T^4.3	M₈ = all except H, H₂, υ = 1, 2
7b_υ	H₂(υ) + M₉ = H₂(υ − 1) + M₉	k₇_{b_υ} = υ(10⁻³T^4.3)	M₉ = H, H₂, υ = 1, 2

A_τ	Energy, J/cc				Time, μsec

	E₁₀	E₂₁	E₃₂	E	t₁	t_½
Rotational equilibrium	0.00590	0.00723	0.00185	0.0150	0.320	0.130
2 × 10⁻⁹T^−½	0.00593	0.00723	0.00135	0.0150	0.330 (est)	0.140
2 × 10⁻⁸T^−½	0.00579	0.00689	0.00169	0.0144	0.364	0.140
2 × 10⁻⁷T^−½	0.00468	0.00581	0.00110	0.0116	0.390	0.135

Operating mode	Energy, J/cc				Time, μsec

	E₁₀	E₂₁	E₃₂	E	t₁	t_½
Multiline	0.00579	0.00689	0.00169	0.0144	0.364	0.140
P₁ (8) Single line	0.00287	0	0	0.00287	0.235	0.120
P₂ (7) single line	0	0.00425	0	0.00425	0.288	0.143
P₃ (6) single line	0	0	0.00001	0.00001	0.030	0.015
P₁ (8), P₂ (7), P₃ (6)	0.00435	0.00542	0.00119	0.0110	0.265	0.116
P₁ (9), P₂ (7), P₃ (5)	0.00342	0.00476	0,00032	0.0085	0.275	0.150
Multiline with no pref. pumping	0.00562	0.00676	0.00176	0.0142	0.355	0.140

Rate	Energy, J/cc							Time, μsec

	E₁₀	E₂₁	E₃₂	E₄₃	E₅₄	E₆₅	E	t₁	t_½
	Constant-gain model
Standard	0.0208	0.0337	0.0195	0.0115	0.0109	0.0048	0.101	4.1	1.0
High VV HF	0.0151	0.0400	0.0235	0.0123	0.0112	0.0049	0.107	4.0	1.0
	Present model
Standard	0.0184	0.0310	0.0164	0.0092	0.0095	0.0041	0.089	3.2	1.0
High VV HF	0.0131	0.0373	0.0212	0.0102	0.0095	0.0041	0.096	3.0	1.0
Gas kinetic VV HF	0.0044	0.0272	0.0334	0.0266	0.0136	0.0054	0.110	3.2	1.1

Abstract

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Figures (9)

Tables (4)

Equations (20)

Applied Optics