Kinetic Model and Computer Simulation of Continuous Wave DF-CO<sub>2</sub> Chemical Transfer Lasers

W. Baumann; J. A. Blauer; S. W. Zelazny; W. C. Solomon

doi:10.1364/AO.13.002823

Applied Optics
Vol. 13,
Issue 12,
pp. 2823-2834
(1974)
•https://doi.org/10.1364/AO.13.002823

Kinetic Model and Computer Simulation of Continuous Wave DF-CO₂ Chemical Transfer Lasers

W. Baumann, J. A. Blauer, S. W. Zelazny, and W. C. Solomon

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W. Baumann, J. A. Blauer, S. W. Zelazny, and W. C. Solomon, "Kinetic Model and Computer Simulation of Continuous Wave DF-CO₂ Chemical Transfer Lasers," Appl. Opt. 13, 2823-2834 (1974)

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Abstract

A nonequilibrium model has been used to simulate successfully experimental data obtained on two different DF-CO₂ chemical transfer lasers. The sensitivity of the model to changes in the reaction rate constants, to mixing, and to F atom surface recombination has been investigated. The model was found to provide reasonable agreement with the known experimental facts relating to cw DF-CO₂ chain reaction laser flow fields. It was found that considerable simplification of the chemical model is possible at the sacrifice of some analytical precision.

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Reaction No.	Reaction	M	A	N	$E [\frac{kcal}{mole}]$	Comments	Ref.
1	F₂ = F + F	+/2.4F, 2.4F₂	5.0 × 10¹³	0.0	35.3		15
2	D + D = D₂(v)	+/1.75D₂, 20D	1.0 × 10¹⁸	−1.0	0.0	0≤v≤2	3
3	DF(v) = D + F	+	1.2/n × 10¹⁹	−1.0	D − Ev	0≤v≤n-1	15
4	DF(v) = DF(v−1)	F₂, 2He	3.7 × 10⁻⁶v	4.7	0.0	0≤v≤8	3
5	DF(v) = DF(v−1)	D	2.0 × 10¹³	0.0	0.7	0≤v≤8	15
6	DF(v) = DF(v−1)	F	2.8 × 10¹⁵f(v)	−0.77	3.6	0≤v≤8	15
7	DF(v) = DF(v−1)	DF	1.0 × 10²v	2.9	−3.2	0≤v≤8	15
8	DF(v) = DF(v−1)	D₂	0.14v	3.7	0.0	0≤v≤8	3
9	DF(v) = DF(v−1)	CO₂	4.0 × 10³v	2.2	0.0	0≤v≤8	3
10	D₂(v) = D₂(v−1)	+/5D₂, 5000D, 2He	1.8 × 10⁻⁴v	4.3	0.0	0≤v≤2	15
11	CO₂(00⁰1)=CO₂(10⁰0)	CO₂, 1.5He, 0.3N₂	9.7 × 10⁻¹²	7.1	−1.8	*	17
12	CO₂(00⁰1)=CO₂(02⁰0)	CO₂, 1.5He, 0.3N₂	2.9 × 10⁻¹²	7.1	−1.8		17
13	CO₂(00⁰1)=CO₂(03¹0)	2F₂, 4D, CO₂, He, 0.3N₂	8.7 × 10⁻¹¹	6.6	−2.4		4
14	CO₂(00⁰1)=CO₂(11¹0)	2F₂, 4D, CO₂, He, 0.3N₂	5.5 × 10⁻²	4.0	−0.7	*	17
15	CO₂(00⁰1)=CO₂(11¹0)	DF, F, 0.02D₂	6.4 × 10⁷	1.5	0.0	*	4
16	CO₂(00⁰1)=CO₂(03¹0)	DF, F, 0.02D₂	4.9 × 10⁴	2.3	0.0	*	4
17	CO₂(03¹0)=CO₂(02⁰0)	+/2D, 2D₂, 1.5He	3.9 × 10²	3.3	1.2	*	3
18	CO₂(03¹0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	5.7 × 10²	3.3	1.2	*	3
19	CO₂(03¹0)=CO₂(10⁰0)	+/2D, 2D₂, 1.5He	4.9 × 10²	3.0	1.1		3
20	CO₂(10⁰0)=CO₂(02⁰0)	+/2D, 2D₂, 1.5He	2.6 × 10⁸	1.5	0.0	*	3
21	CO₂(02⁰0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	5.7 × 10⁷	1.6	−0.3	*	17
22	CO₂(10⁰0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	5.7 × 10⁷	1.6	−0.3	*	17
23	CO₂(11¹0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	4.0 × 10¹	3.2	−0.6	*	17
24	CO₂(11¹0)=CO₂(10⁰0)	+/2D, 2D₂, 1.5He	2.4 × 10¹	3.2	−0.6		17
25	CO₂(11¹0)=CO₂(02⁰0)	+/2D, 2D₂, 1.5He	5.4 × 10¹	3.2	−0.6	*	17
26	CO₂(11¹0)=CO₂(03³0)	+/2D. 2D₂, 1.5He	2.1 × 10⁸	1.6	−0.3	*	17
27	CO₂(01¹0)=CO₂(00⁰0)	F₂, F, DF, CO₂, 0.7N₂	1.5 × 10²	2.9	−0.2		17
28	CO₂(02⁰0)=CO₂(01¹0)	F₂, F, DF, CO₂, 0.7N₂	2.4 × 10¹	3.2	−0.6		17
29	CO₂(10⁰0)=CO₂(01¹0)	F₂, F, DF, CO₂, 0.7N₂	1.2 × 10²	3.2	−0.6		17
30	CO₂(02²0)=CO₂(01¹0)	F₂, F, DF, CO₂, 0.7N₂	3.0 × 10²	2.9	−0.3		17
31	CO₂(10⁰0)=CO₂(01¹0)	D₂, D	1.7 × 10¹⁴	−1.0	0.0	*	3
32	CO₂(02⁰0)=CO₂(01¹0)	D₂, D	3.1 × 10¹⁴	−1.0	0.0	*	3
33	CO₂(02²0)=CO₂(01¹0)	D₂, D	3.7 × 10¹⁴	−1.0	0.0	*	3
34	CO₂(01¹0)=CO₂(00⁰0)	D₂, D	9.2 × 10¹³	−1.0	0.0	*	3
35	CO₂(03¹0)=CO₂(02²0)	CO₂, 1.5He, 0.7N₂	4.0 × 10¹	3.2	−0.6	*	17
36	CO₂(10⁰0)=CO₂(01¹0)	He	1.5 × 10³	3.0	−0.8	*	3
37	CO₂(02⁰0)=CO₂(01¹0)	He	2.8 × 10³	3.0	−0.8	*	3
38	CO₂(02²0)=CO₂(01¹0)	He	3.3 × 10³	3.0	−0.8	*	3
39	CO₂(01¹0)=CO₂(00⁰0)	He	8.3 × 10²	3.0	−0.8	*	3
40	CO₂(00⁰1)=CO₂(00⁰0)	FNO	1.0 × 10¹²	0.0	0.0	*	18
41	DF(v) = DF(v-1)	FNO	(v+1) × 10¹¹	0.0	0.0	v = 1, 2	18
42	N₂(1) = N₂(0)	DF	2.3 × 10¹	3.3	−0.7	*	19

Reaction No.	Reaction	A	N	$E [\frac{kcal}{mole}]$	Comments	Ref.
43	F + D₂ = DF(1) + D	1.6 × 10¹³	0.0	2.0	*	20, 21
44	F + D₂ = DF(2) + D	3.7 × 10¹³	0.0	2.0	*	20, 21
45	F + D₂ = DF(3) + D	6.6 × 10¹³	0.0	2.0	*	20, 21
46	F + D₂ = DF(4) + D	2.7 × 10¹³	0.0	2.0	*	20, 21
47	DF(v) + D = F + D₂	1.0 × 10¹³	0.0	0.5	5 ≤ v ≤ 7	15
48	D + F₂ = DF(1) + F	2.6 × 10¹²	0.0	2.4		4
49	D + F₂ = DF(2) + F	3.3 × 10¹²	0.0	2.4		4
50	D + F₂ = DF(3) + F	3.8 × 10¹²	0.0	2.4		4
51	D + F₂ = DF(4) + F	0.7 × 10¹³	0.0	2.4		15
52	D + F₂ = DF(5) + F	1.2 × 10¹³	0.0	2.4		15
53	D + F₂ = DF(6) + F	2.4 × 10¹³	0.0	2.4	*	15
54	D + F₂ = DF(7) + F	4.2 × 10¹³	0.0	2.4	*	15
55	D + F₂ = DF(8) + F	6.6 × 10¹³	0.0	2.4	*	15
56	D + F₂ = DF(9) + F	1.9 × 10¹³	0.0	2.4	*	15
57	DF(v) + DF(v) = DF(v − 1) + DF(v + 1)	1.2 × 10¹²	0.5	0.0	*1 ≤ v ≤ 8	15
58	DF(v) + DF(v + 1) = DF(v − 1) + DF(v + 2)	0.6 × 10¹²	0.5	0.0	1 ≤ v ≤ 8	15
59	DF(v) + DF(v + 2) = DF(v − 1) + DF(v + 3)	0.3 × 10¹²	0.5	0.0	1 ≤ v ≤ 3	15
60	DF(v) + D₂ (v″) = DF (v − v′) + D₂ (v″ + v′)	3.0 × 10¹⁰v	0.5	0.0	*1 ≤ v ≤ 5	15
61	DF(v) + CO₂ (00⁰0) = DF(v − 1) + CO₂ (00⁰1)	9.2 × 10¹⁴v	−1.0	0.0	*1 ≤ v ≤ 8	4
62	D₂(v) + CO₂ (00⁰0) = D₂ (v − 1) + CO₂ (00⁰1)	5.4 × 10⁸v	1.0	−0.1	*1 ≤ v ≤ 2	24, 25
63	CO₂ (00⁰1) + CO₂ (00⁰0) = CO₂ (01¹0) + CO₂ (02⁰0)	1.3 × 10⁻²	4.0	−0.5		17
64	CO₂ (00⁰1) + CO₂ (00⁰0) = CO₂ (10⁰0) + CO₂ (01¹0)	0.2	4.0	−0.5	*	17
65	CO₂ (02²0) + CO₂ (00⁰0) = CO₂ (01¹0) + CO₂ (02⁰0)	1.0 × 10⁸	1.4	−0.2	*	17
66	CO₂ (10⁰0) + CO₂ (00⁰0) = CO₂ (01¹0) + CO₂ (01¹0)	1.0 × 10⁶	1.4	−0.2		17
67	CO₂ (02²0) + CO₂ (00⁰0) = CO₂ (01¹0) + CO₂ (01¹0)	1.0 × 10⁸	1.4	−0.2	*	17
68	CO₂ (11¹0) + CO₂ (00⁰0) = CO₂ (02⁰0) + CO₂ (01¹0)	1.6 × 10⁸	1.4	−0.2	*	17
69	CO₂ (11¹0) + CO₂ (00⁰0) = CO₂ (10⁰0) + CO₂ (01¹0)	3.0 × 10⁶	1.4	−0.2		17
70	CO₂ (11¹0) + CO₂ (00⁰0) = CO₂ (02²0) + CO₂ (01¹0)	9.1 × 10⁷	1.4	−0.2	*	17
71	CO₂ (03³0) + CO₂ (00⁰0) = CO₂ (02²0) + CO₂ (01¹0)	1.5 × 10⁸	1.4	−0.2	*	17
72	DF(v) + N₂ (0) = DF (v − 1) + N₂ (1)	4.0 × 10³v	2.2	0.0		19
73	CO₂ (00⁰1) + N₂(0) = CO₂ (00⁰) + N₂(1)	2.5 × 10¹¹	0.0	0.0	*	17
74	F₂ + NO = FNO + F	3.3 × 10¹⁰	0.0	1.5		27
75	F + NO + M = FNO + M	3.3 × 10¹⁹	−1.0	0.0		27

v	1	2	3	4	5	6
f(v)	1.0	1.17	1.58	3.0	4.0	5.0

Experiment	Diluent	Velocity (m/sec)	Pressure (torr)	Temp. (K)	F-atom (mole fract.)
Shirley, et. al.	Helium	137	17.0	312	0.0009 (0.0006)*
Falk, Run 3	Helium	94	19.2	311	0.0006
Falk, Run 6	Helium	66	26.6	303	0.0004
Falk, Run 11	Helium	27	58.2	302	0.0002
Falk, Run 13	Nitrogen	90	19.6	307	0.0006
Falk, Run 15	Nitrogen	72	24.6	306	0.0005
Falk, Run 18	Nitrogen	38	45.9	299	0.0003

Reaction No.	Reaction	M	A	N	$E [\frac{kcal}{mole}]$	Comments	Ref.
1	F₂ = F + F	+/2.4F, 2.4F₂	5.0 × 10¹³	0.0	35.3		15
2	D + D = D₂(v)	+/1.75D₂, 20D	1.0 × 10¹⁸	−1.0	0.0	0≤v≤2	3
3	DF(v) = D + F	+	1.2/n × 10¹⁹	−1.0	D − Ev	0≤v≤n-1	15
4	DF(v) = DF(v−1)	F₂, 2He	3.7 × 10⁻⁶v	4.7	0.0	0≤v≤8	3
5	DF(v) = DF(v−1)	D	2.0 × 10¹³	0.0	0.7	0≤v≤8	15
6	DF(v) = DF(v−1)	F	2.8 × 10¹⁵f(v)	−0.77	3.6	0≤v≤8	15
7	DF(v) = DF(v−1)	DF	1.0 × 10²v	2.9	−3.2	0≤v≤8	15
8	DF(v) = DF(v−1)	D₂	0.14v	3.7	0.0	0≤v≤8	3
9	DF(v) = DF(v−1)	CO₂	4.0 × 10³v	2.2	0.0	0≤v≤8	3
10	D₂(v) = D₂(v−1)	+/5D₂, 5000D, 2He	1.8 × 10⁻⁴v	4.3	0.0	0≤v≤2	15
11	CO₂(00⁰1)=CO₂(10⁰0)	CO₂, 1.5He, 0.3N₂	9.7 × 10⁻¹²	7.1	−1.8	*	17
12	CO₂(00⁰1)=CO₂(02⁰0)	CO₂, 1.5He, 0.3N₂	2.9 × 10⁻¹²	7.1	−1.8		17
13	CO₂(00⁰1)=CO₂(03¹0)	2F₂, 4D, CO₂, He, 0.3N₂	8.7 × 10⁻¹¹	6.6	−2.4		4
14	CO₂(00⁰1)=CO₂(11¹0)	2F₂, 4D, CO₂, He, 0.3N₂	5.5 × 10⁻²	4.0	−0.7	*	17
15	CO₂(00⁰1)=CO₂(11¹0)	DF, F, 0.02D₂	6.4 × 10⁷	1.5	0.0	*	4
16	CO₂(00⁰1)=CO₂(03¹0)	DF, F, 0.02D₂	4.9 × 10⁴	2.3	0.0	*	4
17	CO₂(03¹0)=CO₂(02⁰0)	+/2D, 2D₂, 1.5He	3.9 × 10²	3.3	1.2	*	3
18	CO₂(03¹0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	5.7 × 10²	3.3	1.2	*	3
19	CO₂(03¹0)=CO₂(10⁰0)	+/2D, 2D₂, 1.5He	4.9 × 10²	3.0	1.1		3
20	CO₂(10⁰0)=CO₂(02⁰0)	+/2D, 2D₂, 1.5He	2.6 × 10⁸	1.5	0.0	*	3
21	CO₂(02⁰0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	5.7 × 10⁷	1.6	−0.3	*	17
22	CO₂(10⁰0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	5.7 × 10⁷	1.6	−0.3	*	17
23	CO₂(11¹0)=CO₂(02²0)	+/2D, 2D₂, 1.5He	4.0 × 10¹	3.2	−0.6	*	17
24	CO₂(11¹0)=CO₂(10⁰0)	+/2D, 2D₂, 1.5He	2.4 × 10¹	3.2	−0.6		17
25	CO₂(11¹0)=CO₂(02⁰0)	+/2D, 2D₂, 1.5He	5.4 × 10¹	3.2	−0.6	*	17
26	CO₂(11¹0)=CO₂(03³0)	+/2D. 2D₂, 1.5He	2.1 × 10⁸	1.6	−0.3	*	17
27	CO₂(01¹0)=CO₂(00⁰0)	F₂, F, DF, CO₂, 0.7N₂	1.5 × 10²	2.9	−0.2		17
28	CO₂(02⁰0)=CO₂(01¹0)	F₂, F, DF, CO₂, 0.7N₂	2.4 × 10¹	3.2	−0.6		17
29	CO₂(10⁰0)=CO₂(01¹0)	F₂, F, DF, CO₂, 0.7N₂	1.2 × 10²	3.2	−0.6		17
30	CO₂(02²0)=CO₂(01¹0)	F₂, F, DF, CO₂, 0.7N₂	3.0 × 10²	2.9	−0.3		17
31	CO₂(10⁰0)=CO₂(01¹0)	D₂, D	1.7 × 10¹⁴	−1.0	0.0	*	3
32	CO₂(02⁰0)=CO₂(01¹0)	D₂, D	3.1 × 10¹⁴	−1.0	0.0	*	3
33	CO₂(02²0)=CO₂(01¹0)	D₂, D	3.7 × 10¹⁴	−1.0	0.0	*	3
34	CO₂(01¹0)=CO₂(00⁰0)	D₂, D	9.2 × 10¹³	−1.0	0.0	*	3
35	CO₂(03¹0)=CO₂(02²0)	CO₂, 1.5He, 0.7N₂	4.0 × 10¹	3.2	−0.6	*	17
36	CO₂(10⁰0)=CO₂(01¹0)	He	1.5 × 10³	3.0	−0.8	*	3
37	CO₂(02⁰0)=CO₂(01¹0)	He	2.8 × 10³	3.0	−0.8	*	3
38	CO₂(02²0)=CO₂(01¹0)	He	3.3 × 10³	3.0	−0.8	*	3
39	CO₂(01¹0)=CO₂(00⁰0)	He	8.3 × 10²	3.0	−0.8	*	3
40	CO₂(00⁰1)=CO₂(00⁰0)	FNO	1.0 × 10¹²	0.0	0.0	*	18
41	DF(v) = DF(v-1)	FNO	(v+1) × 10¹¹	0.0	0.0	v = 1, 2	18
42	N₂(1) = N₂(0)	DF	2.3 × 10¹	3.3	−0.7	*	19

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