Kinetic Model for Thermal Blooming in the Atmosphere

H. E. Bass; H.-J. Bauer

doi:10.1364/AO.12.001506

Applied Optics
Vol. 12,
Issue 7,
pp. 1506-1510
(1973)
•https://doi.org/10.1364/AO.12.001506

Kinetic Model for Thermal Blooming in the Atmosphere

H. E. Bass and H.-J. Bauer

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H. E. Bass and H.-J. Bauer, "Kinetic Model for Thermal Blooming in the Atmosphere," Appl. Opt. 12, 1506-1510 (1973)

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Abstract

A kinetic model is proposed to account for the translational heating of the atmosphere in the vicinity of an ir laser beam. The theory required to link the kinetic model to the temperature rise is developed assuming a still atmosphere. The kinetic model and theoretical method are applied to 10–6-μ CO₂ laser radiation propagation.

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Reactions	Forward rate constants (sec⁻¹ atm⁻¹)
CO₂(ν₃) + O₂ ⇌ CO₂**(ν₂) + O₂	6.0 × 10⁴
CO₂*(ν₂) + O₂ ⇄ CO₂ + O₂	3.0 × 10⁴
CO₂ + O₂* ⇌ CO₂*(ν₂) + O₂	3.0 × 10⁵
CO₂(ν₁) + O₂ ⇌ CO₂*(ν₂) + O₂	4.5 × 10⁸
CO₂*(ν₂) + CO₂ ⇌ CO₂ + CO₂	1.8 × 10⁵
CO₂(ν₃) + CO₂ ⇌ CO₂**(ν₂) + CO₂	1.5 × 10⁵
CO₂(ν₁) + CO₂ ⇌ CO₂*(ν₂) + CO₂	4.5 × 10⁸
CO₂*(ν₂) + N₂ ⇌ CO₂ + N₂	3.4 × 10⁴
CO₂ + N₂* ⇌ CO₂ + N₂	1.0
CO₂(ν₃) + N₂ ⇌ CO₂ + N₂	1.8 × 10⁷
CO₂(ν₃) + N₂ ⇄ CO₂**(ν₂) + N₂	6.0 × 10⁴
CO₂(ν₁) + N₂ ⇌ CO₂*(ν₂) + N₂	4.5 × 10⁸
CO₂*(ν₂) + H₂O ⇌ CO₂ + H₂O	4.2 × 10⁸
N₂* + O₂ ⇌ N₂ + O₂*	1.5 × 10²
O₂* + N₂ ⇌ O₂ + N₂	4.0 × 10
N₂* + O₂ ⇌ N₂ + O₂	1.0
O₂* + O₂ ⇌ O₂ + O₂	6.3 × 10
H₂O(ν₂) + O₂ ⇌ H₂O + O₂	4.6 × 10⁷
O₂* + H₂O ⇌ O₂ + H₂O	1.1 × 10⁶
H₂O*(ν₂) + O₂ ⇌ H₂O + O₂	6.0 × 10⁴
N₂* + N₂ ⇌ N₂ + N₂	1.0
N₂* + H₂O ⇌ N₂ + H₂O	1.1 × 10⁵
H₂O*(ν₂) + N₂ ⇌ H₂O + N₂	1.4 × 10⁶
H₂O*(ν₂) + H₂O ⇌ H₂O + H₂O	1.0 × 10⁹

Relaxation rates Λ_i = 1/pτ_psⁱ-[sec⁻¹ atm⁻¹]	Relaxation strengths $δ_{i} = (\tilde{u} r_{i}) ({\tilde{r}}_{i} x^{- 1} {\dot{n}}_{opt}) - [J {sec}^{- 1} {mole}^{- 1}]$	Comments
5.6 × 10⁸	−4.8 × 10⁻²	Important for very short pulses only
1.4 × 10⁷	2.5 × 10⁻²	Insignificant
1.1 × 10⁷	2.2 × 10⁻²	Important at high humidity, Λ₁
2.8 × 10⁶	1.4 × 10⁻⁵	Insignificant
2.4 × 10⁶	1.8 × 10⁻²	Insignificant
1.3 × 10⁶	2.3 × 10⁻¹	Important acoustically
7.3 × 10⁵	−1.8	Major cooling term, Λ₂
1.2 × 10⁴	1.4 × 10⁻¹	Important acoustically, Λ₃
4.0 × 10³	6.3 × 10⁻⁵	Insignificant
2.5 × 10²	2.7	Major heating term, Λ₄
		Also important acoustically

Reactions	Forward rate constants (sec⁻¹ atm⁻¹)
CO₂(ν₃) + O₂ ⇌ CO₂**(ν₂) + O₂	6.0 × 10⁴
CO₂*(ν₂) + O₂ ⇄ CO₂ + O₂	3.0 × 10⁴
CO₂ + O₂* ⇌ CO₂*(ν₂) + O₂	3.0 × 10⁵
CO₂(ν₁) + O₂ ⇌ CO₂*(ν₂) + O₂	4.5 × 10⁸
CO₂*(ν₂) + CO₂ ⇌ CO₂ + CO₂	1.8 × 10⁵
CO₂(ν₃) + CO₂ ⇌ CO₂**(ν₂) + CO₂	1.5 × 10⁵
CO₂(ν₁) + CO₂ ⇌ CO₂*(ν₂) + CO₂	4.5 × 10⁸
CO₂*(ν₂) + N₂ ⇌ CO₂ + N₂	3.4 × 10⁴
CO₂ + N₂* ⇌ CO₂ + N₂	1.0
CO₂(ν₃) + N₂ ⇌ CO₂ + N₂	1.8 × 10⁷
CO₂(ν₃) + N₂ ⇄ CO₂**(ν₂) + N₂	6.0 × 10⁴
CO₂(ν₁) + N₂ ⇌ CO₂*(ν₂) + N₂	4.5 × 10⁸
CO₂*(ν₂) + H₂O ⇌ CO₂ + H₂O	4.2 × 10⁸
N₂* + O₂ ⇌ N₂ + O₂*	1.5 × 10²
O₂* + N₂ ⇌ O₂ + N₂	4.0 × 10
N₂* + O₂ ⇌ N₂ + O₂	1.0
O₂* + O₂ ⇌ O₂ + O₂	6.3 × 10
H₂O(ν₂) + O₂ ⇌ H₂O + O₂	4.6 × 10⁷
O₂* + H₂O ⇌ O₂ + H₂O	1.1 × 10⁶
H₂O*(ν₂) + O₂ ⇌ H₂O + O₂	6.0 × 10⁴
N₂* + N₂ ⇌ N₂ + N₂	1.0
N₂* + H₂O ⇌ N₂ + H₂O	1.1 × 10⁵
H₂O*(ν₂) + N₂ ⇌ H₂O + N₂	1.4 × 10⁶
H₂O*(ν₂) + H₂O ⇌ H₂O + H₂O	1.0 × 10⁹

Relaxation rates Λ_i = 1/pτ_psⁱ-[sec⁻¹ atm⁻¹]	Relaxation strengths $δ_{i} = (\tilde{u} r_{i}) ({\tilde{r}}_{i} x^{- 1} {\dot{n}}_{opt}) - [J {sec}^{- 1} {mole}^{- 1}]$	Comments
5.6 × 10⁸	−4.8 × 10⁻²	Important for very short pulses only
1.4 × 10⁷	2.5 × 10⁻²	Insignificant
1.1 × 10⁷	2.2 × 10⁻²	Important at high humidity, Λ₁
2.8 × 10⁶	1.4 × 10⁻⁵	Insignificant
2.4 × 10⁶	1.8 × 10⁻²	Insignificant
1.3 × 10⁶	2.3 × 10⁻¹	Important acoustically
7.3 × 10⁵	−1.8	Major cooling term, Λ₂
1.2 × 10⁴	1.4 × 10⁻¹	Important acoustically, Λ₃
4.0 × 10³	6.3 × 10⁻⁵	Insignificant
2.5 × 10²	2.7	Major heating term, Λ₄
		Also important acoustically

Abstract

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Figures (2)

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Equations (18)

Applied Optics