R. L. Kerber, R. C. Brown, and K. A. Emery, "Rotational nonequilibrium mechanisms in pulsed H2 + F2 chain reaction lasers. 2: Effect of VR energy exchange," Appl. Opt. 19, 293-300 (1980)
The occurrence of pure rotational-to-rotational lasing from high J levels suggests that present rotational nonequilibrium mechanisms are inadequate to explain all lasing behavior of the HF laser. A possible mechanism for explaining this behavior is vibrational-to-rotational energy transfer. The usual assumption that vibrational relaxation occurs with rotational levels at equilibrium at the translational temperature is replaced with a near resonant multiquanta VR process that results in the formation of highly excited rotational states. Computer simulations incorporating VR relaxation predicted significant occurrence of rotational lasing. A simpler model that produced rotational nonequilibrium from pumping and P-branch lasing did not exhibit rotational lasing. Rotational lasing did not decrease energy available to P-branch lasing and produced effects resembling an increase in rotational relaxation rates. Rotational lasing is very sensitive to kinetics for both VR energy exchange and rotational relaxation.
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Gas mixture: 0.02F:0.99F2:1 H2:20He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.8, L = 20 cm, l = 20 cm, P-branch lasing.
The distributions for V–R relaxation are listed in Table V.
The degree of completion ∊ is (F2 final)/(F2 initial).
Table V
Comparison of Vibrational-to-Rotational Energy Exchange Model with Vibrational-to-Translational Energy Exchange Model
Gas mixture: 0.02F:0.99F2:1H2:20 He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm. All models assume Polanyi pumping.
Distribution no. 3 is used for multiquanta VR relaxation.
Run not to completion; integration problems encountered.
Gas mixture: 0.02F:0.99F2:1H2:20 He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm.
Distributions for VR relaxation are listed in Table V; multiquanta relaxation and Boltzmann pumping are assumed.
Rotational lasing was not allowed to occur for this case.
Table VII
Impact of Important Kinetics on Laser Performance b
Gas mixture: 0.02F:0.99F2:1H2:20He; Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm.
Distribution no. 3 is used for V–R relaxation; multiquanta VR and Boltzmann pumping are assumed.
RR lasing was strong at P-branch lasing cutoff.
Case not run to completion; computation time excessive.
Table VIII
Effect of Rotational Relaxation Rate on Laser Performance
Relative rotational lasing energy on vibrational levels
ERR (J/litre)
PRRmax (W/cc)
TRRmax (μsec)
0
1
2
3
4
5
6
106
Wilkins
1.00/12
0.58/10
0.12/9
0.10/22
0.08/13
0.02/11
0.007/4
0.016
1.83
31.00
115
Revised Wilkins
0.88/12
1.00/5
0
0
0
0
0
0.67E-4
0.0028
18.50
Gas mixture: 0.02F:0.99F2:1H2:20He; Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm.
Distribution no. 3 is used for V–R relaxation; multiquanta V–R and Polanyi pumping are assumed.
Tables (8)
Table I
Relative J Dependence of Rotational Relaxation
J
ΔJ = −1
ΔJ = −2
1
1.0
2
0.89
1.0
3
0.82
0.85
4
0.78
0.72
5
0.71
0.62
6
0.67
0.46
7
0.62
0.38
8
0.56
0.26
9
0.49
0.23
10
0.44
0.15
11
0.40
0.14
12
0.33
0.12
13
0.31
0.11
14
0.27
0.09
15
0.22
0.08
Table II
Relative Rotational Relaxation Efficiencies
Species
Relative efficiency
HF
1.0
He
0.03
Ar
0.03
N2
0.03
SF6
0.03
F2
0.03
F
0.03
H2
0.1
H
0.03
Table III
Possible V–R Relaxation Distributions About Jmin for HF(v,J) + M ⇋ HF(v′,J′) + M
Distribution
Jmin − 4
Jmin − 3
Jmin − 2
Jmin − 1
Jmin
Jmin + 1
Jmin + 2
1
0
0
0
1/3
1/3
1/3
0
2
0
0
0
0
1
0
0
3
0.05
0.05
0.05
0.25
0.3
0.25
0.05
Table IV
Effect of V–R Mechanisms for Cases Without R-R Lasing
Gas mixture: 0.02F:0.99F2:1 H2:20He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.8, L = 20 cm, l = 20 cm, P-branch lasing.
The distributions for V–R relaxation are listed in Table V.
The degree of completion ∊ is (F2 final)/(F2 initial).
Table V
Comparison of Vibrational-to-Rotational Energy Exchange Model with Vibrational-to-Translational Energy Exchange Model
Gas mixture: 0.02F:0.99F2:1H2:20 He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm. All models assume Polanyi pumping.
Distribution no. 3 is used for multiquanta VR relaxation.
Run not to completion; integration problems encountered.
Gas mixture: 0.02F:0.99F2:1H2:20 He, Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm.
Distributions for VR relaxation are listed in Table V; multiquanta relaxation and Boltzmann pumping are assumed.
Rotational lasing was not allowed to occur for this case.
Table VII
Impact of Important Kinetics on Laser Performance b
Gas mixture: 0.02F:0.99F2:1H2:20He; Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm.
Distribution no. 3 is used for V–R relaxation; multiquanta VR and Boltzmann pumping are assumed.
RR lasing was strong at P-branch lasing cutoff.
Case not run to completion; computation time excessive.
Table VIII
Effect of Rotational Relaxation Rate on Laser Performance
Relative rotational lasing energy on vibrational levels
ERR (J/litre)
PRRmax (W/cc)
TRRmax (μsec)
0
1
2
3
4
5
6
106
Wilkins
1.00/12
0.58/10
0.12/9
0.10/22
0.08/13
0.02/11
0.007/4
0.016
1.83
31.00
115
Revised Wilkins
0.88/12
1.00/5
0
0
0
0
0
0.67E-4
0.0028
18.50
Gas mixture: 0.02F:0.99F2:1H2:20He; Ti = 300 K, Pi = 20 Torr. Cavity conditions: R0 = 1.0, RL = 0.7, L = 10.0 cm, l = 10.0 cm.
Distribution no. 3 is used for V–R relaxation; multiquanta V–R and Polanyi pumping are assumed.