R. L. Kerber and J. J. T. Hough, "Rotational nonequilibrium mechanisms in pulsed H2
+ F2 chain reaction lasers. 1: Effect on gross laser
performance parameters," Appl. Opt. 17, 2369-2380 (1978)
A rate equation model of a pulsed H2 + F2 chemical
laser is used to examine the relative importance of rotational nonequilibrium
mechanisms on laser performance. This computer model yields the time history of
the first thirteen rotational levels and the first twelve
vibrational–rotational P-branch transitions for the
first six vibrational bands of HF. With this model, the general effects of
rotational nonequilibrium on the H2 + F2 laser
were found (1) to increase the number of transitions that lase simultaneously,
(2) to lower the intensity of each transition, and (3) to extend the duration of
lasing on each transition; these trends are similar to those observed earlier
for the F + H2 laser. The major thrust of the present work is
to isolate the relative importance of the various rotational nonequilibrium
mechanisms. To this end, we have examined and compared several approaches to
modeling R–T and V–R relaxation, nonequilibrium pumping
distributions, and line-selected operation. The effects of these mechanisms (and
their relative importance) on the laser output are clearly revealed by the
model. The character of the spectra for the H2 +
F2 model is significantly different from that observed for the F
+ H2 model. The ability of the model to predict spectra
observed in experiments is assessed, and the model is found to compare well with
discharge-initiated lasers. Additional calculations demonstrate the effect of
multiquanta V-T deactivation of HF by HF.
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Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
For these calculations, the multiquanta HF VT relaxation model was used.
Note, the rotational level scaling constant is
denoted as B.
Table IV
Effect of HF-HF VT Deactivation Model on H2 +
F2 Laser Performancea
Case
Total VT rate
variation
Multiquanta HF–HF
VT
Relative band
energy/Jmax
E (J/l
atm)
Pp
watts/cc
Time
(μsec)
1–0
2–1
3–2
4–3
5–4
6–5
t1%,
tp
16
υ2.4
without
0.42/7
1.0/7
0.72/7
0.42/6
0.28/5
0.09/4
53.6
26.2
84.4
47.1
1
υ2.4
with
0.51/6
1.0/6
0.42/6
0.21/5
0.25/5
0.14/4
20.4
16.4
58.1
20.7
34
υ
without
0.30/7
0.90/7
1.0/8
0.95/8
0.80/7
0.40/6
123.1
43.8
129.0
69.3
Gas mixture: 0.02 F:0.99 F2:H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm. Rotational relaxation probably
(PR) = 1.0.
Table V
Effect of Rotational Relaxation Model on H2 +
F2 Laser Performance (at low pressure)a
Gas mixture: 0.02 F:0.99 F2:H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
For these calculations, the single quantum HF VT relaxation model was
used.
Complete calculation is not available at the present time.
Table VI
Maximum J Level for Strong Rotational Pumping
Distributiona
υ
Jmax
Reaction F + H2
→ HF(υ) + H
1
11
2
10
3
8
4
2
Reaction H + F2
→ HF(υ) + H
0–6
12
The distribution was 50% into the
Jmax level and 25% into the
level directly above and below Jmax.
Table VII
Effect of Preferential Pumping on H2 + F2 Laser
Performancea
Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
For these calculations, the time constant rotational relaxation model
(τ) was used with multiquanta HF VT
relaxation and Pr =
1.0.
Table VIII
Effect of Line-Selected Operation on H2 + F2
Laser Performancea
Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
These calculations are from Model ΔJ with
PR = 1.0, and
the HF–HF VT relaxation rate is assumed to vary as
υ2.4 with the single quantum
model.
Maximum J is noted only when it is not obvious from line
selection.
Table IX
Effect of Preferential VV and VT Relaxation on H2 +
F2 Laser Performancea
Case
Vibrational relaxation
distribution
Relative band
energy/Jmax
E
(J/liter atm)
Pp W/cc
Time
(μsec)
1–0
2–1
3–2
4–3
5–4
6–5
t1%
tp
34
Boltzmann
0.30/7
0.90/7
1.0/8
0.95/8
0.80/7
0.40/6
123.1
43.8
129.0
69.3
35
Preferential
0.32/7
0.92/7
1.0/8
0.96/8
0.81/7
0.41/6
123.5
43.9
129.3
69.4
Rate coefficients are the same as those given in Table II (i.e., HF–HF VT rate is
linear in υ and proportional to
υ). Calculations were made with model
τ and
PR = 1.0.
Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 30 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
Tables (9)
Table I
Effect of Rotational Nonequilibrium on H2 + F2
Laser Performance (at atmospheric pressure)a
Case
PR
Relative band
energy/Jmax
E
(J/liter atm)
Pp W/cc
Time
(μsec)
1–0
2–1
3–2
4–3
5–4
6–5
t1%
tp
A
Equil.
0.32/8
1.0/9
0.76/7
0.61/7
0.53/7
0.36/6
126
6.46
4.28
1.21
B
0.2
0.47/9
1.0/8
0.85/8
0.71/8
0.62/7
0.35/6
124
6.24
4.16
1.15
C
0.02
0.55/9
1.0/8
0.91/8
0.80/8
0.71/7
0.40/6
102
5.27
4.03
1.16
Gas mixture: 0.1 F:1 F2:1 H2:50 Ar,
Ti = 300 K,
Pi = 1.2 atm.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 100 cm.
Table II
Relative Rotational Relaxation Efficiencies
Species
Relative efficiency
HF
1.0
He
0.03
Ar
0.03
F2
0.03
H2
0.1
H
0.03
F
0.03
Table III
Effect of Rotational Relaxation Model on H2 +
F2 Laser Performance (at low pressure)a
Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
For these calculations, the multiquanta HF VT relaxation model was used.
Note, the rotational level scaling constant is
denoted as B.
Table IV
Effect of HF-HF VT Deactivation Model on H2 +
F2 Laser Performancea
Case
Total VT rate
variation
Multiquanta HF–HF
VT
Relative band
energy/Jmax
E (J/l
atm)
Pp
watts/cc
Time
(μsec)
1–0
2–1
3–2
4–3
5–4
6–5
t1%,
tp
16
υ2.4
without
0.42/7
1.0/7
0.72/7
0.42/6
0.28/5
0.09/4
53.6
26.2
84.4
47.1
1
υ2.4
with
0.51/6
1.0/6
0.42/6
0.21/5
0.25/5
0.14/4
20.4
16.4
58.1
20.7
34
υ
without
0.30/7
0.90/7
1.0/8
0.95/8
0.80/7
0.40/6
123.1
43.8
129.0
69.3
Gas mixture: 0.02 F:0.99 F2:H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm. Rotational relaxation probably
(PR) = 1.0.
Table V
Effect of Rotational Relaxation Model on H2 +
F2 Laser Performance (at low pressure)a
Gas mixture: 0.02 F:0.99 F2:H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
For these calculations, the single quantum HF VT relaxation model was
used.
Complete calculation is not available at the present time.
Table VI
Maximum J Level for Strong Rotational Pumping
Distributiona
υ
Jmax
Reaction F + H2
→ HF(υ) + H
1
11
2
10
3
8
4
2
Reaction H + F2
→ HF(υ) + H
0–6
12
The distribution was 50% into the
Jmax level and 25% into the
level directly above and below Jmax.
Table VII
Effect of Preferential Pumping on H2 + F2 Laser
Performancea
Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
For these calculations, the time constant rotational relaxation model
(τ) was used with multiquanta HF VT
relaxation and Pr =
1.0.
Table VIII
Effect of Line-Selected Operation on H2 + F2
Laser Performancea
Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 300 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
These calculations are from Model ΔJ with
PR = 1.0, and
the HF–HF VT relaxation rate is assumed to vary as
υ2.4 with the single quantum
model.
Maximum J is noted only when it is not obvious from line
selection.
Table IX
Effect of Preferential VV and VT Relaxation on H2 +
F2 Laser Performancea
Case
Vibrational relaxation
distribution
Relative band
energy/Jmax
E
(J/liter atm)
Pp W/cc
Time
(μsec)
1–0
2–1
3–2
4–3
5–4
6–5
t1%
tp
34
Boltzmann
0.30/7
0.90/7
1.0/8
0.95/8
0.80/7
0.40/6
123.1
43.8
129.0
69.3
35
Preferential
0.32/7
0.92/7
1.0/8
0.96/8
0.81/7
0.41/6
123.5
43.9
129.3
69.4
Rate coefficients are the same as those given in Table II (i.e., HF–HF VT rate is
linear in υ and proportional to
υ). Calculations were made with model
τ and
PR = 1.0.
Gas mixture: 0.02 F:0.99 F2:1 H2:20 He,
Ti = 30 K,
Pi = 20 Torr.
Cavity conditions: RO
= 1.0, RL =
0.8, L = 20 cm.
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