R. L. Kerber and J. J. T. Hough, "Rotational nonequilibrium mechanisms in pulsed H_{2}
+ F_{2} chain reaction lasers. 1: Effect on gross laser
performance parameters," Appl. Opt. 17, 2369-2380 (1978)

A rate equation model of a pulsed H_{2} + F_{2} 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 H_{2} + F_{2} 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 + H_{2} 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 H_{2} +
F_{2} model is significantly different from that observed for the F
+ H_{2} 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 F_{2}:1 H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
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 H_{2} +
F_{2} Laser Performance^{a}

Gas mixture: 0.02 F:0.99 F_{2}:H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
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
Distribution^{a}

υ

J_{max}

Reaction F + H_{2}
→ HF(υ) + H

1

11

2

10

3

8

4

2

Reaction H + F_{2}
→ HF(υ) + H

0–6

12

The distribution was 50% into the
J_{max} level and 25% into the
level directly above and below J_{max}.

Table VII

Effect of Preferential Pumping on H_{2} + F_{2} Laser
Performance^{a}

Gas mixture: 0.02 F:0.99 F_{2}:1 H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
0.8, L = 20 cm.
For these calculations, the time constant rotational relaxation model
(τ) was used with multiquanta HF VT
relaxation and P_{r} =
1.0.

Table VIII

Effect of Line-Selected Operation on H_{2} + F_{2}
Laser Performance^{a}

Gas mixture: 0.02 F:0.99 F_{2}:1 H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
0.8, L = 20 cm.
These calculations are from Model ΔJ with
P_{R} = 1.0, and
the HF–HF VT relaxation rate is assumed to vary as
υ^{2.4} 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 H_{2} +
F_{2} Laser Performance^{a}

Case

Vibrational relaxation
distribution

Relative band
energy/J_{max}

E
(J/liter atm)

P_{p} W/cc

Time
(μsec)

1–0

2–1

3–2

4–3

5–4

6–5

t_{1%}

t_{p}

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
P_{R} = 1.0.
Gas mixture: 0.02 F:0.99 F_{2}:1 H_{2}:20 He,
T_{i} = 30 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
0.8, L = 20 cm.

Tables (9)

Table I

Effect of Rotational Nonequilibrium on H_{2} + F_{2}
Laser Performance (at atmospheric pressure)^{a}

Case

P_{R}

Relative band
energy/J_{max}

E
(J/liter atm)

P_{p} W/cc

Time
(μsec)

1–0

2–1

3–2

4–3

5–4

6–5

t_{1%}

t_{p}

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 F_{2}:1 H_{2}:50 Ar,
T_{i} = 300 K,
P_{i} = 1.2 atm.
Cavity conditions: R_{O}
= 1.0, R_{L} =
0.8, L = 100 cm.

Table II

Relative Rotational Relaxation Efficiencies

Species

Relative efficiency

HF

1.0

He

0.03

Ar

0.03

F_{2}

0.03

H_{2}

0.1

H

0.03

F

0.03

Table III

Effect of Rotational Relaxation Model on H_{2} +
F_{2} Laser Performance (at low pressure)^{a}

Gas mixture: 0.02 F:0.99 F_{2}:1 H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
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 H_{2} +
F_{2} Laser Performance^{a}

Gas mixture: 0.02 F:0.99 F_{2}:H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
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
Distribution^{a}

υ

J_{max}

Reaction F + H_{2}
→ HF(υ) + H

1

11

2

10

3

8

4

2

Reaction H + F_{2}
→ HF(υ) + H

0–6

12

The distribution was 50% into the
J_{max} level and 25% into the
level directly above and below J_{max}.

Table VII

Effect of Preferential Pumping on H_{2} + F_{2} Laser
Performance^{a}

Gas mixture: 0.02 F:0.99 F_{2}:1 H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
0.8, L = 20 cm.
For these calculations, the time constant rotational relaxation model
(τ) was used with multiquanta HF VT
relaxation and P_{r} =
1.0.

Table VIII

Effect of Line-Selected Operation on H_{2} + F_{2}
Laser Performance^{a}

Gas mixture: 0.02 F:0.99 F_{2}:1 H_{2}:20 He,
T_{i} = 300 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
0.8, L = 20 cm.
These calculations are from Model ΔJ with
P_{R} = 1.0, and
the HF–HF VT relaxation rate is assumed to vary as
υ^{2.4} 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 H_{2} +
F_{2} Laser Performance^{a}

Case

Vibrational relaxation
distribution

Relative band
energy/J_{max}

E
(J/liter atm)

P_{p} W/cc

Time
(μsec)

1–0

2–1

3–2

4–3

5–4

6–5

t_{1%}

t_{p}

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
P_{R} = 1.0.
Gas mixture: 0.02 F:0.99 F_{2}:1 H_{2}:20 He,
T_{i} = 30 K,
P_{i} = 20 Torr.
Cavity conditions: R_{O}
= 1.0, R_{L} =
0.8, L = 20 cm.