Abstract

A rate equation model of a pulsed DF-CO2 chemical transfer laser is Simplified by investigating the relationship of kinetic mechanisms. The model reduces to one equation which when Solved permits calculation of all pulse characteristics as a function of time. At low levels of initiation, predictions of this laser simulation model are in excellent agreement with those of a more comprehensive model presented in an earlier paper. Model predictions are also found to be consistent with experiment. The simplicity of the present model lends itself to easy physical interpretation and permits efficient and accurate prediction of transfer laser performance characteristics in regimes of practical interest.

© 1973 Optical Society of America

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References

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  1. R. L. Kerber, N. Cohen, G. Emanuel, IEEE J. Quantum Electron. QE-9, 94 (1973).
    [CrossRef]
  2. R. L. Kerber, “A Parametric Study of a Pulsed DF-CO2 Chemical Transfer Laser,” to be published.
  3. G. Emanuel, W. D. Adams, E. B. Turner, RESALE-1: A Chemical Laser Computer Program, Report TR-0172(2776)-1 (Aerospace Corp., El Segundo, Calif., July1971; G. Emanuel, W. D. Adams, RESALE-2, CO2, and INHALE, Report TR-0172(2776)-5 (Aerospace Corp., El Segundo, Calif., April1972).
  4. S. N. Suchard, A. Ching, J. S. Whittier, Appl. Phys. Lett. 21, 274 (1972).
    [CrossRef]
  5. S. N. Suchard, private communication, 1972.
  6. W. D. Breshears; private communication, 1972.
  7. J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
    [CrossRef]
  8. J. Herbelin, G. Emanuel, Einstein Coefficients for Diatomic Molecules, a technical report to be published by Aerospace Corp.
  9. J. F. Bott, N. Cohen, submitted to J. Chem. Phys.
  10. J. F. Bott; private communication, 1972.
  11. J. F. Bott, N. Cohen, to be published.
  12. J. R. Airey, I. W. M. Smith, J. Chem. Phys. 57, 1169 (1972).
    [CrossRef]

1973

R. L. Kerber, N. Cohen, G. Emanuel, IEEE J. Quantum Electron. QE-9, 94 (1973).
[CrossRef]

1972

S. N. Suchard, A. Ching, J. S. Whittier, Appl. Phys. Lett. 21, 274 (1972).
[CrossRef]

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

J. R. Airey, I. W. M. Smith, J. Chem. Phys. 57, 1169 (1972).
[CrossRef]

Adams, W. D.

G. Emanuel, W. D. Adams, E. B. Turner, RESALE-1: A Chemical Laser Computer Program, Report TR-0172(2776)-1 (Aerospace Corp., El Segundo, Calif., July1971; G. Emanuel, W. D. Adams, RESALE-2, CO2, and INHALE, Report TR-0172(2776)-5 (Aerospace Corp., El Segundo, Calif., April1972).

Airey, J. R.

J. R. Airey, I. W. M. Smith, J. Chem. Phys. 57, 1169 (1972).
[CrossRef]

Bott, J. F.

J. F. Bott; private communication, 1972.

J. F. Bott, N. Cohen, to be published.

J. F. Bott, N. Cohen, submitted to J. Chem. Phys.

Breshears, W. D.

W. D. Breshears; private communication, 1972.

Ching, A.

S. N. Suchard, A. Ching, J. S. Whittier, Appl. Phys. Lett. 21, 274 (1972).
[CrossRef]

Cohen, N.

R. L. Kerber, N. Cohen, G. Emanuel, IEEE J. Quantum Electron. QE-9, 94 (1973).
[CrossRef]

J. F. Bott, N. Cohen, submitted to J. Chem. Phys.

J. F. Bott, N. Cohen, to be published.

Emanuel, G.

R. L. Kerber, N. Cohen, G. Emanuel, IEEE J. Quantum Electron. QE-9, 94 (1973).
[CrossRef]

G. Emanuel, W. D. Adams, E. B. Turner, RESALE-1: A Chemical Laser Computer Program, Report TR-0172(2776)-1 (Aerospace Corp., El Segundo, Calif., July1971; G. Emanuel, W. D. Adams, RESALE-2, CO2, and INHALE, Report TR-0172(2776)-5 (Aerospace Corp., El Segundo, Calif., April1972).

J. Herbelin, G. Emanuel, Einstein Coefficients for Diatomic Molecules, a technical report to be published by Aerospace Corp.

Herbelin, J.

J. Herbelin, G. Emanuel, Einstein Coefficients for Diatomic Molecules, a technical report to be published by Aerospace Corp.

Kerber, R. L.

R. L. Kerber, N. Cohen, G. Emanuel, IEEE J. Quantum Electron. QE-9, 94 (1973).
[CrossRef]

R. L. Kerber, “A Parametric Study of a Pulsed DF-CO2 Chemical Transfer Laser,” to be published.

Polanyi, J. C.

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

Smith, I. W. M.

J. R. Airey, I. W. M. Smith, J. Chem. Phys. 57, 1169 (1972).
[CrossRef]

Suchard, S. N.

S. N. Suchard, A. Ching, J. S. Whittier, Appl. Phys. Lett. 21, 274 (1972).
[CrossRef]

S. N. Suchard, private communication, 1972.

Turner, E. B.

G. Emanuel, W. D. Adams, E. B. Turner, RESALE-1: A Chemical Laser Computer Program, Report TR-0172(2776)-1 (Aerospace Corp., El Segundo, Calif., July1971; G. Emanuel, W. D. Adams, RESALE-2, CO2, and INHALE, Report TR-0172(2776)-5 (Aerospace Corp., El Segundo, Calif., April1972).

Whittier, J. S.

S. N. Suchard, A. Ching, J. S. Whittier, Appl. Phys. Lett. 21, 274 (1972).
[CrossRef]

Woodall, K. B.

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

Appl. Phys. Lett.

S. N. Suchard, A. Ching, J. S. Whittier, Appl. Phys. Lett. 21, 274 (1972).
[CrossRef]

IEEE J. Quantum Electron.

R. L. Kerber, N. Cohen, G. Emanuel, IEEE J. Quantum Electron. QE-9, 94 (1973).
[CrossRef]

J. Chem. Phys.

J. C. Polanyi, K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
[CrossRef]

J. R. Airey, I. W. M. Smith, J. Chem. Phys. 57, 1169 (1972).
[CrossRef]

Other

J. Herbelin, G. Emanuel, Einstein Coefficients for Diatomic Molecules, a technical report to be published by Aerospace Corp.

J. F. Bott, N. Cohen, submitted to J. Chem. Phys.

J. F. Bott; private communication, 1972.

J. F. Bott, N. Cohen, to be published.

R. L. Kerber, “A Parametric Study of a Pulsed DF-CO2 Chemical Transfer Laser,” to be published.

G. Emanuel, W. D. Adams, E. B. Turner, RESALE-1: A Chemical Laser Computer Program, Report TR-0172(2776)-1 (Aerospace Corp., El Segundo, Calif., July1971; G. Emanuel, W. D. Adams, RESALE-2, CO2, and INHALE, Report TR-0172(2776)-5 (Aerospace Corp., El Segundo, Calif., April1972).

S. N. Suchard, private communication, 1972.

W. D. Breshears; private communication, 1972.

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Figures (3)

Fig. 1
Fig. 1

Effect of level of initiation on peak power.

Fig. 2
Fig. 2

(a) Effect of level of initiation on pulse duration: X(D + F):1F2:1D2:8CO2:40He. (b) Effect of level of initiation on pulse duration: X(D + F):1F2:1D2:50CO2.

Fig. 3
Fig. 3

Effect of level of initiation on laser efficiency.

Tables (2)

Tables Icon

Table I Recommended Rate Coefficients for the D2–F2–CO2 Chemical Laser

Tables Icon

Table II Comparison of Model and Experiment

Equations (53)

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F + D 2 g c ( v ) k c D F ( v ) + D + 30.63 kcal / mole , D + F 2 g h ( v ) k h D F ( v ) + F + 99.33 kcal / mole ;
D F ( v ) + M k d f ( M , v ) D F ( v - 1 ) + M ;
D F ( v ) + CO 2 ( 00 0 0 ) k t ( v ) D F ( v - 1 ) + CO 2 ( 00 0 1 ) ;
CO 2 ( 00 0 1 ) + M k CO 2 ( M ) CO 2 ( ν 1 , ν 2 l , 0 ) + M .
k CO 2 ( M )
v v P v = v T v + v v d [ D F ( v ) ] d t + v D v , v - 1 ,
P v = g c ( v ) k c [ F ] [ D 2 ] + g h ( v ) k h [ D ] [ F 2 ] ,
T v = k t ( v ) [ D F ( v ) ] [ CO 2 ( 00 0 0 ) ] ,
D v , v - 1 = [ D F ( v ) ] M k d f ( M , v ) [ M ] ,
v v P v
v T v
v T v = d [ CO 2 ( 00 0 1 ) ] d t + D c + χ ,
D c = [ CO 2 ( 00 0 1 ) ] M k CO 2 ( M ) [ M ] .
α thr = - ln ( R 0 R L ) / 2 L ,
α = h N A ω B ϕ 4 π [ 2 J + 1 2 J - 1 [ CO 2 ( 00 0 1 ; J - 1 ) ] - [ CO 2 ( 10 0 0 ; J ) ] ] ,
B = 1.08 × 10 13 J / ( 2 J + 1 ) cm 2 / molecule - j - sec .
[ CO 2 ( ν 1 , ν 2 l , ν 3 ; J ) ] = [ CO 2 ( ν 1 , ν 2 l , ν 3 ) ] 2 θ r T ( 2 J + 1 ) × exp [ - h c A J ( J + 1 ) / k T ] ,
[ CO 2 ( 10 0 0 ) ] [ CO 2 ] e 3.97 θ / { 1 + 2 e 1.91 θ + e 3.67 θ + 2 e 3.815 θ + e 3.97 θ } ,
[ CO 2 ( 00 0 1 ) ] = { 2 π α thr T exp [ h c A J ( J - 1 ) / k T ] h N A ω B ϕ θ r ( 2 J + 1 ) } + [ CO 2 ( 10 0 0 ) ] exp ( - 2 h c A J / k T ) .
i [ N i ] C v i d T d t = - P L - i d [ N i ] d t H i ,
C v i
P L = h c N A ω χ .
i [ N i ] C v i d T d t [ F ] [ D 2 ] k c Δ H c + [ D ] [ F 2 ] k h Δ H h ,
d [ F ] d t = [ D ] [ F 2 ] k h - [ F ] [ D 2 ] k c ,
d [ D ] / d t = - d [ F ] / d t .
[ F + D ] t = [ F + D ] t = 0 .
[ F ] [ D 2 ] k c [ D ] [ F 2 ] k h .
v v P v = k c [ F ] [ D 2 ] G v ,
G v = v v [ g c ( v ) + g h ( v ) ] ,
d T d t = k c [ F ] [ D 2 ] Δ H / i [ N i ] C v i ,
d [ D 2 ] d t = - d T d t i [ N i ] C v i / Δ H .
d 2 T d t 2 = d T d t { - k c [ F ] + 1 k c d k c d T d T d t } .
[ D F ] t = 2 { [ D 2 ] t = 0 - [ D 2 ] t } .
χ = k c [ F ] [ D 2 ] G v - d [ CO 2 ( 00 0 1 ) ] d t - [ CO 2 ( 00 0 1 ) ] M k CO 2 ( M ) [ M ] .
E = 0 t c P L d t ,
η = ( E × 100 / mole F 2 ) / 129.96 / mole F 2 .
I 0 = P L L ( 1 - R 0 ) / { [ 1 + ( R 0 / R L ) 1 / 2 ] [ 1 - ( R 0 R L ) 1 / 2 ] } .
k CO 2 ( M )
X ( D + F ) : 1 F 2 : 1 D 2 : 8 CO 2 : 40 He and X ( D + F ) : 1 F 2 : 1 D 2 : 50 CO 2 ,
k c [ F ] [ D 2 ] G v = [ CO 2 ( 00 0 0 ) ] v k t ( v ) [ D F ( v ) ] + v v d [ D F ( v ) ] d t + v [ D F ( v ) ] M k d f ( M , v ) [ M ] .
k t ( v ) = v k t ( 1 ) ,
k d f ( M , v ) v k d f ( M , 1 ) .
k c [ F ] [ D 2 ] G v β [ 1 + 1 β d d t + 1 β M k d f ( M , 1 ) [ M ] ] × v v [ D F ( v ) ] ,
β = k t ( 1 ) [ CO 2 ( 00 0 0 ) ] .
[ CO 2 ( 00 0 0 ) ] [ CO 2 ] .
v v [ D F ( v ) ]
ϕ = ( ln 2 / π ) 1 / 2 e y 2 ( 1 - erf ( y ) ) / α D P ,
y = ( ln 2 ) 1 / 2 α L R / α D P .
α D P = ( 2 × 10 7 N A k T ln 2 W * ) 1 / 2 × ω c ,
α L R = i [ N i ] R T 1 / 2 W j a j [ N j ] / ρ ,
ϕ = [ 1 - ξ + 3 ξ 2 - 15 ξ 3 + 105 ξ 4 ] / [ π α L R ] ,
ξ = 1 / ( 2 y 2 ) .
α = A * / T 1 / 2 ,

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