Abstract

Geometrical and physical optics models for calculating the closed-cavity power of a cw supersonic diffusion chemical laser are presented. The mixing and kinetic gain medium formulation employed in these calculations is described along with its anchoring to HF small signal gain data. Mixing parameters thus established are used to compute the closed-cavity power and spectral distribution with the two models, which agree reasonably well with experimental data. The reasonably good agreement between the two models in their computed spectra, intensity, and loaded gain distributions indicates that in many applications the use of the more economical geometric model may be adequate for extensive closed-cavity power computations and performance analyses of chemical lasers.

© 1983 Optical Society of America

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References

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  1. A. Bhowmik, Appl. Opt. 22, 3338 (1983).
    [CrossRef] [PubMed]
  2. R. R. Mikatarian, AIAA Seventh Fluid Plasma Dynamics Conference, Palo Alto, 1974.
  3. T. T. Yang, J. Phys. 41, C9-51 (1980).
  4. E. A. Sziklas, A. E. Siegman, Appl. Opt. 14, 1874 (1975).
    [CrossRef] [PubMed]
  5. E. O. Brigham, Fast Fourier Transform (Prentice-Hall, Engle-wood Cliffs, N.J., 1964).
  6. T. T. Yang, AIAA J. 18, 1223 (1980).
    [CrossRef]
  7. B. E. Launder, J. Heat Transfer, 86, 360 (1964).
    [CrossRef]
  8. N. Cohen, SAMSO-TR-78-41, June1978.
  9. J. G. Skifstad, C. M. Chao, Appl. Opt. 14, 1713 (1975).
    [CrossRef] [PubMed]
  10. R. J. Hall, IEEE J. Quantum Electron. QE-12, 453 (1976).
    [CrossRef]
  11. J. J. T. Hough, Opt. Lett. 3, 223 (1978).
    [CrossRef] [PubMed]
  12. R. L. Kerber, J. J. T. Hough, Appl. Opt. 17, 2369 (1978).
    [CrossRef] [PubMed]

1983 (1)

1980 (2)

T. T. Yang, J. Phys. 41, C9-51 (1980).

T. T. Yang, AIAA J. 18, 1223 (1980).
[CrossRef]

1978 (2)

1976 (1)

R. J. Hall, IEEE J. Quantum Electron. QE-12, 453 (1976).
[CrossRef]

1975 (2)

1964 (1)

B. E. Launder, J. Heat Transfer, 86, 360 (1964).
[CrossRef]

Bhowmik, A.

Brigham, E. O.

E. O. Brigham, Fast Fourier Transform (Prentice-Hall, Engle-wood Cliffs, N.J., 1964).

Chao, C. M.

Cohen, N.

N. Cohen, SAMSO-TR-78-41, June1978.

Hall, R. J.

R. J. Hall, IEEE J. Quantum Electron. QE-12, 453 (1976).
[CrossRef]

Hough, J. J. T.

Kerber, R. L.

Launder, B. E.

B. E. Launder, J. Heat Transfer, 86, 360 (1964).
[CrossRef]

Mikatarian, R. R.

R. R. Mikatarian, AIAA Seventh Fluid Plasma Dynamics Conference, Palo Alto, 1974.

Siegman, A. E.

Skifstad, J. G.

Sziklas, E. A.

Yang, T. T.

T. T. Yang, J. Phys. 41, C9-51 (1980).

T. T. Yang, AIAA J. 18, 1223 (1980).
[CrossRef]

AIAA J. (1)

T. T. Yang, AIAA J. 18, 1223 (1980).
[CrossRef]

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

R. J. Hall, IEEE J. Quantum Electron. QE-12, 453 (1976).
[CrossRef]

J. Heat Transfer (1)

B. E. Launder, J. Heat Transfer, 86, 360 (1964).
[CrossRef]

J. Phys. (1)

T. T. Yang, J. Phys. 41, C9-51 (1980).

Opt. Lett. (1)

Other (3)

N. Cohen, SAMSO-TR-78-41, June1978.

E. O. Brigham, Fast Fourier Transform (Prentice-Hall, Engle-wood Cliffs, N.J., 1964).

R. R. Mikatarian, AIAA Seventh Fluid Plasma Dynamics Conference, Palo Alto, 1974.

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Figures (8)

Fig. 1
Fig. 1

Wave optics closed-cavity model.

Fig. 2
Fig. 2

Geometric optics closed-cavity model.

Fig. 3
Fig. 3

Small signal gain comparison.

Fig. 4
Fig. 4

Closed-cavity wave optics power convergence is stable.

Fig. 5
Fig. 5

Comparison of wave and geometric optics closed-cavity power with HF experimental data.

Fig. 6
Fig. 6

Comparison of wave and geometric optics spectral content (and experiment at 2Xc = 3.0 cm).

Fig. 7
Fig. 7

Comparison of two-way intensity and loaded gain profiles between wave and geometric optics for P1(7).

Fig. 8
Fig. 8

Comparison of two-way intensity and loaded gain profiles between wave and geometric optics for P2(7).

Equations (16)

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ψ V J ( x ) = ψ V J ( 0 ) exp [ i ϕ ( x ) ] ,
ψ V J [ x n , ϕ ( x n ) ] = ψ V J ( 0 ) exp { i [ R V J ( x n ) 1 / 2 ] 2 π } , [ 0 R V J ( x n ) 1 ] ,
ψ V J ( x , z ) = F 1 { exp ( ikz ) F [ ψ V J ( x , 0 ) ] } ,
I ( x , z ) = V , J | ψ V J ( x , z ) | 2 .
| ψ trans ± | 2 = exp ( α ¯ L G ) | ψ inc ± | 2 ,
Ĩ = [ exp ( α ¯ L G 1 ) ] α ¯ L G ( | ψ inc ± | 2 + | ψ inc | 2 ) ,
P i = ( 1 r j ) x n = A + A | ψ tran ( s ) ( x n ) | 2 , [ i = 1 , s = ( ) ; i = 2 , s = ( + ) ] ,
m ˙ = m ˙ o { 1 [ erf 2 ( r r o L m ) 1 / 2 ] } ,
α ( V , J ) = h ω ( V , J ) S ( V , J ) ρ N o B e ( V , J ) × { 2 J + 1 2 J 1 HF ( V + 1 , J 1 ) HF ( V , J ) } ,
Ĩ ( z ) = I + ( z ) I ( z ) ,
Ĩ = 1 L G L G / 2 L G / 2 [ I + ( z ) + I ( z ) ] d z = ( I + I + ) + ( I I ) α ¯ L G ,
d HF ( V , J ) d t = P ( V , J ) + B ( V , J ) R ( V ) + α V , J Ĩ V , J α V 1 , J + 1 Ĩ V 1 , J + 1 + HF e ( V , J ) HF ( V , J ) τ R ( V , J ) ,
τ R ( V , J ) = 1 k M [ M ] = 1 P R Z HF M exp [ B E ( V , J ) K T ] [ M ] ,
d HF ( V , J ) d t = α V , J Ĩ V , J α V 1 , J + 1 Ĩ V 1 , J + 1 + HF e ( V , J ) HF ( V , J ) τ R ( V , J ) .
α ( V , J ) = ϕ V , J [ 2 J + 1 2 J 1 HF ( V + 1 , J 1 ) HF ( V , J ) ] ,
α V , J = α V , J e + τ V , J ϕ V , J [ 2 J + 1 2 J 1 α V + 1 , J 1 Ĩ V + 1 , J 1 + α V 1 , J + 1 Ĩ V 1 , J + 1 ] 1 + τ V , J ϕ V , J { 2 J + 1 2 J 1 + 1 } Ĩ V , J .

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