Abstract

A theoretical analysis of the behavior of 400-watt Hg + TlI arc lamps with variable mercury loadings is performed. It is quantitatively shown that, as the Hg loading is doubled, the following effects may be predicted: (a) the effective arc temperature decreases from 5100 K to 4800 K, (b) the effective radius increases by ~10%, (c) the escape factor for the imprisoned Tl 5350 Å line increases ~40%, (d) the power radiated in the Tl 5350 Å line increases ~10%, and (e) the power radiated in the Hg visible line decreases ~15%. These results are in agreement with the experimental observations of Larson. These effects result in an increase in the lumen-per-watt ratings, which is of technological significance. Self-absorption is an important factor in the radiation of the Tl 5350 Å line, and it is shown that the experimental observations are reasonably consistent with the assumption of local thermodynamic equilibrium.

© 1970 Optical Society of America

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References

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  1. D. A. Larson, H. D. Fraser, W. V. Cushing, M. C. Unglert, Illum. Engr. 58, 434 (1963).
  2. G. H. Reiling, J. Opt. Soc. Amer. 54, 532 (1964); Inst. Radio Engr. Trans. Electron Devices ED-9, 271 (1962).
    [CrossRef]
  3. W. C. Gungle, F. Koury, J. F. Waymouth, J. Opt. Soc. Amer. 54, 566 (1964); J. F. Waymouth, W. C. Gungle, J. M. Harris, F. Koury, Illum. Engr. 60, 85 (1965).
  4. E. C. Martt, L. J. Smialek, A. C. Green, Illum. Engr. 59, 34 (1964).
  5. T. H. Rautenberg, P. D. Johnson, Appl. Opt. 3, 487 (1964); P. D. Johnson, T. H. Rautenberg, J. Opt. Soc. Amer. 54, 1425 (1964).
    [CrossRef]
  6. L. S. Frost, C. F. Gallo (unpublished studies performed at the Westinghouse Research Laboratory).
  7. D. H. Pollock, J. A. Duardo, Bull. Amer. Phys. Soc. 12, 220 (1967).
  8. C. F. Gallo, Appl. Opt. 5, 1285 (1966). (In this reference, the i.d. of the quartz arc tube is incorrectly given on the top of page 1286 as 9 mm. It should be 18 mm. There is also a typographical error in the Hg atomic density on p. 1287, line 8, which should read 4.5 × 1018 Hg atoms cm−3.)
    [CrossRef] [PubMed]
  9. C. F. Gallo, Appl. Opt. 6, 1563 (1967).
    [CrossRef] [PubMed]
  10. D. A. Larson, U.S. Patent3,431,447 and private communication.
  11. W. Elenbaas, The High Pressure Mercury Vapor Discharge (Wiley-Interscience, New York, 1951), pp. 56–62, 130, Eq. (4.4.5).
  12. Reference 11, pp. 3–10 and Chap. 10.
  13. Reference 11, pp. 18–23.
  14. Reference 11, pp. 41–45, 53–54.
  15. Reference 11, p. 61.
  16. T. Holstein, Phys. Rev. 83, 1159 (1951); Phys. Rev. 72, 1212 (1947).
    [CrossRef]
  17. A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University Press, Cambridge, 1934).
  18. S. Chen, M. Takeo, Rev. Mod. Phys. 29, 20 (1957).
    [CrossRef]
  19. W. Furssov, A. Vlassov, Phys. Z. Sowjetunion 10, 378 (1936). (This reference was taken from Ref. 16.)
  20. C. H. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements (U.S. Government Printing Office, Washington, D.C., 1962), NBS Monograph 53.
  21. Reference 11, pp. 9–10, 23–30, 53, 56–62.
  22. Reference 11, pp. 11–18, 145–148.

1967

D. H. Pollock, J. A. Duardo, Bull. Amer. Phys. Soc. 12, 220 (1967).

C. F. Gallo, Appl. Opt. 6, 1563 (1967).
[CrossRef] [PubMed]

1966

1964

G. H. Reiling, J. Opt. Soc. Amer. 54, 532 (1964); Inst. Radio Engr. Trans. Electron Devices ED-9, 271 (1962).
[CrossRef]

W. C. Gungle, F. Koury, J. F. Waymouth, J. Opt. Soc. Amer. 54, 566 (1964); J. F. Waymouth, W. C. Gungle, J. M. Harris, F. Koury, Illum. Engr. 60, 85 (1965).

E. C. Martt, L. J. Smialek, A. C. Green, Illum. Engr. 59, 34 (1964).

T. H. Rautenberg, P. D. Johnson, Appl. Opt. 3, 487 (1964); P. D. Johnson, T. H. Rautenberg, J. Opt. Soc. Amer. 54, 1425 (1964).
[CrossRef]

1963

D. A. Larson, H. D. Fraser, W. V. Cushing, M. C. Unglert, Illum. Engr. 58, 434 (1963).

1957

S. Chen, M. Takeo, Rev. Mod. Phys. 29, 20 (1957).
[CrossRef]

1951

T. Holstein, Phys. Rev. 83, 1159 (1951); Phys. Rev. 72, 1212 (1947).
[CrossRef]

1936

W. Furssov, A. Vlassov, Phys. Z. Sowjetunion 10, 378 (1936). (This reference was taken from Ref. 16.)

Bozman, W. R.

C. H. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements (U.S. Government Printing Office, Washington, D.C., 1962), NBS Monograph 53.

Chen, S.

S. Chen, M. Takeo, Rev. Mod. Phys. 29, 20 (1957).
[CrossRef]

Corliss, C. H.

C. H. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements (U.S. Government Printing Office, Washington, D.C., 1962), NBS Monograph 53.

Cushing, W. V.

D. A. Larson, H. D. Fraser, W. V. Cushing, M. C. Unglert, Illum. Engr. 58, 434 (1963).

Duardo, J. A.

D. H. Pollock, J. A. Duardo, Bull. Amer. Phys. Soc. 12, 220 (1967).

Elenbaas, W.

W. Elenbaas, The High Pressure Mercury Vapor Discharge (Wiley-Interscience, New York, 1951), pp. 56–62, 130, Eq. (4.4.5).

Fraser, H. D.

D. A. Larson, H. D. Fraser, W. V. Cushing, M. C. Unglert, Illum. Engr. 58, 434 (1963).

Frost, L. S.

L. S. Frost, C. F. Gallo (unpublished studies performed at the Westinghouse Research Laboratory).

Furssov, W.

W. Furssov, A. Vlassov, Phys. Z. Sowjetunion 10, 378 (1936). (This reference was taken from Ref. 16.)

Gallo, C. F.

Green, A. C.

E. C. Martt, L. J. Smialek, A. C. Green, Illum. Engr. 59, 34 (1964).

Gungle, W. C.

W. C. Gungle, F. Koury, J. F. Waymouth, J. Opt. Soc. Amer. 54, 566 (1964); J. F. Waymouth, W. C. Gungle, J. M. Harris, F. Koury, Illum. Engr. 60, 85 (1965).

Holstein, T.

T. Holstein, Phys. Rev. 83, 1159 (1951); Phys. Rev. 72, 1212 (1947).
[CrossRef]

Johnson, P. D.

Koury, F.

W. C. Gungle, F. Koury, J. F. Waymouth, J. Opt. Soc. Amer. 54, 566 (1964); J. F. Waymouth, W. C. Gungle, J. M. Harris, F. Koury, Illum. Engr. 60, 85 (1965).

Larson, D. A.

D. A. Larson, H. D. Fraser, W. V. Cushing, M. C. Unglert, Illum. Engr. 58, 434 (1963).

D. A. Larson, U.S. Patent3,431,447 and private communication.

Martt, E. C.

E. C. Martt, L. J. Smialek, A. C. Green, Illum. Engr. 59, 34 (1964).

Mitchell, A. C. G.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University Press, Cambridge, 1934).

Pollock, D. H.

D. H. Pollock, J. A. Duardo, Bull. Amer. Phys. Soc. 12, 220 (1967).

Rautenberg, T. H.

Reiling, G. H.

G. H. Reiling, J. Opt. Soc. Amer. 54, 532 (1964); Inst. Radio Engr. Trans. Electron Devices ED-9, 271 (1962).
[CrossRef]

Smialek, L. J.

E. C. Martt, L. J. Smialek, A. C. Green, Illum. Engr. 59, 34 (1964).

Takeo, M.

S. Chen, M. Takeo, Rev. Mod. Phys. 29, 20 (1957).
[CrossRef]

Unglert, M. C.

D. A. Larson, H. D. Fraser, W. V. Cushing, M. C. Unglert, Illum. Engr. 58, 434 (1963).

Vlassov, A.

W. Furssov, A. Vlassov, Phys. Z. Sowjetunion 10, 378 (1936). (This reference was taken from Ref. 16.)

Waymouth, J. F.

W. C. Gungle, F. Koury, J. F. Waymouth, J. Opt. Soc. Amer. 54, 566 (1964); J. F. Waymouth, W. C. Gungle, J. M. Harris, F. Koury, Illum. Engr. 60, 85 (1965).

Zemansky, M. W.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University Press, Cambridge, 1934).

Appl. Opt.

Bull. Amer. Phys. Soc.

D. H. Pollock, J. A. Duardo, Bull. Amer. Phys. Soc. 12, 220 (1967).

Illum. Engr.

E. C. Martt, L. J. Smialek, A. C. Green, Illum. Engr. 59, 34 (1964).

D. A. Larson, H. D. Fraser, W. V. Cushing, M. C. Unglert, Illum. Engr. 58, 434 (1963).

J. Opt. Soc. Amer.

G. H. Reiling, J. Opt. Soc. Amer. 54, 532 (1964); Inst. Radio Engr. Trans. Electron Devices ED-9, 271 (1962).
[CrossRef]

W. C. Gungle, F. Koury, J. F. Waymouth, J. Opt. Soc. Amer. 54, 566 (1964); J. F. Waymouth, W. C. Gungle, J. M. Harris, F. Koury, Illum. Engr. 60, 85 (1965).

Phys. Rev.

T. Holstein, Phys. Rev. 83, 1159 (1951); Phys. Rev. 72, 1212 (1947).
[CrossRef]

Phys. Z. Sowjetunion

W. Furssov, A. Vlassov, Phys. Z. Sowjetunion 10, 378 (1936). (This reference was taken from Ref. 16.)

Rev. Mod. Phys.

S. Chen, M. Takeo, Rev. Mod. Phys. 29, 20 (1957).
[CrossRef]

Other

C. H. Corliss, W. R. Bozman, Experimental Transition Probabilities for Spectral Lines of Seventy Elements (U.S. Government Printing Office, Washington, D.C., 1962), NBS Monograph 53.

Reference 11, pp. 9–10, 23–30, 53, 56–62.

Reference 11, pp. 11–18, 145–148.

A. C. G. Mitchell, M. W. Zemansky, Resonance Radiation and Excited Atoms (University Press, Cambridge, 1934).

L. S. Frost, C. F. Gallo (unpublished studies performed at the Westinghouse Research Laboratory).

D. A. Larson, U.S. Patent3,431,447 and private communication.

W. Elenbaas, The High Pressure Mercury Vapor Discharge (Wiley-Interscience, New York, 1951), pp. 56–62, 130, Eq. (4.4.5).

Reference 11, pp. 3–10 and Chap. 10.

Reference 11, pp. 18–23.

Reference 11, pp. 41–45, 53–54.

Reference 11, p. 61.

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Tables (1)

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Table I Summary of Effective Temperatures

Equations (33)

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P r = P i - P c ,
P r = P i - P c ,
T 39 , 300 K 7.4 - log [ ( P i - 10 ) / M ] ,
σ = n e μ ,
σ = n e μ ,
( σ / σ ) = ( n / n ) ( μ / μ ) .
( μ / μ ) = ( D / D ) = 1 2 .
n n exp [ - e V i 2 k ( 1 T - 1 T ) ] 0.65 ,
σ σ ( D D ) exp [ - e V i 2 k ( 1 T - 1 T ) ] 0.33.
G / G 0.4.
G / G = ( σ / σ ) [ π R eff 2 / ( π R eff 2 ) ] .
( R eff / R eff ) 2 = ( G / G ) ( σ / σ ) 1.22.
P T 1 = g η E A ,
( P T 1 / P T 1 ) = ( g / g ) ( η / η ) .
η η ( R eff R eff ) 2 1.22 exp [ - e V 1 k ( 1 T - 1 T ) ] 0.63 0.77 ,
g = ( 1.115 ) ( π K p R ) - 1 2 ,
K p = ( λ 2 N / 4 π ) ( g 2 / g 1 ) ( A / Z T ) ,
g / g = ( K p / K p ) 1 2 ( R eff / R eff ) 1 2 = ( N / N ) 1 2 ( Z T / Z T ) 1 2 × ( R eff / R eff ) 1 2 .
( N N ) = exp [ + e V k 2 k ( 1 T - 1 T ) ] 1.07 ,
Z T = Z Hg + Z T 1 .
Z Hg = 2 ρ 2 D ( 2 π K T ) 1 2 ( M 1 - 1 + M 2 - 1 ) 1 2 ,
Z Hg ( 4.25 ) ( 10 ) 10 sec - 1 .
Z T 1 = ( 2 3 ) ( e 2 / m ν ) f d ,
Z T 1 ( 0.13 ) ( 10 ) 10 sec - 1 .
Z T = Z Hg + Z T 1 Z Hg ( 4.4 ) ( 10 ) 10 sec - 1 .
Z Hg 2 Z Hg .
Z ' T 1 = Z T 1 .
( Z T / Z T ) 1 2 1.38.
g / g = ( N / N ) 1 2 1.07 ( Z T / Z T ) 1.38 1 2 ( R eff / R eff ) 1 2 0.95 1.4.
( P T 1 / P T 1 ) = ( g / g ) 1.4 ( η / η ) 0.77 1.08.
( P Hg / P Hg ) ( D / D ) 2 ( R eff / R eff ) 2 1.22 exp [ - e V m k ( 1 T - 1 T ) ] 0.34 0.83 ,
P T 1 / P Hg exp [ ( Hg - T 1 ) / k T ] exp ( 4.5 eV / k T ) .
( P T 1 / P Hg P T 1 / P Hg ) = exp [ 4.5 eV ( 1 T - 1 T ) ] 1.87.

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