Abstract

In a search for an x-ray laser capable of operating in a quasi-cw mode, a suggested -innershell scheme is examined using recently calculated rates. This scheme involves the decay of a K-shell vacancy followed by a more rapid (for certain elements) L-vacancy decay, which maintains the inversion. The present analysis indicates that the scheme is only marginally feasible unless a depletion of resonant absorbers is accomplished through line shifts associated with multiple ionization following K-vacancy production. The pumping requirements for overcoming photoionization losses in the beam and the associated gain conditions are estimated for three elements, namely silicon, calcium, and copper, and it is concluded that photoionization pumping in a selective energy band is required, with emission approaching the blackbody level. A multiline heavy-ion plasma source is suggested.

© 1975 Optical Society of America

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References

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  1. M. A. Duguay, R. M. Rentzepis, Appl. Phys. Lett. 10, 350 (1967).
    [CrossRef]
  2. R. C. Elton, R. W. Waynant, R. A. Andrews, M. H. Reilly, Naval Research Laboratory Report 7412 (May1972).
  3. Yu. L. Stankevich, Sov. Phys. Dokl. 15, 356 (1970).
  4. As used here, innershell implies that at least one additional electron exists in a shell of larger principal quantum number than for that shell in which the initial vacancy is produced.
  5. R. C. Elton, Naval Research Laboratory Memorandum Report No. 2906, (1974);also Physica Fennica 9, Suppl. Sl, 397 (1974).
  6. M. A. Blokhin, V. P. Sachenko, Izv. Akad. Nauk. USSR 21, 1333 (1957).
  7. M. A. Blokhin, “The Physics of X-Rays” (translated), USAEC Report AEC-tr-4502 (1961).
  8. E. J. McGuire, Phys. Rev. 185, 1 (1969);Phys. Rev. A 2, 273 (1970).
    [CrossRef]
  9. D. L. Walters, C. P. Bhalla, Phys. Rev. A 3, 1919 (1971);At. Data 3, 301 (1971).
    [CrossRef]
  10. J. H. Scofield, Phys. Rev. 179, 9 (1969);also LLL Report UCRL-51231 (1June1972).
    [CrossRef]
  11. J. H. Scofield, Phys. Rev. A 9, 1041 (1974).
    [CrossRef]
  12. E. J. McGuire, Phys. Rev. A 3, 587 (1971).
    [CrossRef]
  13. P. J. Mallozzi, private communication (1973);M. A. Duguay, private communication to R. A. Andrews (1974).
  14. F. T. Arecchi, G. P. Banfi, A. M. Malvezzi, Opt. Commun. 10, 214 (1974).
    [CrossRef]
  15. R. L. Kelly, D. E. Harrison, At. Data 3, 177 (1971).
    [CrossRef]
  16. L. L. House, Astrophys. J. Suppl. 18, 21 (1969).
  17. T. N. Lie, R. C. Elton, Phys. Rev. A 3, 865 (1971);earlier evidence of innershell ion transitions is reviewed here.
    [CrossRef]
  18. E. J. McGuire, Phys. Rev. A 5, 1052 (1973).
    [CrossRef]
  19. T. Åberg, Phys. Rev. A 4, 1735 (1971).
    [CrossRef]
  20. F. R. Gilmore, Rand Report RM-2367-AEC (10April1959).
  21. R. C. Elton, in Plasma Physics, Vol. 9AMethods of Experimental PhysicsH. R. Griem, R. H. Lovberg, Eds. (Academic, New York, 1970).
  22. S. M. R. Ansari, G. Elwert, P. Mücklich, Z. Naturforsch. 25, 1781 (1970);A. H. Gabriel, T. M. Paget, J. Phys. B 5, 673 (1972).
    [CrossRef]
  23. W. D. Barfield, G. D. Koontz, W. F. Huebner, J. Quant. Spectrosc. Radiat. Transfer 12, 1409 (1972).
    [CrossRef]
  24. H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).
  25. W. W. Jones, A. W. Ali, NRL Memorandum Report 2807;P. Bey, NRL Memorandum Report 2847 (1974).
  26. H. R. Griem, private communication (1974).
  27. H. R. Griem, Broadening of Spectral Lines by Charged Particles in Plasmas (Academic, New York, 1974).
  28. C. P. Bhalla, N. O. Folland, M. A. Hein, Phys. Rev. A 8, 649 (1973).
    [CrossRef]

1974 (2)

J. H. Scofield, Phys. Rev. A 9, 1041 (1974).
[CrossRef]

F. T. Arecchi, G. P. Banfi, A. M. Malvezzi, Opt. Commun. 10, 214 (1974).
[CrossRef]

1973 (2)

E. J. McGuire, Phys. Rev. A 5, 1052 (1973).
[CrossRef]

C. P. Bhalla, N. O. Folland, M. A. Hein, Phys. Rev. A 8, 649 (1973).
[CrossRef]

1972 (1)

W. D. Barfield, G. D. Koontz, W. F. Huebner, J. Quant. Spectrosc. Radiat. Transfer 12, 1409 (1972).
[CrossRef]

1971 (5)

T. N. Lie, R. C. Elton, Phys. Rev. A 3, 865 (1971);earlier evidence of innershell ion transitions is reviewed here.
[CrossRef]

T. Åberg, Phys. Rev. A 4, 1735 (1971).
[CrossRef]

R. L. Kelly, D. E. Harrison, At. Data 3, 177 (1971).
[CrossRef]

E. J. McGuire, Phys. Rev. A 3, 587 (1971).
[CrossRef]

D. L. Walters, C. P. Bhalla, Phys. Rev. A 3, 1919 (1971);At. Data 3, 301 (1971).
[CrossRef]

1970 (2)

Yu. L. Stankevich, Sov. Phys. Dokl. 15, 356 (1970).

S. M. R. Ansari, G. Elwert, P. Mücklich, Z. Naturforsch. 25, 1781 (1970);A. H. Gabriel, T. M. Paget, J. Phys. B 5, 673 (1972).
[CrossRef]

1969 (3)

L. L. House, Astrophys. J. Suppl. 18, 21 (1969).

E. J. McGuire, Phys. Rev. 185, 1 (1969);Phys. Rev. A 2, 273 (1970).
[CrossRef]

J. H. Scofield, Phys. Rev. 179, 9 (1969);also LLL Report UCRL-51231 (1June1972).
[CrossRef]

1967 (1)

M. A. Duguay, R. M. Rentzepis, Appl. Phys. Lett. 10, 350 (1967).
[CrossRef]

1957 (1)

M. A. Blokhin, V. P. Sachenko, Izv. Akad. Nauk. USSR 21, 1333 (1957).

Åberg, T.

T. Åberg, Phys. Rev. A 4, 1735 (1971).
[CrossRef]

Ali, A. W.

W. W. Jones, A. W. Ali, NRL Memorandum Report 2807;P. Bey, NRL Memorandum Report 2847 (1974).

Andrews, R. A.

R. C. Elton, R. W. Waynant, R. A. Andrews, M. H. Reilly, Naval Research Laboratory Report 7412 (May1972).

Ansari, S. M. R.

S. M. R. Ansari, G. Elwert, P. Mücklich, Z. Naturforsch. 25, 1781 (1970);A. H. Gabriel, T. M. Paget, J. Phys. B 5, 673 (1972).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, G. P. Banfi, A. M. Malvezzi, Opt. Commun. 10, 214 (1974).
[CrossRef]

Banfi, G. P.

F. T. Arecchi, G. P. Banfi, A. M. Malvezzi, Opt. Commun. 10, 214 (1974).
[CrossRef]

Barfield, W. D.

W. D. Barfield, G. D. Koontz, W. F. Huebner, J. Quant. Spectrosc. Radiat. Transfer 12, 1409 (1972).
[CrossRef]

Bhalla, C. P.

C. P. Bhalla, N. O. Folland, M. A. Hein, Phys. Rev. A 8, 649 (1973).
[CrossRef]

D. L. Walters, C. P. Bhalla, Phys. Rev. A 3, 1919 (1971);At. Data 3, 301 (1971).
[CrossRef]

Blokhin, M. A.

M. A. Blokhin, V. P. Sachenko, Izv. Akad. Nauk. USSR 21, 1333 (1957).

M. A. Blokhin, “The Physics of X-Rays” (translated), USAEC Report AEC-tr-4502 (1961).

Duguay, M. A.

M. A. Duguay, R. M. Rentzepis, Appl. Phys. Lett. 10, 350 (1967).
[CrossRef]

Elton, R. C.

T. N. Lie, R. C. Elton, Phys. Rev. A 3, 865 (1971);earlier evidence of innershell ion transitions is reviewed here.
[CrossRef]

R. C. Elton, in Plasma Physics, Vol. 9AMethods of Experimental PhysicsH. R. Griem, R. H. Lovberg, Eds. (Academic, New York, 1970).

R. C. Elton, R. W. Waynant, R. A. Andrews, M. H. Reilly, Naval Research Laboratory Report 7412 (May1972).

R. C. Elton, Naval Research Laboratory Memorandum Report No. 2906, (1974);also Physica Fennica 9, Suppl. Sl, 397 (1974).

Elwert, G.

S. M. R. Ansari, G. Elwert, P. Mücklich, Z. Naturforsch. 25, 1781 (1970);A. H. Gabriel, T. M. Paget, J. Phys. B 5, 673 (1972).
[CrossRef]

Folland, N. O.

C. P. Bhalla, N. O. Folland, M. A. Hein, Phys. Rev. A 8, 649 (1973).
[CrossRef]

Gilmore, F. R.

F. R. Gilmore, Rand Report RM-2367-AEC (10April1959).

Griem, H. R.

H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).

H. R. Griem, private communication (1974).

H. R. Griem, Broadening of Spectral Lines by Charged Particles in Plasmas (Academic, New York, 1974).

Harrison, D. E.

R. L. Kelly, D. E. Harrison, At. Data 3, 177 (1971).
[CrossRef]

Hein, M. A.

C. P. Bhalla, N. O. Folland, M. A. Hein, Phys. Rev. A 8, 649 (1973).
[CrossRef]

House, L. L.

L. L. House, Astrophys. J. Suppl. 18, 21 (1969).

Huebner, W. F.

W. D. Barfield, G. D. Koontz, W. F. Huebner, J. Quant. Spectrosc. Radiat. Transfer 12, 1409 (1972).
[CrossRef]

Jones, W. W.

W. W. Jones, A. W. Ali, NRL Memorandum Report 2807;P. Bey, NRL Memorandum Report 2847 (1974).

Kelly, R. L.

R. L. Kelly, D. E. Harrison, At. Data 3, 177 (1971).
[CrossRef]

Koontz, G. D.

W. D. Barfield, G. D. Koontz, W. F. Huebner, J. Quant. Spectrosc. Radiat. Transfer 12, 1409 (1972).
[CrossRef]

Lie, T. N.

T. N. Lie, R. C. Elton, Phys. Rev. A 3, 865 (1971);earlier evidence of innershell ion transitions is reviewed here.
[CrossRef]

Mallozzi, P. J.

P. J. Mallozzi, private communication (1973);M. A. Duguay, private communication to R. A. Andrews (1974).

Malvezzi, A. M.

F. T. Arecchi, G. P. Banfi, A. M. Malvezzi, Opt. Commun. 10, 214 (1974).
[CrossRef]

McGuire, E. J.

E. J. McGuire, Phys. Rev. A 5, 1052 (1973).
[CrossRef]

E. J. McGuire, Phys. Rev. A 3, 587 (1971).
[CrossRef]

E. J. McGuire, Phys. Rev. 185, 1 (1969);Phys. Rev. A 2, 273 (1970).
[CrossRef]

Mücklich, P.

S. M. R. Ansari, G. Elwert, P. Mücklich, Z. Naturforsch. 25, 1781 (1970);A. H. Gabriel, T. M. Paget, J. Phys. B 5, 673 (1972).
[CrossRef]

Reilly, M. H.

R. C. Elton, R. W. Waynant, R. A. Andrews, M. H. Reilly, Naval Research Laboratory Report 7412 (May1972).

Rentzepis, R. M.

M. A. Duguay, R. M. Rentzepis, Appl. Phys. Lett. 10, 350 (1967).
[CrossRef]

Sachenko, V. P.

M. A. Blokhin, V. P. Sachenko, Izv. Akad. Nauk. USSR 21, 1333 (1957).

Scofield, J. H.

J. H. Scofield, Phys. Rev. A 9, 1041 (1974).
[CrossRef]

J. H. Scofield, Phys. Rev. 179, 9 (1969);also LLL Report UCRL-51231 (1June1972).
[CrossRef]

Stankevich, Yu. L.

Yu. L. Stankevich, Sov. Phys. Dokl. 15, 356 (1970).

Walters, D. L.

D. L. Walters, C. P. Bhalla, Phys. Rev. A 3, 1919 (1971);At. Data 3, 301 (1971).
[CrossRef]

Waynant, R. W.

R. C. Elton, R. W. Waynant, R. A. Andrews, M. H. Reilly, Naval Research Laboratory Report 7412 (May1972).

Appl. Phys. Lett. (1)

M. A. Duguay, R. M. Rentzepis, Appl. Phys. Lett. 10, 350 (1967).
[CrossRef]

Astrophys. J. (1)

L. L. House, Astrophys. J. Suppl. 18, 21 (1969).

At. Data (1)

R. L. Kelly, D. E. Harrison, At. Data 3, 177 (1971).
[CrossRef]

Izv. Akad. Nauk. USSR (1)

M. A. Blokhin, V. P. Sachenko, Izv. Akad. Nauk. USSR 21, 1333 (1957).

J. Quant. Spectrosc. Radiat. Transfer (1)

W. D. Barfield, G. D. Koontz, W. F. Huebner, J. Quant. Spectrosc. Radiat. Transfer 12, 1409 (1972).
[CrossRef]

Opt. Commun. (1)

F. T. Arecchi, G. P. Banfi, A. M. Malvezzi, Opt. Commun. 10, 214 (1974).
[CrossRef]

Phys. Rev. (2)

E. J. McGuire, Phys. Rev. 185, 1 (1969);Phys. Rev. A 2, 273 (1970).
[CrossRef]

J. H. Scofield, Phys. Rev. 179, 9 (1969);also LLL Report UCRL-51231 (1June1972).
[CrossRef]

Phys. Rev. A (7)

J. H. Scofield, Phys. Rev. A 9, 1041 (1974).
[CrossRef]

E. J. McGuire, Phys. Rev. A 3, 587 (1971).
[CrossRef]

T. N. Lie, R. C. Elton, Phys. Rev. A 3, 865 (1971);earlier evidence of innershell ion transitions is reviewed here.
[CrossRef]

E. J. McGuire, Phys. Rev. A 5, 1052 (1973).
[CrossRef]

T. Åberg, Phys. Rev. A 4, 1735 (1971).
[CrossRef]

D. L. Walters, C. P. Bhalla, Phys. Rev. A 3, 1919 (1971);At. Data 3, 301 (1971).
[CrossRef]

C. P. Bhalla, N. O. Folland, M. A. Hein, Phys. Rev. A 8, 649 (1973).
[CrossRef]

Sov. Phys. Dokl. (1)

Yu. L. Stankevich, Sov. Phys. Dokl. 15, 356 (1970).

Z. Naturforsch. (1)

S. M. R. Ansari, G. Elwert, P. Mücklich, Z. Naturforsch. 25, 1781 (1970);A. H. Gabriel, T. M. Paget, J. Phys. B 5, 673 (1972).
[CrossRef]

Other (11)

H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).

W. W. Jones, A. W. Ali, NRL Memorandum Report 2807;P. Bey, NRL Memorandum Report 2847 (1974).

H. R. Griem, private communication (1974).

H. R. Griem, Broadening of Spectral Lines by Charged Particles in Plasmas (Academic, New York, 1974).

As used here, innershell implies that at least one additional electron exists in a shell of larger principal quantum number than for that shell in which the initial vacancy is produced.

R. C. Elton, Naval Research Laboratory Memorandum Report No. 2906, (1974);also Physica Fennica 9, Suppl. Sl, 397 (1974).

R. C. Elton, R. W. Waynant, R. A. Andrews, M. H. Reilly, Naval Research Laboratory Report 7412 (May1972).

M. A. Blokhin, “The Physics of X-Rays” (translated), USAEC Report AEC-tr-4502 (1961).

F. R. Gilmore, Rand Report RM-2367-AEC (10April1959).

R. C. Elton, in Plasma Physics, Vol. 9AMethods of Experimental PhysicsH. R. Griem, R. H. Lovberg, Eds. (Academic, New York, 1970).

P. J. Mallozzi, private communication (1973);M. A. Duguay, private communication to R. A. Andrews (1974).

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Figures (4)

Fig. 1
Fig. 1

Ratio of rates RL/RK for total transitions out of L- and K-vacancy states, respectively, vs atomic number Z. This ratio is equivalent to N2/N3 in Eq. (2) for equilibrium conditions reached after long times in cw operation. Values exceeding unity and one-half indicate gain for the 2 and 1 lines, respectively. The model here assumes all K-vacancy decay transitions produce potential absorbers for laser radiation. Present analysis is based on recent data812; an attempt to reproduce the results of Stankevich3 is shown dashed. Both KLII and KLIII, α2 and α1 respective transitions are shown.

Fig. 2
Fig. 2

Vacancy diagram according to binding energies EB for copper. K, L, and M designate shell vacancies. P, X, and Γ are the rates for pumping, x-ray, [emission or absorption (dashed)] and Auger transitions, respectively.

Fig. 3
Fig. 3

Ratio of rates RL/RKL for total transitions out of a L-vacancy state and radiative decay out of a K-vacancy state vs atomic number Z. This ratio is equivalent to N2/N3 in Eq. (2) for equilibrium conditions reached after long times in cw operation. Values exceeding unity and one-half indicate gain for the 2 and 1 lines, respectively. The model used assumes only radiative transitions produce absorbers, with Auger transitions generating shifted ion lines. Both KLII and KLIII, α2 and α1 respective transitions are shown.

Fig. 4
Fig. 4

Estimates of line widths for type transitions vs wavelength λ [with natural (ΔλN), Doppler (ΔλD), and Stark (ΔλS) effects included]. The decrease in natural broadening with ionization is indicated by circles for neon; and hydrogenic and heliumlike ionic species are included.

Tables (2)

Tables Icon

Table I Selected Atomic Rates Used (In 10−2 atu−1)a,b

Tables Icon

Table II Pumping Requirements

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

λ 2 A 4 π 2 Δ ν [ T N 1 ( N 2 N 1 ) ] 2 κ ρ 10 23 N 1 ,
Δ N N 2 ( g 2 / g 3 ) N 3 = N 1 ( N 2 N 1 ) ( 1 g 2 N 3 g 3 N 2 ) T N 1 ( N 2 N 1 ) ,
λ 2 A 2 π T N 1 [ N ν σ p i K c ( Γ + X ) 2 ] 2 σ p i L N 1 ,
α L = 2 N 1 σ p i K ( σ p i L / σ p i K ) L N 1 σ p i K L / 4 .
Δ λ D / λ Δ ν D / ν = 7.7 × 10 5 ( k T i / μ ) 1 / 2 ,
Δ λ H 2 n 2 λ 2 π c m Z ¯ p Z i N p 2 / 3 ,
Δ λ H 2 n 2 λ 2 π c m N e 2 / 3
Δ λ e 3 n 4 λ 2 c ( m Z i ) N e υ e ,
10 20 σ p i K ( cm 2 )

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