Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T22:35:34.175Z Has data issue: false hasContentIssue false
  • English
  • Français

The inversion condition for the X-ray Balmer-α transition in consideration of the modeled time-dependent Lyman-α reabsorption in a rapidly recombining laser-produced plasma

Published online by Cambridge University Press:  09 March 2009

R.W. John
R.W. John
Affiliation:
Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, Postfach 11 07, D-12474 Berlin, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The time-dependent condition for population inversion in the X-ray 3 → 2 transition in hydrogen-like ions of a recombining plasma produced by a short laser pulse is studied. The population densities of the energy levels are theoretically obtained in a collisional-radiative plasma model; the reabsorption of the 2 → 1 resonance line is taken into account via the escape probability. A new feature is first that the escape probability is treated as an explicitly time-dependent function, E21(r,t). On the basis of a four-level model of the H-like ions, the rate differential equations governing the time development of the population densities are considered, including time-dependent pumping terms and coefficients. Furthermore, specially modeling the time dependence of E21 (r,t), and assuming the other rate coefficients to be approximately constant with respect to time, via the explicit closed-form solution of the corresponding rate equations, the Balmer-α inversion condition ΔN32(r,t) > 0 is given in terms containing confluent hypergeometric functions and depends on rate coefficients, pumping terms, and explicitly on the time. For the free-electron density Ne of the recombining plasma, this relation means a condition depending on atomic and plasma state parameters and qualitatively changing in the course of time.

Type
Research Article
Information
Laser and Particle Beams , Volume 13 , Issue 3 , September 1995 , pp. 365 - 375
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Biberman, L.M. 1948 Dokl. Akad. Nauk SSSR 59, 659.Google Scholar
Brunner, W. & John, R.W. 1991 Laser Part. Beams 9, 817; Corrigendum (1993) 11, 277.CrossRefGoogle Scholar
Brunner, W. & John, R.W. 1995 Laser Part. Beams 13, 403.CrossRefGoogle Scholar
Derzhiev, V.I. et al. 1986 Radiation of Ions in a Non-Equilibrium Dense Plasma (Energoatomizdat, Moscow) (in Russian).Google Scholar
Elton, R.C. 1990 X-Ray Lasers (Academic Press, Boston).Google Scholar
Erdélyi, A. et al. 1953 Higher Transcendental Functions: The Bateman Manuscript Project, Vol. I (McGraw-Hill, New York-Toronto-London), p. 248.Google Scholar
Griem, H.R. 1964 Plasma Spectroscopy (McGraw-Hill, New York).Google Scholar
Holstein, T. 1947 Phys. Rev. 72, 1212.CrossRefGoogle Scholar
Holstein, T. 1951 Phys. Rev. 83, 1159.CrossRefGoogle Scholar
Irons, F.E. 1979 J. Quant. Spectrosc. Radiat. Transf. 22, 1.CrossRefGoogle Scholar
John, R.W. 1994 In Laser Interaction and Related Plasma Phenomena, 11th International Workshop, Miley, G.H., ed. (AIP Press, New York), p. 540.Google Scholar
John, R.W. & Brunner, W. 1993 In Book of Abstracts, 11th International Workshop on Laser Interaction and Related Plasma Phenomena, Monterey (California), October 25–29 (sponsored in part by Fusion Studies Laboratory, University of Illinois, Urbana, Illinois), p. 166.Google Scholar
John, R.W. & Brunner, W. 1994 Laser Part. Beams 12, 515.CrossRefGoogle Scholar
Jones, W.W. & Ali, A.W. 1975 Appl. Phys. Lett. 26, 450.CrossRefGoogle Scholar
Kamke, E. 1959 Differentialgleichungen, Lösungsmethoden und Lösungen, Bd.I (Akadem. Verlagsgesellschaft Geest & Portig K.-G., Leipzig).Google Scholar
Kato, Y. et al. 1988 In OSA Proc. on Short Wavelength Coherent Radiation: Generation and Applications, Falcone, R.W. and Kirz, J., eds. (Optical Society of America, Washington, DC), Vol. 2, p. 47.CrossRefGoogle Scholar
Keane, C.J. 1992 In Ultrashort-Wavelength Lasers, Suckewer, S., ed. (Proc. SPIE 1551, Bellingham), p. 2.CrossRefGoogle Scholar
McWhirter, R.W.P. 1965 In Plasma Diagnostic Techniques, Huddlestone, R.H. and Leonard, S.L., eds. (Academic Press, New York), p. 201.Google Scholar
Pert, G.J. 1987 J. Opt. Soc. Am. B4, 602.CrossRefGoogle Scholar
Rybicki, G.B. 1984 In Methods in Radiative Transfer, Kalkofen, W., ed. (Cambridge Univ. Press, Cambridge), p. 21.Google Scholar
Yariv, A. 1975 Quantum Electronics, 2nd ed. (John Wiley, New York).Google Scholar