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Scaling laws for pressure, temperature, and ionization with two-temperature equation-of-state effects in laser-produced plasmas

Published online by Cambridge University Press:  09 March 2009

H. Szichman  and
S. Eliezer
H. Szichman
Affiliation:
Plasma Physics Department, Soreq Nuclear Research Center, Yavneh 70600, Israel
S. Eliezer
Affiliation:
Plasma Physics Department, Soreq Nuclear Research Center, Yavneh 70600, Israel
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Abstract

A two-temperature equation of state (EOS) for a plasma medium was developed. The cold-electron temperature is taken from semiempirical calculations, while the thermal contribution of the electrons is calculated from the Thomas–Fermi–Dirac model. The ion EOS is obtained by the Gruneisen–Debye solid–gas interpolation method. These EOS are well behaved and are smoothed over the whole temperature and density regions, so that the thermodynamical derivatives are also well behaved. Moreover, these EOS were used to calculate the average ionization 〈Z〉 and 〈Z2〉 of the plasma medium. Furthermore, the thermal conductivities have been calculated with the use of an extrapolation between the conductivities in the solid and plasma (Spitzer) states. The two-temperature EOS, the average ionization 〈Z〉 and 〈Z2〉, and the thermal conductivities for electrons and ions were introduced into a two-fluid hydrodynamic code to calculate the laser-plasma interaction in carbon, aluminum, copper, and gold slab targets. It was found that the two EOS are important mainly from the ablation surface outward (toward the laser). In particular, the creation of cavitons in the distribution of the electrons is predicted here, especially for light materials such as aluminum. These studies enable us also to establish that the commonly used exponential scaling laws of the type Pa = A[I/(1014 W/cm2)]α for the ablation pressure and similar laws for the temperature are valid only for absorbed laser intensities in the range 3 × 1012-3 × 1014 W/cm2, while the degree of ionization (at the corona) follows a quite different scaling law. We also found that the parameters A and α. in the above expression are dependent on material, laser wavelength, and pulse shape. Thus we determined for the ablation pressure, using a trapezoidal Nd laser pulse, that α varies between 0.78 and 0.84 and that A varies between 14 and 8 Mbar for 6 ≤ Z ≤ 79. Beyond the range of validity the scaling laws may give values at least twice as large as those obtained by the simulation.

Type
Research Article
Information
Laser and Particle Beams , Volume 10 , Issue 1 , March 1992 , pp. 23 - 40
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

Briand, J. et al. 1984 Phys. Fluids 27, 2588.CrossRefGoogle Scholar
Cowan, R. D. & Ashkin, J. 1957 Phys. Rev. 105, 144.CrossRefGoogle Scholar
Eliezer, S., Ghatak, A. & Hora, H. 1986 Introduction to Equations of State: Theory and Applications (Cambridge University, London).Google Scholar
Emery, M. H. et al. 1982 Phys. Rev. Lett. 48, 253.CrossRefGoogle Scholar
Fabbro, R., Max, C. & Fabre, E. 1985 Phys. Fluids 28, 1463.CrossRefGoogle Scholar
Hora, H. 1981. Physics of Laser Driven Plasmas (Wiley-Interscience, New York).Google Scholar
Hora, H., Lalousis, P. & Eliezer, S. 1984 Phys. Rev. Lett. 53, 1650.CrossRefGoogle Scholar
Jackel, S. et al. 1982 J. Phys. E 15, 255.CrossRefGoogle Scholar
Kidder, R. E. 1968 Nucl. Fusion 8, 3.CrossRefGoogle Scholar
Kittel, C. 1963 Quantum Theory of Solids (Wiley, New York), p. 343.Google Scholar
Kormer, S. B. et al. 1962 Sov. Phys. JETP 15, 77.Google Scholar
Kruer, W. L. 1988 The Physics of Laser Plasma Interactions (Addison-Wesley, Redwood City, A).Google Scholar
Lee, Y. T. & More, R. M. 1984 Phys. Fluids 27, 1273.CrossRefGoogle Scholar
More, R. M. 1983 In Atomic and Molecular Physics of Controlled Thermonuclear Fusion, Joachim, C. J. & Post, D. E. eds. (Plenum, New York), pp. 359–440.Google Scholar
More, R. M. 1985 In Advances in Atomic and Molecular Physics, Bates, D. R. & Estermann, I. eds. (Academic, New York), Vol. 21, p. 305.Google Scholar
Phipps, C. R. et al. 1988 J. Appl. Phys. 64, 1083.CrossRefGoogle Scholar
Phipps, C. R. et al. 1990 Laser Part. Beams 8, 281.CrossRefGoogle Scholar
Rosen, M. D. et al. 1979 Phys. Fluids 22, 2020.CrossRefGoogle Scholar
Salzmann, D. et al. 1983 Phys. Rev. A 28, 1738.CrossRefGoogle Scholar
Schmaltz, R. F. & Meyer-Ter-Vehn, J. 1985 Phys. Fluids 28, 932.CrossRefGoogle Scholar
Spitzer, L. 1962 Physics of Fully Ionized Gases (Interscience, New York).Google Scholar
Szichman, H. & Krumbein, A. D. 1986 Phys. Rev. A 33, 706.CrossRefGoogle Scholar
Szichman, H., Salzmann, D. & Krumbein, A. D. 1986 Laser Part. Beams 4, 403.CrossRefGoogle Scholar
Szichman, H., Eliezer, S. & Salzmann, D. 1987 J. Quant. Spectrosc. Radiat. Transfer 38, 281.CrossRefGoogle Scholar
Zel'Dovich, Y. B. & Raizer, Y. P. 1967 In Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Hayes, W. D. & Probstein, R. F. eds. (Academic, New York), Vol. 2, p. 694.Google Scholar
Ziman, J. M. 1969 Principle of Theory of Solids (Cambridge University, London).Google Scholar
Zimmerman, G. B. & Kruer, W. L. 1975 Comments Plasma Phys. Controlled Fusion 2, 85.Google Scholar