Advertisement

Mesh-ray model and method for calculating the laser radiation absorption

  • I. P. Tsygvintsev
  • A. Yu. Krukovskiy
  • V. A. Gasilov
  • V. G. Novikov
  • I. V. Popov
Article

Abstract

The present paper puts forward a mathematical model of laser radiation absorption in a laser target, which combines approximations of geometrical and wave optics and the corresponding numerical algorithm. This model depends on the principles of geometrical optics in the range of weak variation of the plasma refractive index on the scale of the wave length. This enables one to describe the refraction of the radiation. A transition to wave approximation is carried out near the surface of critical density, where the approximation of the geometrical optics is a fortiori inapplicable. For this aim, the plasma medium is approximately represented as a set of plane layers, on which the one-dimensional Helmholtz equation is solved. This makes it possible to construct a simple and relatively accurate method for calculating the absorption and reflection of laser radiation near the critical density surface in order to effectively take into account the dependence of the interaction of radiation with matter on the polarization direction, etc. The proposed model is adapted for implementation in the radiation gas dynamics (RGD) code. A numerical computation subroutine is presented based on the analytical solution of the differential equations corresponding to the optical ray model of the laser radiation energy flux. This solution is obtained under the assumption that the squared gradient of the refractive index is constant in any cell of the mesh. The convergence rates of the proposed algorithms are estimated using the data obtained in the numerical experiments.

Keywords

laser radiation geometrical optics radiation gas dynamics numerical algorithm computer simulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. E. Fortov, Extreme States of Matter on Earth and in the Cosmos (Fizmatlit, Moscow, 2009; Springer, Berlin, 2011).MATHGoogle Scholar
  2. 2.
    Nuclear Synthesis with Inertion Confinement, Ed. by B. Yu. Sharkov (Fizmatlit, Moscow, 2009) [in Russian].Google Scholar
  3. 3.
    Laser Technologies of Material Processing. Modern Problems of Fundamental Studies and Application Development, Ed. by V. Ya. Panchenko (Fizmatlit, Moscow, 2009) [in Russian].Google Scholar
  4. 4.
    M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, Cambridge, 1999).CrossRefMATHGoogle Scholar
  5. 5.
    I. G. Lebo and V. F. Tishkin, Study of Hydrodynamical Instability in Problems of Thermonuclear Fusion (Fizmatlit, Moscow, 2006) [in Russian].Google Scholar
  6. 6.
    T. B. Kaiser, “Laser ray tracing and power deposition on an unstructured three-dimensional grid,” Phys. Rev. E 61, 895–905 (2000).CrossRefGoogle Scholar
  7. 7.
    L. Friedland and I. Bernstein, “Comparison of geometric and wave optics in an absorbing spherical plasma,” Phys. Rev. A 21, 666–671 (1980).MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. E. Povarnitsyn et al., “Dynamics of thin metal foils irradiated by moderate-contrast high-intensity laser beams,” Phys. Plasmas 19 (2) (2012).Google Scholar
  9. 9.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Pergamon, New York, 1984).Google Scholar
  10. 10.
    V. L. Ginzburg and A. A. Rukhadze, Waves in Magnetically Active Plasma (Nauka, Moscow, 1975) [in Russian].Google Scholar
  11. 11.
    A. F. Aleksandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Vyssh. Shkola, Moscow, 1988; Springer, Berlin, Heidelberg, New York, Tokio, 1984).Google Scholar
  12. 12.
    I. P. Tsygvintsev, A. Yu. Krukovskii, V. G. Novikov, and I. V. Popov, “Three-dimensional modeling of laser radiation absorbtion in geometrical optics approach,” KIAM Preprint No. 41 (Keldysh Inst. Appl. Math., Moscow, 2012). http://keldysh.ru/papers/2012/prep2012_41.pdfGoogle Scholar
  13. 13.
    A. Yu. Krukovskii, V. G. Novikov, and I. P. Tsygvintsev, “3DLINE program: numerical simulation of threedimensional non-stationary problems of radiation gas dynamics,” KIAM Preprint No. 78 (Keldysh Inst. Appl. Math., Moscow, 2013). http://library.keldysh.ru/preprint.asp?id=2013-20Google Scholar
  14. 14.
    V. A. Gasilov et al., “Numerical simulation of current in vacuum diode with laser ignition,” KIAM Preprint No. 41 (Keldysh Inst. Appl. Math., Moscow, 2013). http://library.keldysh.ru/preprint.asp?id=2013-78Google Scholar
  15. 15.
    V. Bakshi, EUV Sources for Lithography (SPIE Press, Bellingham, WA, 2005).Google Scholar
  16. 16.
    J. Fujimoto, T. Hori, T. Yanagida, and H. Mizoguchi, “Development of laser-produced tin plasma-based EUV light source technology for HVM EUV lithography,” Phys. Res. Int. 2012, ID 249495 (2012). doi 10.1155/2012/249495Google Scholar
  17. 17.
    H. Mizoguchi, T. Abe, Y. Watanabe, et al., “100W 1st generation laser-produced plasma light source system for HVM EUV lithography,” Proc. SPIE 7969 (2011).Google Scholar
  18. 18.
    S. I. Anisimov, Ya. A. Imas, G. S. Romanov, and Yu. V. Khodyko, in Effect of High-Power Radiation on Metals, Ed. by A. M. Bonch-Bruevich and M. A. El’yashevich (Nauka, Moscow, 1970) [in Russian].Google Scholar
  19. 19.
    A. Colaïtis, G. Duchateau, P. Nicolaï, and V. Tikhonchuk, “Towards modeling of nonlinear laser-plasma interactions with hydrocodes: the thick-ray approach,” Phys. Rev. E 89 (3) (2014).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • I. P. Tsygvintsev
    • 1
  • A. Yu. Krukovskiy
    • 1
  • V. A. Gasilov
    • 1
  • V. G. Novikov
    • 1
  • I. V. Popov
    • 1
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

Personalised recommendations