Free access
Issue
ESAIM: M2AN
Volume 39, Number 2, March-April 2005
Page(s) 275 - 318
DOI http://dx.doi.org/10.1051/m2an:2005014
Published online 15 April 2005
  1. M.R. Amin, C.E. Capjack, P. Fricz, W. Rozmus and V.T. Tikhonchuk, Two-dimensional studies of stimulated Brillouin scattering, filamentation. Phys. Fluids B 5 (1993) 3748–3764. [CrossRef]
  2. A. Arnold and M. Ehrhardt, Discrete transparent boundary conditions for wide angle parabolic equations. J. Comput. Phys. 145 (1998) 611–638. [CrossRef] [MathSciNet]
  3. P. Ballereau, M. Casanova, F. Duboc, D. Dureau, H. Jourdren, P. Loiseau, J. Metral, O. Morice and R. Sentis, Coupling hydrodynamics with a paraxial solver for laser propagation. CEA internal report (2005).
  4. J.D. Benamou, An introduction to Eulerian geometrical optics. J. Sci. Comp. 19 (2003) 63–95. [CrossRef]
  5. J.D. Benamou, F. Castella, T. Katsaounis and B. Perthame, High Frequency limit of the Helmholtz equations. Rev. Mat. Iberoamericana 18 (2002) 187–209. [MathSciNet]
  6. J.D. Benamou, O. Lafitte, R. Sentis and I. Solliec, A geometrical optics based numerical method for high frequency electromagnetic fields computations near fold caustics (part I). J. Comput. Appl. Math. 156 (2003) 93–125. [MathSciNet]
  7. J.D. Benamou, O. Lafitte, R. Sentis and I. Solliec, A geometrical optics based numerical method for high frequency electromagnetic fields computations near fold caustics (part II, the Energy). J. Comput. Appl. Math. 167 (2004) 91–134. [CrossRef] [MathSciNet]
  8. J.P. Berenger. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185–200.
  9. R.L. Berger, C.H. Still, E.A. Williams and A.B. Langdon, On the dominant subdominant behavior of stimulated Raman and Brillouin scattering. Phys. Plasmas 5 (1998) 4337. [CrossRef]
  10. R.L. Berger et al., Theory and three-dimensional simulation of light filamentation. Phys. Fluids B 5 (1993) 2243. [CrossRef]
  11. C. Besse, N.J. Mauser and H.P. Stimming, Numerical study of the Davey-Stewartson System. ESAIM: M2AN 38 (2004) 1035–1054. [CrossRef] [EDP Sciences]
  12. H. Brezis, F. Golse and R. Sentis, Analyse asymptotique de l'équation de Poisson couplée à la relation de Boltzmann. Quasi-neutralité dans les plasmas. Note C. R. Acad. Sci. Paris Sér. I 321 (1995) 953–959.
  13. F. Castella, B. Perthame and O. Runborg, High frequency limit of the Helmholtz equations, II. Source on a manifold. Comm. Partial Differential Equations 27 (2002) 607–651. [CrossRef] [MathSciNet]
  14. F.F. Chen, Introduction to Plasmas Physics. Plenum, New York (1974).
  15. M. Colin and T. Colin, On a Quasilinear Zakharov system describing Laser-Plasma Interaction. Differential Integral Equations 17 (2004) 297–330. [MathSciNet]
  16. M. Colin and T. Colin, Cauchy problem and numerical simulation for a quasi-linear Zakharov system. Accepted for publication in Nonlinear Analysis.
  17. F. Collino, Perfectly matched absorbing layers for the paraxial equation. J. Comput. Phys. 131 (1997) 164–180.
  18. A. Decoster, Fluid equations and transport coefficient of plasmas, in Modelling of collisions. P.-A. Raviart Ed., Masson, Paris (1997).
  19. S. Desroziers, Modelisation de la propagation laser par résolution de l'équation d'Helmholtz, CEA internal report (2005).
  20. M. Doumic, F. Golse and R. Sentis, Propagation laser paraxiale en coordonnées obliques: équation d'advection-Schrödinger. Note C. R. Acad. Sci. Paris Sér. I 336 (2003) 23–28.
  21. M. Doumic, F. Duboc, F. Golse and R. Sentis, Numerical simulation for paraxial model of light propagation in a tilted frame: the advection-Schrödinger equation. CEA internal report (2005), preprint.
  22. M.R. Dorr, F.X. Garaizar and J.A. Hittinger, Simuation of laser-plasma filamentation. J. Comput. Phys. 17 (2002) 233–263. [CrossRef]
  23. V.V. Eliseev, W. Rozmus, V.T. Tikhonchuk and C.E. Capjack, Phys. Plasmas 2 (1996) 2215 and Phys. Plasmas 3 (1996) 3754.
  24. M.D. Feit and J.A. Fleck, Beam nonparaxiality, filament formation. J. Opt. Soc. Amer. B 5 (1988) 633–640. [CrossRef]
  25. F.G. Friedlander and J.B. Keller, Asymptotic expansion of solutions of (Δ + k²)u = 0 Comm. Pure Appl. Math. 5 (1955) 387.
  26. S. Hüller, Ph. Mounaix, V.T. Tikhonchuk and D. Pesme, Interaction of two neighboring laser beams. Phys. Plasmas 4 (1997) 2670–2680. [CrossRef]
  27. J.D. Jackson, Classical Electrodynamics. Wiley, New York (1962).
  28. H. Jourdren, HERA hydrodynamics AMR Plateform for multiphysics simulation, in Proc. of Chicago workshop on AMR methods (Sept. 2003). Springer Verlag, Berlin (2004).
  29. J.B. Keller and R.M. Lewis, Asymptotic Methods for P.D.E: The reduced Wave Equation. Research report Courant Inst. (1964); reprinted in Surveys Appl. Math. 1, J.B. Keller, W. McLaughlin, G.C. Papanicolaou, Eds. Plenum, New York (1995).
  30. J.B. Keller and J.S. Papadakis, Eds., Wave Propagation and underwater Accoustics. Springer, Berlin. Lecture Notes in Phys. 70 (1977).
  31. Y.A. Krastsov and Y.I. Orlov, Geometric optics for Inhomogeneous Media. Springer, Berlin (1990).
  32. W.L. Kruer, The Physics of Laser-Plasma Interaction. Addison-Wesley, New York (1988).
  33. D. Lee, A.D. Pierce, E.S. Shang, Parabolic equation development in the twentieth century. J. Comput. Acoust. 8 (2000) 527–637. [MathSciNet]
  34. P. Loiseau, O. Morice et al., Laser-beam smoothing induced by stimulated Brillouin scattering. CEA internal report (2005).
  35. P. Mounaix, D. Pesme and M. Casanova, Nonlinear reflectivity of an inhomogeneous plasma. Phys. Rev. E 55 (1997) 4653–4664.
  36. J.S. Papadakis, M.I. Taroudakis, P.J. Papadakis and B. Mayfield, A new method for a realistic treatement of the sea bottom in parabolic approximation. J. Acoust. Soc. Amer. 92 (1992) 2030–2038. [CrossRef]
  37. G.C. Papanicolaou, C. Sulem, P.L. Sulem and X.P. Wang, Singular solutions of the Zaharov equations for Langmuir turbulence. Phys. Fluids B 3 (1991) 969–980. [CrossRef] [MathSciNet]
  38. D. Pesme, Interaction collisionnelle et collective (Chap. 2) in La fusion par Confinement Inertiel I. Interaction laser-matière. R. Dautray-Watteau Ed., Eyrolles, Paris (1995).
  39. D. Pesme et al., Fluid-type Effects in the nonlinear Stimulated Brillouin Scatter, in Laser-Plasma Interaction Workshop at Wente, L. Divol Ed., Lawrence Livermore Nat. Lab. report UCRL-JC-148983 (2002).
  40. G. Riazuelo and G. Bonnaud, Coherence properties of a smoothed laser beam in a hot plasma. Phys. Plasmas 7 (2000) 3841. [CrossRef]
  41. H.A. Rose, Laser beam deflection. Phys. Plasmas 3 (1996) 1709–1727. [CrossRef]
  42. Shao et al., Spectral methods simulations of light scattering. IEEE J. Quantum Electronics 37 (2001) 617. [CrossRef]
  43. G. Schurtz, Les codes numériques en FCI (Chap. 13), in La fusion par Confinement Inertiel, III. Techniques exp. et numériques, R. Dautray-Watteau Ed., Eyrolles, Paris (1995).
  44. W.W. Symes and J. Qian, A slowness matching eulerian method. J. Sci. Comput. 19 (2003) 501–526. [CrossRef] [MathSciNet]
  45. F.D. Tappert, The parabolic equation approximation method, in Wave Propagation and underwater Accoustics, J.B. Keller and J.S. Papadakis Eds., Springer, Berlin. Lecture Notes in Phys. 70 (1977).
  46. V.E. Zakharov, Collapse of Langmuir waves. Sov. Phys. JETP 35 (1972) 908.

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