Free Access
Volume 39, Number 2, March-April 2005
Page(s) 275 - 318
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] [Google Scholar]
  2. A. Arnold and M. Ehrhardt, Discrete transparent boundary conditions for wide angle parabolic equations. J. Comput. Phys. 145 (1998) 611–638. [CrossRef] [MathSciNet] [Google Scholar]
  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). [Google Scholar]
  4. J.D. Benamou, An introduction to Eulerian geometrical optics. J. Sci. Comp. 19 (2003) 63–95. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  8. J.P. Berenger. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185–200. [Google Scholar]
  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] [Google Scholar]
  10. R.L. Berger et al., Theory and three-dimensional simulation of light filamentation. Phys. Fluids B 5 (1993) 2243. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  14. F.F. Chen, Introduction to Plasmas Physics. Plenum, New York (1974). [Google Scholar]
  15. M. Colin and T. Colin, On a Quasilinear Zakharov system describing Laser-Plasma Interaction. Differential Integral Equations 17 (2004) 297–330. [MathSciNet] [Google Scholar]
  16. M. Colin and T. Colin, Cauchy problem and numerical simulation for a quasi-linear Zakharov system. Accepted for publication in Nonlinear Analysis. [Google Scholar]
  17. F. Collino, Perfectly matched absorbing layers for the paraxial equation. J. Comput. Phys. 131 (1997) 164–180. [Google Scholar]
  18. A. Decoster, Fluid equations and transport coefficient of plasmas, in Modelling of collisions. P.-A. Raviart Ed., Masson, Paris (1997). [Google Scholar]
  19. S. Desroziers, Modelisation de la propagation laser par résolution de l'équation d'Helmholtz, CEA internal report (2005). [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  22. M.R. Dorr, F.X. Garaizar and J.A. Hittinger, Simuation of laser-plasma filamentation. J. Comput. Phys. 17 (2002) 233–263. [CrossRef] [Google Scholar]
  23. V.V. Eliseev, W. Rozmus, V.T. Tikhonchuk and C.E. Capjack, Phys. Plasmas 2 (1996) 2215 and Phys. Plasmas 3 (1996) 3754. [Google Scholar]
  24. M.D. Feit and J.A. Fleck, Beam nonparaxiality, filament formation. J. Opt. Soc. Amer. B 5 (1988) 633–640. [CrossRef] [Google Scholar]
  25. F.G. Friedlander and J.B. Keller, Asymptotic expansion of solutions of (Δ + k²)u = 0 Comm. Pure Appl. Math. 5 (1955) 387. [Google Scholar]
  26. S. Hüller, Ph. Mounaix, V.T. Tikhonchuk and D. Pesme, Interaction of two neighboring laser beams. Phys. Plasmas 4 (1997) 2670–2680. [CrossRef] [Google Scholar]
  27. J.D. Jackson, Classical Electrodynamics. Wiley, New York (1962). [Google Scholar]
  28. H. Jourdren, HERA hydrodynamics AMR Plateform for multiphysics simulation, in Proc. of Chicago workshop on AMR methods (Sept. 2003). Springer Verlag, Berlin (2004). [Google Scholar]
  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). [Google Scholar]
  30. J.B. Keller and J.S. Papadakis, Eds., Wave Propagation and underwater Accoustics. Springer, Berlin. Lecture Notes in Phys. 70 (1977). [Google Scholar]
  31. Y.A. Krastsov and Y.I. Orlov, Geometric optics for Inhomogeneous Media. Springer, Berlin (1990). [Google Scholar]
  32. W.L. Kruer, The Physics of Laser-Plasma Interaction. Addison-Wesley, New York (1988). [Google Scholar]
  33. D. Lee, A.D. Pierce, E.S. Shang, Parabolic equation development in the twentieth century. J. Comput. Acoust. 8 (2000) 527–637. [MathSciNet] [Google Scholar]
  34. P. Loiseau, O. Morice et al., Laser-beam smoothing induced by stimulated Brillouin scattering. CEA internal report (2005). [Google Scholar]
  35. P. Mounaix, D. Pesme and M. Casanova, Nonlinear reflectivity of an inhomogeneous plasma. Phys. Rev. E 55 (1997) 4653–4664. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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). [Google Scholar]
  40. G. Riazuelo and G. Bonnaud, Coherence properties of a smoothed laser beam in a hot plasma. Phys. Plasmas 7 (2000) 3841. [CrossRef] [Google Scholar]
  41. H.A. Rose, Laser beam deflection. Phys. Plasmas 3 (1996) 1709–1727. [CrossRef] [Google Scholar]
  42. Shao et al., Spectral methods simulations of light scattering. IEEE J. Quantum Electronics 37 (2001) 617. [CrossRef] [Google Scholar]
  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). [Google Scholar]
  44. W.W. Symes and J. Qian, A slowness matching eulerian method. J. Sci. Comput. 19 (2003) 501–526. [CrossRef] [MathSciNet] [Google Scholar]
  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). [Google Scholar]
  46. V.E. Zakharov, Collapse of Langmuir waves. Sov. Phys. JETP 35 (1972) 908. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you