We address here mathematical models related to the Laser-Plasma Interaction. After a simplified introduction to the physical background concerning the modelling of the laser propagation and its interaction with a plasma, we recall some classical results about the geometrical optics in plasmas. Then we deal with the well known paraxial approximation of the solution of the Maxwell equation; we state a coupling model between the plasma hydrodynamics and the laser propagation. Lastly, we consider the coupling with the ion acoustic waves which has to be taken into account to model the so called Brillouin instability. Here, besides the macroscopic density and the velocity of the plasma, one has to handle the space-time envelope of the main laser wave, the space-time envelope of the stimulated Brillouin backscattered laser wave and the space envelope of the Brillouin ion acoustic waves. Numerical methods are also described to deal with the paraxial model and the three-wave coupling system related to the Brillouin instability.
Mots clés : Euler-Maxwell system, numerical plasma simulation, geometrical optics, paraxial approximation, Schrödinger equation, three-wave coupling system, Brillouin instability
@article{M2AN_2005__39_2_275_0,
author = {Sentis, R\'emi},
title = {Mathematical models for laser-plasma interaction},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {275--318},
publisher = {EDP-Sciences},
volume = {39},
number = {2},
year = {2005},
doi = {10.1051/m2an:2005014},
mrnumber = {2143950},
zbl = {1080.35157},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2005014/}
}
TY - JOUR AU - Sentis, Rémi TI - Mathematical models for laser-plasma interaction JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 275 EP - 318 VL - 39 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2005014/ DO - 10.1051/m2an:2005014 LA - en ID - M2AN_2005__39_2_275_0 ER -
%0 Journal Article %A Sentis, Rémi %T Mathematical models for laser-plasma interaction %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 275-318 %V 39 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2005014/ %R 10.1051/m2an:2005014 %G en %F M2AN_2005__39_2_275_0
Sentis, Rémi. Mathematical models for laser-plasma interaction. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 275-318. doi : 10.1051/m2an:2005014. http://archive.numdam.org/articles/10.1051/m2an:2005014/
[1] ,,, and, Two-dimensional studies of stimulated Brillouin scattering, filamentation. Phys. Fluids B 5 (1993) 3748-3764.
[2] and, Discrete transparent boundary conditions for wide angle parabolic equations. J. Comput. Phys. 145 (1998) 611-638. | Zbl
[3] ,,,,,,, and, Coupling hydrodynamics with a paraxial solver for laser propagation. CEA internal report (2005).
[4] , An introduction to Eulerian geometrical optics. J. Sci. Comp. 19 (2003) 63-95. | Zbl
[5] ,, and, High Frequency limit of the Helmholtz equations. Rev. Mat. Iberoamericana 18 (2002) 187-209. | Zbl
[6] ,, and, 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. | Zbl
[7] ,, and, 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. | Zbl
[8] . A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185-200. | Zbl
[9] ,, and, On the dominant subdominant behavior of stimulated Raman and Brillouin scattering. Phys. Plasmas 5 (1998) 4337.
[10] et al., Theory and three-dimensional simulation of light filamentation. Phys. Fluids B 5 (1993) 2243.
[11] , and, Numerical study of the Davey-Stewartson System. ESAIM: M2AN 38 (2004) 1035-1054. | Numdam | Zbl
[12] , and, 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. | Zbl
[13] , and, High frequency limit of the Helmholtz equations, II. Source on a manifold. Comm. Partial Differential Equations 27 (2002) 607-651.
[14] , Introduction to Plasmas Physics. Plenum, New York (1974).
[15] and, On a Quasilinear Zakharov system describing Laser-Plasma Interaction. Differential Integral Equations 17 (2004) 297-330.
[16] and, Cauchy problem and numerical simulation for a quasi-linear Zakharov system. Accepted for publication in Nonlinear Analysis.
[17] , Perfectly matched absorbing layers for the paraxial equation. J. Comput. Phys. 131 (1997) 164-180. | Zbl
[18] , Fluid equations and transport coefficient of plasmas, in Modelling of collisions. P.-A. Raviart Ed., Masson, Paris (1997).
[19] , Modelisation de la propagation laser par résolution de l'équation d'Helmholtz, CEA internal report (2005).
[20] , and, Propagation laser paraxiale en coordonnées obliques: équation d'advection-Schrödinger. Note C. R. Acad. Sci. Paris Sér. I 336 (2003) 23-28. | Zbl
[21] ,, and, Numerical simulation for paraxial model of light propagation in a tilted frame: the advection-Schrödinger equation. CEA internal report (2005), preprint.
[22] , and, Simuation of laser-plasma filamentation. J. Comput. Phys. 17 (2002) 233-263. | Zbl
[23] ,, and, Phys. Plasmas 2 (1996) 2215 and Phys. Plasmas 3 (1996) 3754.
[24] and, Beam nonparaxiality, filament formation. J. Opt. Soc. Amer. B 5 (1988) 633-640.
[25] and, Asymptotic expansion of solutions of Comm. Pure Appl. Math. 5 (1955) 387. | MR | Zbl
[26] ,, and, Interaction of two neighboring laser beams. Phys. Plasmas 4 (1997) 2670-2680.
[27] , Classical Electrodynamics. Wiley, New York (1962). | MR | Zbl
[28] , HERA hydrodynamics AMR Plateform for multiphysics simulation, in Proc. of Chicago workshop on AMR methods (Sept. 2003). Springer Verlag, Berlin (2004).
[29] and, 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). | MR
[30] and, Eds., Wave Propagation and underwater Accoustics. Springer, Berlin. Lecture Notes in Phys. 70 (1977). | MR | Zbl
[31] and, Geometric optics for Inhomogeneous Media. Springer, Berlin (1990). | MR
[32] , The Physics of Laser-Plasma Interaction. Addison-Wesley, New York (1988).
[33] ,,, Parabolic equation development in the twentieth century. J. Comput. Acoust. 8 (2000) 527-637.
[34] , et al., Laser-beam smoothing induced by stimulated Brillouin scattering. CEA internal report (2005).
[35] , and, Nonlinear reflectivity of an inhomogeneous plasma. Phys. Rev. E 55 (1997) 4653-4664.
[36] ,, and, A new method for a realistic treatement of the sea bottom in parabolic approximation. J. Acoust. Soc. Amer. 92 (1992) 2030-2038.
[37] ,, and, Singular solutions of the Zaharov equations for Langmuir turbulence. Phys. Fluids B 3 (1991) 969-980.
[38] , Interaction collisionnelle et collective (Chap. 2) in La fusion par Confinement Inertiel I. Interaction laser-matière. R. Dautray-Watteau Ed., Eyrolles, Paris (1995).
[39] 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] and, Coherence properties of a smoothed laser beam in a hot plasma. Phys. Plasmas 7 (2000) 3841.
[41] , Laser beam deflection. Phys. Plasmas 3 (1996) 1709-1727.
[42] Shao et al., Spectral methods simulations of light scattering. IEEE J. Quantum Electronics 37 (2001) 617.
[43] , 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] and, A slowness matching eulerian method. J. Sci. Comput. 19 (2003) 501-526. | Zbl
[45] , 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). | MR
[46] , Collapse of Langmuir waves. Sov. Phys. JETP 35 (1972) 908.
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