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April  2012, 5(2): 329-343. doi: 10.3934/dcdss.2012.5.329

Models and simulations for the laser-plasma interaction and the three-wave coupling problem

1. 

CEA, DAM, DIF. Bruyeres, 91297 Arpajon, France

Received  September 2009 Revised  March 2010 Published  September 2011

We are concerned here with the modelling of the laser propagation and its interaction with a plasma. In a first part, we recall first some features related to the paraxial approximation of the solution of the wave equation and the coupling model between the plasma hydrodynamics and the laser propagation. In a second part, we consider the coupling with the ion acoustic waves which has to be accounted to model the Brillouin instability. It leads to the three-wave coupling problem which is a crucial in plasma physics. We give some mathematical properties of this system specially in the case when the speed of light is assumed to be infinite. We also propose a numerical method based on a implicit time discretization. It is illustrated on test cases.
Citation: Remi Sentis. Models and simulations for the laser-plasma interaction and the three-wave coupling problem. Discrete & Continuous Dynamical Systems - S, 2012, 5 (2) : 329-343. doi: 10.3934/dcdss.2012.5.329
References:
[1]

Ph. Ballereau, M. Casanova, F. Duboc, D. Dureau, H. Jourdren, P. Loiseau, J. Metral, O. Morice and R. Sentis, Simulation of the paraxial laser propagation coupled with hydrodynamics in 3D geometry,, J. Sci. Comp., 33 (2007), 1. doi: 10.1007/s10915-007-9135-y. Google Scholar

[2]

P. G. Baines, The stability of planetary waves on a sphere,, J. Fluid Mech., 73 (1976), 193. doi: 10.1017/S0022112076001341. Google Scholar

[3]

T. J. M. Boyd and J. G. Turner, Lagrangian studies of plasma wave interaction,, \textbf{5} (1972), 5 (1972), 881. Google Scholar

[4]

M. Casanova, et al., Self-generated loss of coherency in Brillouin scattering and reduction of reflectivity,, Phys. Review Letters, 54 (1985), 2230. doi: 10.1103/PhysRevLett.54.2230. Google Scholar

[5]

M. Colin and T. Colin, On a quasilinear Zakharov system describing laser-plasma interaction,, Differential Integral Equations, 17 (2004), 297. Google Scholar

[6]

S. Desroziers, F. Nataf and R. Sentis, Simulation of laser propagation in a plasma with a frequency wave equation,, J. Comp. Physics, 227 (2008), 2610. doi: 10.1016/j.jcp.2007.11.008. Google Scholar

[7]

M. Doumic, F. Duboc, F. Golse and R. Sentis, Simulation of laser beam propagation with a paraxial model in a tilted frame,, J. Comp. Physics, 228 (2009), 861. doi: 10.1016/j.jcp.2008.10.009. Google Scholar

[8]

L. Divol and R. L. Berger, et al., Three-dimensional modeling of laser-plasma interaction: Benchmarking our predictive modeling tools versus experiments,, Phys. of Plasmas, 15 (2008). Google Scholar

[9]

B. B. Kadomtsev, "Plasma Turbulence,", translated from the Russian, (1965). Google Scholar

[10]

J. B. Keller and R. M. Lewis, Asymptotic methods for partial differential equations: The reduced wave equation and Maxwell's equations,, in, (1995), 1. Google Scholar

[11]

W. L. Kruer, "The Physics of Laser-Plasma Interaction,", Addison-Wesley, (1988). Google Scholar

[12]

P. Loiseau, et al., Laser-beam smoothing induced by stimulated Brillouin scattering in an inhomogeneous plasma,, Physical Review Letters, 97 (2006). doi: 10.1103/PhysRevLett.97.205001. Google Scholar

[13]

G. Metivier and R. Sentis, On the Boyd-Kadomtsev System and its asymptotic limit,, Comm. Math. Physics, (2011). Google Scholar

[14]

Ph. Mounaix, D. Pesme and M. Casanova, Nonlinear reflectivity of an inhomogeneous plasma,, Phys. Review E, 55 (1997). doi: 10.1103/PhysRevE.55.4653. Google Scholar

[15]

S. Novikov, S. V. Manakov, L. P. Pitaevskiĭ and V. E. Zakharov, "Theory of Solitons. The Inverse Scattering Method,", Contemporary Soviet Mathematics, (1984). Google Scholar

[16]

D. Pesme, Interaction collisionnelle et collective,, in, (1995). Google Scholar

[17]

R. Sentis, On the Boyd-Kadomtsev system for the three-wave coupling problem,, C. R. Math. Ac. Sciences Paris, 347 (2009), 933. Google Scholar

[18]

R. Sentis, Mathematical models for laser-plasma interaction,, M2AN Math. Modelling Num. Analysis, 39 (2005), 275. Google Scholar

show all references

References:
[1]

Ph. Ballereau, M. Casanova, F. Duboc, D. Dureau, H. Jourdren, P. Loiseau, J. Metral, O. Morice and R. Sentis, Simulation of the paraxial laser propagation coupled with hydrodynamics in 3D geometry,, J. Sci. Comp., 33 (2007), 1. doi: 10.1007/s10915-007-9135-y. Google Scholar

[2]

P. G. Baines, The stability of planetary waves on a sphere,, J. Fluid Mech., 73 (1976), 193. doi: 10.1017/S0022112076001341. Google Scholar

[3]

T. J. M. Boyd and J. G. Turner, Lagrangian studies of plasma wave interaction,, \textbf{5} (1972), 5 (1972), 881. Google Scholar

[4]

M. Casanova, et al., Self-generated loss of coherency in Brillouin scattering and reduction of reflectivity,, Phys. Review Letters, 54 (1985), 2230. doi: 10.1103/PhysRevLett.54.2230. Google Scholar

[5]

M. Colin and T. Colin, On a quasilinear Zakharov system describing laser-plasma interaction,, Differential Integral Equations, 17 (2004), 297. Google Scholar

[6]

S. Desroziers, F. Nataf and R. Sentis, Simulation of laser propagation in a plasma with a frequency wave equation,, J. Comp. Physics, 227 (2008), 2610. doi: 10.1016/j.jcp.2007.11.008. Google Scholar

[7]

M. Doumic, F. Duboc, F. Golse and R. Sentis, Simulation of laser beam propagation with a paraxial model in a tilted frame,, J. Comp. Physics, 228 (2009), 861. doi: 10.1016/j.jcp.2008.10.009. Google Scholar

[8]

L. Divol and R. L. Berger, et al., Three-dimensional modeling of laser-plasma interaction: Benchmarking our predictive modeling tools versus experiments,, Phys. of Plasmas, 15 (2008). Google Scholar

[9]

B. B. Kadomtsev, "Plasma Turbulence,", translated from the Russian, (1965). Google Scholar

[10]

J. B. Keller and R. M. Lewis, Asymptotic methods for partial differential equations: The reduced wave equation and Maxwell's equations,, in, (1995), 1. Google Scholar

[11]

W. L. Kruer, "The Physics of Laser-Plasma Interaction,", Addison-Wesley, (1988). Google Scholar

[12]

P. Loiseau, et al., Laser-beam smoothing induced by stimulated Brillouin scattering in an inhomogeneous plasma,, Physical Review Letters, 97 (2006). doi: 10.1103/PhysRevLett.97.205001. Google Scholar

[13]

G. Metivier and R. Sentis, On the Boyd-Kadomtsev System and its asymptotic limit,, Comm. Math. Physics, (2011). Google Scholar

[14]

Ph. Mounaix, D. Pesme and M. Casanova, Nonlinear reflectivity of an inhomogeneous plasma,, Phys. Review E, 55 (1997). doi: 10.1103/PhysRevE.55.4653. Google Scholar

[15]

S. Novikov, S. V. Manakov, L. P. Pitaevskiĭ and V. E. Zakharov, "Theory of Solitons. The Inverse Scattering Method,", Contemporary Soviet Mathematics, (1984). Google Scholar

[16]

D. Pesme, Interaction collisionnelle et collective,, in, (1995). Google Scholar

[17]

R. Sentis, On the Boyd-Kadomtsev system for the three-wave coupling problem,, C. R. Math. Ac. Sciences Paris, 347 (2009), 933. Google Scholar

[18]

R. Sentis, Mathematical models for laser-plasma interaction,, M2AN Math. Modelling Num. Analysis, 39 (2005), 275. Google Scholar

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