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On a quasilinear Zakharov system describing laserplasma interaction
"... In this paper, starting from the bifluid EulerMaxwell system, we derive a complete set of Zakharov’s equations type describing laserplasma interactions. This system involves a quasilinear part which is not hyperbolic and exhibits some elliptic zones. This difficulty is overcome by making a chan ..."
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Cited by 26 (5 self)
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In this paper, starting from the bifluid EulerMaxwell system, we derive a complete set of Zakharov’s equations type describing laserplasma interactions. This system involves a quasilinear part which is not hyperbolic and exhibits some elliptic zones. This difficulty is overcome by making a change of unknowns that are strongly related to the dispersive part. This change of variable is a symmetrization of the quasilinear part and is the key of this paper. This shows that the Cauchy problem is locally wellposed.
A perturbative analysis of the timeenvelope approximation in strong Langmuir turbulence
, 1997
"... We investigate a nonlinear set of coupledwave equations describing the inertial regime of the strong Langmuir turbulence, namely 8 ? ? ? ? ! ? ? ? ? : 1 ! 2 @ 2 E @t 2 \Gamma 2i @E @t \Gamma \DeltaE = \GammanE; 1 c 2 @ 2 n @t 2 \Gamma \Deltan = \DeltajEj 2 ; which differs from t ..."
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Cited by 9 (2 self)
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We investigate a nonlinear set of coupledwave equations describing the inertial regime of the strong Langmuir turbulence, namely 8 ? ? ? ? ! ? ? ? ? : 1 ! 2 @ 2 E @t 2 \Gamma 2i @E @t \Gamma \DeltaE = \GammanE; 1 c 2 @ 2 n @t 2 \Gamma \Deltan = \DeltajEj 2 ; which differs from the usual Zakharov equations through a perturbative !dependent parameter that vanishes under the socalled timeenvelope approximation ! 2 ! +1. From these perturbed Zakharov equations, it is shown that the latter limit is not compatible with a strongly dominant ion inertia corresponding to the formal case c 2 ! 0. In the opposite case, i.e. as c 2 remains of order unity, the localintime Cauchy problem attached to the above equations is solved and the limit ! 2 ! +1 is detailed for a fixed value of c 2 . Under some specific initial data, the solution E is proved to blow up at least in an infinite time provided that ! lies below a threshold value. When this condition is not fulfi...
Justification of the Zakharov model from KleinGordonWave systems
 Comm. Part. Diff. Eq
"... Abstract. We study semilinear and quasilinear systems of the type KleinGordonwaves in the highfrequency limit. These systems are derived from the EulerMaxwell system describing laserplasma interactions. We prove the existence and the stability of highamplitude WKB solutions for these systems. ..."
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Cited by 8 (4 self)
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Abstract. We study semilinear and quasilinear systems of the type KleinGordonwaves in the highfrequency limit. These systems are derived from the EulerMaxwell system describing laserplasma interactions. We prove the existence and the stability of highamplitude WKB solutions for these systems. The leading terms of the solutions satisfy Zakharovtype equations. The key is the existence of transparency equalities for the KleinGordonwaves systems. These equalities are comparable to the transparency equalities exhibited by J.L. Joly, G. Métivier and J. Rauch for MaxwellBloch systems.
Nonlinear models for laserplasma interactions
, 2007
"... In this paper, we present a nonlinear model for laserplasma interaction describing the Raman amplification. This system is a quasilinear coupling of several Zakharov systems. We handle the Cauchy problem and we give some wellposedness and illposedness result for some subsystems. ..."
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Cited by 3 (1 self)
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In this paper, we present a nonlinear model for laserplasma interaction describing the Raman amplification. This system is a quasilinear coupling of several Zakharov systems. We handle the Cauchy problem and we give some wellposedness and illposedness result for some subsystems.
Theoretical and numerical study of a quasilinear Zakharov system describing Landau damping
"... In this paper, we study a Zakharov system coupled to an electron diffusion equation describing laserplasma interactions. Starting from the VlasovMaxwell system, and using a transformation that decomposes slowly varying components on the plasma frequency time scale, we derive a nonlinear Schrödinge ..."
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In this paper, we study a Zakharov system coupled to an electron diffusion equation describing laserplasma interactions. Starting from the VlasovMaxwell system, and using a transformation that decomposes slowly varying components on the plasma frequency time scale, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Then, by using a timesplitting spectral discretizations for the Zakharov system and a finite difference scheme for the electron diffusion equation, we investigate numerical simulations and show how Landau damping works. 1 Introduction and physical situation The interaction of an intense laser pulse with a plasma is a complex physical phenomenon where numerical simulation plays a key role in its understanding. One of the main goal is to simulate nuclear fusion by inertial confinement in a laboratory. We therefore need some accurate and reliable numerical models of laserplasma interactions. Vlasov or particleincell