2. Centre de PhysiqueThéorique 1. DAM; Bruyères-le-Châtel DCSA 1. : M. Casanova 1., 2. : Thomas Fouquet 2. : S. Hüller, D. Pesme HEDP Summer School UC Berkeley, 2005 Nonlinear Evolution of Stimulated Raman Scattering driven by a RPP Laser Beam in a 2D Inhomogeneous Plasma CPHT

Aim : Study the Stimulated Raman Scattering (SRS) and its saturation via the coupling of the plasma waves generated by this instability, with the sound waves; in the case of an inhomogeneous plasma in density. 2D modelization case of a linear density profile laser beam : monospeckle or RPP Raman instability results of the coupling of an incident laser wave with a plasma electronic wave to give birth to a transverse wave named scattered : it is a three waves coupling process. The conditions of the resoning coupling imply that this instability can be developed in a field called 'under quarter critical'. This field corresponds to ne< nc/4 densities.

Model and equations..

Raman Autofocalisation Raman LDI Autofocalisation ponderomotive forces pump backscattered plasma sound Linear propagator Envelope and paraxial approximation for the pump and backscattered waves Inhomogeneity

SRS in a 2D homogeneous plasma Test of the numerical scheme Monospeckle pump wave L = L = Backscattered wave Plasma wave Gaussian beam

TransmissionReflectivity Energy conservation OK ! time T R

Raman in an inhomogeneous 1D plasma « finite length » effect Resonance conditions cannot be satisfied in the whole plasma slab : Solutions of parametric resonance conditions in.. 2 effects of distinct nature : Dispersion relation is local

« Linear profile » : Monotonous profile of density Rosenbluth’s result : Finite spatial amplification PRL 1972 Non robust Absolute instability z Mismatch : /. !! Difficulty !!!

Numerical difficulties : Non robustness of the Rosenbluth’s result Realistic plasma = finite length + inhomogeneous in density Numerical techniques in order to control the behaviour at the boundaries : Difficulties = Numerical artefacts. numerical dampings. « window » function in the simulation box absolute instability If the variation is too fast

SRS without its coupling to the IAWs : inhomogeneous plasma with a linear density profile; RPP laser beam pump backscatteredplasma keV t = 1ps t = 2ps L = L =

pump backscatteredplasma Raman reflectivity w.o LDI t = 3ps t = 5ps SRS reflectivity saturates at ~ 10% : -filamentation -finite amplification gain= time R

pump backscatteredplasma sound SRS with its coupling to the IAWs (LDI)* : inhomogeneous plasma with a linear density profile; RPP laser beam t = 2ps t = 1ps and same parameters as used before * generalizing in a 2D inhomogeneous plasma, the results investigated by Bezzerides, DuBois, Rose, Rozmus, Russel, Tikhonchuk, Vu

pumpplasmasoundbackscattered t = 3ps t = 5ps

Raman reflectivity w. LDI red : Raman reflectivity black : Raman reflectivity w.o LDI } Evidence of saturation effects due to LDI SRS reflectivity saturates at ~ 1.5% when plasma and sound waves are coupled; compared to 10% without coupling to the IAW’s R time

Summary/conclusions *Design of a 2D numerical code : - inhomogeneous plasma - SRS coupled to LDI *First simulations of SRS with LDI in an inhomogeneous 2D plasma * Evidence of saturation due to LDI; generalizing in an inhomogeneous plasma the results already seen in a homogeneous one