1. 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

2. 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.

3. Model and equations..

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

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

6. TransmissionReflectivity Energy conservation OK ! time T R

7. 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

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

9. 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

10. 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 =

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

12. 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

13. pumpplasmasoundbackscattered t = 3ps t = 5ps

14. 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

15. 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