**Acknowledgements**

We showed for the first time in this study that a seemless transition occurs from Raman forward scatter, to the standing wave excited KEEN wave very near the backscattering plasma wave so that the distribution function is strongly modified by the KEEN wave before the EPW can be excited in SRBS. For the parameters we have investigated, the SRBS process is preceded by KEEN waves and then competes with SKEENS for supremacy and eventual merging. This rich physics was not observed when strong seeding of the backscattered wave prevented any

The accurate representation and evolution of the particles distribution function provided by the Eulerian Vlasov code offers a powerful tool to study highly nonlinear nonstationary processes in high energy density plasmas. We have uncovered some distinctive features of KEEN waves participating in the Raman process, using a 1D Eulerian Vlasov-Maxwell code that relativistically evolves both ions and electrons. To avoid any interference from artificially distorted distribution functions or imposed linear wave seeding, we start the code from an initial Maxwellian distribution, and a very weak scattered light field standing wave pattern which is enough to trigger both SRFS and then SKEENS. The system evolves under the influence of a pump light wave which provides fluctuations from which SRBS eventu‐ ally develops. We identify in the early phase of the Raman interaction a reflected light that matches the backscattering of the pump laser off a KEEN wave whose fundamental harmonic has the same wavelength as the forward scattered light, and its appearance precedes the growth and saturation of SRBS. The evolution of the system is however modified with the results presented in section 4.2, close to the center of the simulation domain. In this region, the round-off errors have reached a level where they act as a perturbation, leading to the simultaneous appearance and growth of the SRBS process, in addition to the KEEN wave (see Figure (14)). So we have two distinct evolution scenarios of Raman scattering in the domain we study. To the right of the region *x* ∈(500,519) in Figure (14), we see a simultaneous growth of the SRBS plasma wave and the KEEN wave (see Figure (15)). And to the left of the region *x* ∈(500,519), the growth of the round-off errors acting as a perturbation leads to the appearance of SRBS plasma waves moving to the left in the backward direction. This is where the KEEN wave has already reached saturation, causing heating and relative flattening of the electron distribution function, which shows a structure with a trapped population of electrons. Note the harmonic structure associated with the SRBS mode *ωeB* =1.178, *keB* =5.38 in Figures (11a,12a). Recent publica‐ tions have pointed to the importance of 2D and 3D effects for a rigorous theory of SRS saturation [41]. This is beyond the scope of the present work. We have restricted our study to the initial phase of the evolution of Raman scattering, and we have shown that in this case scattering off a KEEN wave can produce a backward wave which contributes to the

inflation of the Raman signal well before the SRBS starts growing on its own.

In future studies, we propose to investigate the physics of the interaction between SKEENS and SRBS, but eliminating the need for SRFS initiation. This can be achieved by driving the KEEN wave directly by the ponderomotive force generated by the beating of the pump and the appropriate seed electromagnetic wave. Driving KEEN waves directly and electromag‐ netically generalizes the work of Afeyan et al. [18-20] which has been based on the Vlasov-

detection of these intermediate processes.

278 Computational and Numerical Simulations

The authors are grateful to the Centre de calcul scientifique de l'IREQ (CASIR) for computer time for the simulations presented in this work. BA would like to acknowledge the financial assistance of DOE OFES HEDP program through a subcontract via UCSD.
