Topic/Type: 1. Plasma Simulation, Poster

### A Vlasov-Maxwell Code for the Numerical Study of the Stimulated Raman Scattering in the Kinetic regime

M. Shoucri1, B. Afeyan2

1 Institut de Recherche Hydro-Qu?bec (IREQ), Varennes, Qu?bec, Canada
2 Polymath Research Inc., Pleasanton, CA, USA

An Eulerian code is used for the numerical solution of the one-dimensional relativistic Vlasov-Maxwell equations to study the stimulated Raman scattering (SRS) for the case of a strong Landau damping, when $\small k \lambda_{De} > 0.29$, where $\small k$ is the plasma wavenumber, and $\small \lambda_{De}$ is the Debye length. This regime is referred to as the kinetic regime [1], the Langmuir Decay instability driven by the primary Langmuir wave is too heavily Landau damped [1]. We start our simulation in a homogeneous plasma slab. A propagating pump is injected at $\small (\omega_0, k_0)$, and a counter-propagating low intensity seed scattered light $\small (\omega_s, k_s)$ is injected. The intensities are $\small I_{\mathrm{seed}} = 10^{-4} I_{\mathrm{pump}}$, and the waves are linearly polarized. The total length of the system is 1171.78 $\small c/\omega_p$. It consists of a slab of length 1122.56 $\small c/\omega_p$, surrounded by a vacuum of length 16.8 $\small c/\omega_p$ on each side, and the jump of the density on each side of the slab is of length is 7.81 $\small c/\omega_p$. The quiver momentum of the pump wave is $\small a_0 = 0.025$. The maximum of the electron density is $\small n = 0.0825 n_c$ for an electron temperature $\small T_e =2$ keV. Ions are allowed to move, since they usually help provide a correct transition sheath at the plasma slab edges, but otherwise should have little effect on the other physical processes considered. Normalizing frequencies to the initial plasma frequency, we have initially for the pump wave $\small \omega_0 = 3.481\,\omega_p$ and $\small k_0 = 3.334\,c/\omega_p$, for the back-scattered (SRS-B) wave $\small \omega_{sB} = 2.344\,\omega_p$ and $\small k_{sB} = 2.12\,c/\omega_p$, and finally for the plasma wave $\small k_{eB} = 5.45\,c/\omega_p$, and $\small \omega_{eB} = 1.16\,\omega_p$. Then $\small k_{eB} \lambda_{De} = 0.34$, so the plasma wave with the SRS-B is strongly damped. We are exciting the SRS-B, but the forward SRS-F wave is coupled, and the plasma wave grows more rapidly than in the SRS-B case, it is very weakly damped. With $\small k_0 = k_{sF} + k_{eF}$, we have $\small k_{sF} = 2.264$ and $\small k_{eF} = 1.07$, $\small \omega_{eF} = 1007$, then $\small k_{eF} \lambda_{De} = 0.0668$, which is very weakly damped. For the frequencies we have $\small \omega_0 = \omega_{sF} + \omega_{eF}$, then $\small \omega_{sF} = 2.474$. The growth, coupling and saturation of these modes will be studied.

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The contribution of B.Afeyan is funded by the DOE NNSA SSAA Grants program.

[1] J.L. Kline, D.S. Montgomery, B. Bezerrides et al Phys. Rev. Lett. 94, 175003 (2005)