Vlasov simulation of 2D Modulational Instability of Ion Acoustic Waves and Prospects for Modeling such instabilities in Laser Propagation Codes

We present 2D+2V Vlasov simulations of Ion Acoustic waves (IAWs) driven by an external traveling-wave potential, $\phi_0(x,t)$, with frequency, $\omega$, and wavenumber, k, obeying the kinetic dispersion relation. Both electrons and ions are treated kinetically. Simulations with $\phi_0(x,t)$, localized transverse to the propagation direction, model IAWs driven in a laser speckle. The waves bow with a positive or negative curvature of the wave fronts that depends on the sign of the nonlinear frequency shift $\Delta \omega_{NL}$, which is in turn determined by the magnitude of $ZT_e /T_i $ where Z is the charge state and $T_{e,i}$ is the electron, ion temperature. These kinetic effects result can cause modulational and self-focusing instabilities that transfer wave energy to kinetic energy. Linear dispersion properties of IAWs are used in laser propagation codes that predict the amount of light reflected by stimulated Brillouin scattering. At high enough amplitudes, the linear dispersion is invalid and these kinetic effects should be incorporated. Including the spatial and time scales of these instabilities is computationally prohibitive. We report progress including kinetic models in laser propagation codes.