Effects of Ion-ion Collisions and Inhomogeneity in Two-dimensional Simulations of Stimulated Brillouin Backscattering*

Two-dimensional simulations of stimulated Brillouin backscattering (SBBS) with the BZOHAR$^{1}$ code have been extended to include ion-ion collisions and spatial nonuniformity in the mean ion flow. BZOHAR hybrid simulations (particle-in-cell kinetic ions and Boltzmann fluid electrons) have shown$^{2}$ that SBBS saturation is dominated by ion trapping effects and secondary instability of the primary ion wave (decay into subharmonic ion waves and ion quasi-modes). Here we address the effects of ion collisions$^{3}$ on SBBS saturation and employ the efficient Langevin ion collision algorithm of Ref. 4 and the Fokker-Planck collision operator of Ref. 5. We also report simulations of SBBS with a linear gradient in the mean ion drift, which in conjunction with the nonlinear frequency shift due to ion trapping can introduce auto-resonance effects that may enhance reflectivities.$^{6}$ For SBBS in a high-gain limit with ion collisions or inhomogeneity, we find that ion trapping and secondary ion wave instabilities are robust saturation mechanisms. *Work performed for US DOE by UC LLNL under Contr. W-7405-ENG-48. $^{1}$B.I. Cohen, \textit{et al.,} Phys. Plasmas \textbf{4}, 956 (1997). $^{2}$B.I. Cohen, \textit{et al.}\textbf{, }Phys. Plasmas, \textbf{12}, 052703 (2005),. $^{ 3}$P.W. Rambo, \textit{et al.}, Phys. Rev. Lett. \textbf{79}, 83 (1997). $^{ 4}$M.E. Jones, \textit{et al.,} J. Comp. Phys. \textbf{123}, 169, (1996). $^{ 5}$W. M. Manheimer, \textit{et al}., J. Comp. Phys. \textbf{138}, 563 (1997). $^{ 6}$E.A. Williams, \textit{et al.}, Phys. Plasmas \textbf{11}, 231 (2004).