The effect on parametric instability growth of pump wave incoherence is treated by deriving a set of equations governing the space-time evolution of the ensemble-average coupled-mode amplitudes and intensities. Particular attention is paid to establi
shing the regions of validity of the statistical description. Thresholds, growth rates, and amplification rates are given for both spatially and temporally incoherent pump waves. Both absolutely and convectively unstable modes are considered. The statistical results are verified where appropriate by numerical integration of the coupled-mode equations with different models of pump incoherence.
An investigation of the possible inflation of stimulated Brillouin backscattering (SBS) due to ion kinetic effects is presented using electromagnetic particle simulations and integrations of three-wave coupled-mode equations with linear and nonlinear
models of the nonlinear ion physics. Electrostatic simulations of linear ion Landau damping in an ion acoustic wave, nonlinear reduction of damping due to ion trapping, and nonlinear frequency shifts due to ion trapping establish a baseline for modeling the electromagnetic SBS simulations. Systematic scans of the laser intensity have been undertaken with both one-dimensional particle simulations and coupled-mode-equations integrations, and two values of the electron-to-ion temperature ratio (to vary the linear ion Landau damping) are considered. Three of the four intensity scans have evidence of SBS inflation as determined by observing more reflectivity in the particle simulations than in the corresponding three-wave mode-coupling integrations with a linear ion-wave model, and the particle simulations show evidence of ion trapping.
