Suppression of parametric instability by weakly incoherent laser beams

The linearized coupled-mode equations in two dimensions are solved numerically within the paraxial approximation to find the absolute-mode threshold of parametric instabilities driven by an incoherent laser beam. The results show that, for plasma lengths only a few times threshold, a surprisingly small temporal bandwidth Δω that is substantially less than the growth rate ${\gamma }_0$ is effective in suppressing absolute growth. Only if the plasma length greatly exceeds the threshold is the necessary temporal bandwidth the larger value obtained from homogeneous plasma theory.