Computer simulation of the saturation of the parametric instability in the weak turbulence regime

The theory of nonlinear saturation of the parametric decay instability in the weak turbulence limit is developed, and the resulting kinetic equation solved numerically for a variety of cases. These solutions are compared with the results of a series of computer simulations. Agreement is found to be good only for pump powers below threshold, with the reason for partial failure above threshold unclear. The validity of the random phase approximation is also discussed. A summary of computational methods is provided.