Structure in the nonlinear saturation spectrum of parametric instabilities

The nonlinear saturation spectrum of the decay instability is obtained in the limit of small spontaneous emission, for comparable ion and electron temperatures, from numerical solutions of a kinetic equation based on an accurate expression for the nonlinearity. The spectral energy occupies several pairs of isolated saucer-shaped regions in wave-vector space. The regions increase in thickness, angular diameter, and number as the pump power is increased. The theory thus predicts the generation of waves propagating in directions which can differ substantially from the direction of the pump field. Ionospheric observations confirm this prediction; they were difficult to reconcile with the predictions of previous theories based on an approximate expression for the nonlinearity. The present work also corrects the results of previous one-dimensional theories that used an accurate expression for the nonlinearity and predicted “spectral lines” in the limit of vanishing spontaneous emission. Excitation of the purely growing instability is predicted for pump powers greater than about 2.5 times the threshold of the decay instability.