Nonlinear saturation of parametric instability: basic theory and application to the ionosphere

A calculation is presented of the nonlinear level of Langmuir and acoustic wave plasma fluctuations excited by parametric decay instability, and saturated by induced scattering of the plasma waves from dynamically screened ions (low-frequency spontaneous emission). This is found to be an important weak turbulence saturation mechanism for instabilities excited parametrically in the ionosphere. The cross section for incoherent scattering from the excited waves is obtained and comparisons are made with recent experiments.