Coupling Saturation in the Nonlinear Theory of Parametric Decay Instabilities

A new saturation mechanism for the nonlinear stage of parametric decay instabilities arises from pump-induced cross-correlations between Fourier modes. These correlations result in a renormalization—usually a reduction—of the mode coupling coefficients. Coupling saturation arises from the same order of approximation as the familiar induced-scattering nonlinearity. When applied to the $2{\omega }_{\mathrm{pe}}$ decay instability and the electron-ion decay instability, coupling saturation greatly reduces the turbulent wave energy compared to earlier calculations.