The role of nonlinear beating currents on parametric instabilities in magnetoplasmas

A general coupled mode equation for the low-frequency decay modes of parametric instabilities in magnetoplasmas is derived. The relative importance of the nonlinear contributions from the ponderomotive force, nonlinear beating current, and anisotropic effect to the parametric coupling is then manifested by the coupling terms of the equation. It is first shown in the unmagnetized case, that the contribution of the nonlinear beating current is negligibly small because of the small coefficient (i.e., weight) of this current contribution, instead of the beating current itself. It then follows that the weight of the beating current contribution increases significantly in the magnetized case, and consequently, this contribution to the parametric coupling is found to be important, as exemplified by two specific examples.