Nonlinear wave interactions in quantum magnetoplasmas

Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfvén waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfvén waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.