Parametric instabilities in a quantum magnetoplasma with electron exchange-correlations.

Relying on the density functional theory, we have examined the impact of electron exchange-correlations on the nonlinear dispersion relations and associated parametric instabilities induced by nonlinear couplings of high-frequency quantum upper-hybrid waves (QUHWs) with different low-frequency waves, like quantum lower-hybrid waves (QLHWs), quantum ion-cyclotron waves (QICWs), and quantum Alfvén waves (QAWs) in a dense quantum magnetoplasma. For theoretical description of waves, we make use of quantum hydrodynamic equations to account for the electron exchange-correlation and Bohm potentials, strongly dependent on the density fluctuations. At quantum scales, nonlinear dispersion equations are derived for QUHWs, QICWs, QLHWs, and QAWs and then Fourier transformed for obtaining the nonlinear dispersion relations and growth rates involving the three wave decay and modulational instabilities in dense quantum magnetoplasmas. The relevance to nonlinear interactions due to high- and low-frequency waves in perspective of electron exchange-correlations is highlighted. [ABSTRACT FROM AUTHOR]