Nonlinear coupling of upper-hybrid waves with lower-hybrid waves in a degenerate dense plasma

The nonlinear coupling of high-frequency upper-hybrid (UH) pump waves with low-frequency lower-hybrid (LH) waves is studied in a degenerate magnetoplasma, comprising of quantum electrons and classical ions. For this purpose, the framework of quantum hydrodynamic model is utilized to examine the Fermi pressure effects on the nonlinear dispersion relations of UH and LH waves with quantum settings. Furthermore, by applying the Fourier analysis and collecting the same phasor terms, the nonlinear dispersion relations can be coupled to investigate the growth rates of three-wave decay and modulational instabilities under certain approximations. It is noticed that inclusion of electron Fermi pressure significantly alters the parametric three-wave decay and modulational instabilities besides the corrections due to quantum exchange-correlations and Bohm potential in degenerate magnetoplasmas. The present findings might be useful to understand the nonlinear wave interactions in superdense astrophysical environments, e.g., white dwarfs, magnetars, neutron stars, etc.