Jeans instability is examined in detail in uniform dusty magnetoplasmas taking care of collisional and non-zero finite thermal effects in addition to the quantum characteristics arising through the Bohm potential and the Fermi degenerate pressure using the quantum hydrodynamic model of plasmas. It is found that the presence of the dust-lower-hybrid wave, collisional effects of plasma species, thermal effects of electrons, and the quantum mechanical effects of electrons have significance over the Jeans instability. Here, we have pointed out a new class of dissipative instability in quantum plasma regime.
The beat phenomenon due to the coupling of two signals at slightly different frequencies that generates the low frequency signal is studied. The linear dispersive properties of the pump and sideband are analyzed. The modified nonlinear dispersion relation through the field coupling of linear modes against the beat frequency is derived in the homogeneous quantum dusty magnetoplasmas. The dispersion relation is used to derive the modified growth rate of three wave parametric instability. Moreover, significant quantum effects of electrons through the exchange-correlation potential, the Bohm potential, and the Fermi pressure evolved in macroscopic three wave interaction are presented. The analytical results are interpreted graphically describing the significance of the work. The applications of this study are pointed out at the end of introduction.
The dust shear Alfvén wave is studied in three species dusty quantum plasmas. The quantum effects are incorporated through the Fermi degenerate pressure, tunneling potential, and in particular the exchange-correlation potential. The significance of exchange-correlation potential is pointed out by a graphical description of the dispersion relation, which shows that the exchange potential magnifies the phase speed. The low-frequency shear Alfvén wave is studied while considering many variables. The shear Alfvén wave gains higher phase speed at the range of small angles for the upper end of the wave vector spectrum. The increasing dust charge and the external magnetic field reflect the increasing tendency of phase speed. This study may explain many natural mechanisms associated with long wavelength radiations given in the summary.
The propagation of dust-ion acoustic (DIA) wave is studied with the streaming effects of ion particles in a quantum dusty plasmas. The quantum effects arising from Landau magnetization, Fermi degenerate pressure, tunneling potential and exchange-correlation potential are considered for the electrons. Linear dispersion relation is derived using Quantum Hydrodynamic Model and the results are graphically presented showing the propagation and growth rate of the electrostatic mode in the dense plasma environment.
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