Effect of Fermi Pressure and Bohm Potential on Jeans Instability of Quantum Dusty Plasma in Presence of Polarization Force

Abstract

The quantum hydrodynamic model is considered to investigate the Jeans instability of three species ultracold inhomogeneous dusty plasma. The formulation of this paper is based on the assumption that the electron and ion inertial force is negligible in comparison with the electron and ion pressure and force associated with the electron and ion correlations at the quantum scale. The gravitational force acting on the negatively charged dust grains is considered in the presence of both the electrostatic and polarization forces taking into account the quantum diffraction and statistical contributions of dust particles. The modified dispersion relation is derived and analyzed to obtain the instability criterion by including the dust polarization force and the quantum corrections. Numerical results are presented to show the effect of these modifications on the growth rate of Jeans instability. The present investigation is relevant to the collapse of ultracold astrophysical objects like the inner core of white dwarf and neutron star.