The effect of the Hall term on Jeans instability in quantum magnetoplasma with resistive effects

The Jeans instability in dense quantum plasmas is investigated by taking into account the Hall term and resistivity in the presence of two-dimensional magnetic fields. The general dispersion relation is presented. The presence of the Hall term introduces a new wave mode which does not exist in the ideal magnetohydrodynamic framework. Two limiting cases with respect to the Hall effect are discussed. The Hall effect is shown to induce a frequency shift but does not change the instability criterion. The resistivity exhibits damping or destabilizing effects on the plasma system under different circumstances. The analytical expressions of the growth/damping rate of Jeans instability are obtained for both the finite and remarkable resistivity cases in the absence of the Hall term.