Stability analysis of self-gravitational electrostatic drift waves for a streaming nonuniform quantum dusty magnetoplasma

Abstract

Using the quantum hydrodynamic model of plasmas, the stability analysis of self-gravitational electrostatic drift waves for a streaming non-uniform quantum dusty magnetoplasma is presented. For two different frequency domains, i.e., X0d x < X0i (unmagnetized dust) and x X0d < X0i (magnetized dust), we simplify the general dispersion relation for self-gravitational electrostatic drift waves, which incorporates the effects of density inhomogeneity $n0a, streaming velocity v0a due to magnetic field inhomogeneity $B0, Bohm potential, and the Fermi degenerate pressure. For both frequency domains, the effect of density inhomogeneity gives rise to real oscillations while the ions streaming velocity v0i as well as the effective electron quantum velocity v 0 Fe make these oscillations propagate perpendicular to the ambient magnetic field. This oscillatory behavior of self-gravitational drift waves increases with increase in inhomogeneities and quantum effects while it decreases with increase in the gravitational potential. However, only for the unmagnetized case, the drift waves may become unstable under appropriate conditions giving rise to Jeans instability. The modified threshold condition is also determined for instability by using the intersection method for solving the cubic equation. We note that the inhomogeneity in magnetic field (equilibrium density) through streaming velocity (diamagnetic drift velocity) suppress the Jeans instability depending upon the characteristic scale length of these inhomogeneities. On the other hand, the dust-lower-hybrid wave and the quantum mechanical effects of electrons tend to reduce the growth rate as expected. A number of special cases are also discussed. VC 2012 American Institute of Physics.