Abstract
The effect of Hall current on the Jeans instability of an infinitely conducting, homogeneous, viscous quantum plasma is investigated. The basic equations of the problem are constructed and linearized by using the quantum magnetohydrodynamic model. The contributions of Hall current and viscosity of the medium are incorporated into the present analysis because of their astrophysical importance. The general dispersion relation is obtained using the normal mode analysis technique, which is reduced for both the transverse and the longitudinal mode of propagation. The longitudinal mode is found to be modified by Hall current, while the transverse mode is unaffected by the presence of the Hall parameter. The Jeans criterion of instability is obtained, which is modified by Alfven velocity and quantum corrections but is unaffected by the presence of the Hall parameter and viscosity. The longitudinal mode is found to be modified by Alfven speed and the Hall parameter and is independent of quantum corrections. Viscosity, magnetic field and quantum corrections all have a stabilizing influence on the growth rate of the Jeans instability.
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