Involvement of the quantum radiative effect on Jeans instability with electrical resistance and Hall current

Abstract

The influence of quantum radiative effect and electrical resistivity incorporating the Hall current is studied on the Jeans instability of magnetized plasma. The basic equation of the problem is constructed and linearized by using the QMHD model. The general dispersion relation is derived using a normal mode technique and discussed in the parallel and perpendicular propagation. In the case of longitudinal propagation, the Jeans instability is modified due to quantum radiative impact but is unaffected by electrical resistivity and Hall current. While in transverse propagation the electrical resistivity is modifying the growth rate of instability. In the graphical presentation, we found that the electrical resistivity has destabilizing influence but the presence of a quantum parameter is reduced the destabilizing effect of electrical resistivity in the system. The result is relevant to understanding many astrophysical problems.