Influence of quantum correction on the Jeans instability of strongly coupled magnetized plasma

It is shown that the Jeans instability condition of strongly coupled finitely conducting gaseous plasma is reduced in the presence of magnetic field and quantum correction. The linearized equations are constructed by using the Quantum magneto-hydrodynamic (QMHD) model. With the help of the normal mode analysis method, a general dispersion relation is obtained. This dispersion relation is discussed by a different mode of propagation. In this paper, it has been found that, quantum correction stabilizes the growth rate of the organization but the relaxation time and electrical resistivity destabilize the growth rate in the transverse mode of propagation. Further, the modified Jeans criterion of the instability of the magnetized plasma system has been also found.