The Effect of Radiation on the Jeans Instability of a Viscous Quantum Plasma with Finite Electrical Resistivity

Abstract

The effect of the radiative heat-loss function on the Jeans instability of a quantum plasma, in the presence of finite electrical resistivity and viscosity, is investigated. A general dispersion relation is derived from the linearized perturbation equations using normal mode analysis and discussed for the longitudinal and transverse direction of wave propagation. On the basis of the Routh-Hurwitz criterion, the dynamic stability of the system is discussed. The condition for the Jeans instability of a quantum plasma is discussed in the different cases of our interest. It is found that, owing to the inclusion of a radiative heat-loss function and thermal conductivity, the Jeans criterion of gravitational instability changes into a radiative instability criteria. For the transverse mode, in the case of a resistive medium the expression of the Jeans instability is independent of the magnetic field, while for a perfectly conducting medium the magnetic field gives a stabilizing effect. From the curves it is apparent that the viscosity, temperature dependent heat-loss function, and magnetic field stabilize the system, while the electrical resistivity has a destabilizing effect.