The effects of arbitrary radiative heat-loss functions and Hall current on the self-gravitational instability of a homogeneous, viscous, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, finite electron inertia and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis with the help of relevant linearized perturbation equations of the problem, and a modified Jeans criterion of instability is obtained. The conditions of modified Jeans instabilities and stabilities are discussed in the different cases of our interest. We find that the presence of arbitrary radiative heatloss functions and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. For longitudinal propagation, it is found that the condition of radiative instability is independent of the magnetic field, Hall parameter, finite electron inertia, finite electrical resistivity, viscosity and rotation; but for the transverse mode of propagation it depends on the finite electrical resistivity, the strength of the magnetic field, and it is independent of rotation, electron inertia and viscosity. From the curves we find that the presence of thermal conductivity, finite electrical resistivity and densitydependent heat-loss function has a destabilizing influence, while viscosity and magnetic field have a stabilizing effect on the growth rate of an instability. The effect of arbitrary

The effect of radiative heat-loss function on the Jeans instability of an infinitely conducting, homogeneous partially ionized gaseous plasma is investigated. It is assumed that the medium is carrying a uniform magnetic field in the presence of porosity and thermal conductivity. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained for a such medium using the normal analysis technique, which is reduced for both the transverse and the longitudinal mode of propagation. The longitudinal mode is found to be modified by Alfven speed and parameter of porosity. The thermal mode is obtained separately having the effects of thermal conductivity and arbitrary radiative heat-loss functions. The effect of collision with neutrals and magnetic field have a stabilizing effect, while thermal conductivity has destabilizing influence on the Jeans instability of gaseous plasma. In the transverse mode of propagation, we find the condition of radioactive instability depends on thermal conductivity, magnetic field and the porosity of the medium.

The influence of rotation on the Jeans instability of homogeneous magnetized radiative quantum plasma is investigated. The basic equations of the problem are constructed and linearized by using the Quantum Magnetohydrodynamics (QMHD) model. The general dispersion relation is obtained by using the normal mode analysis technique, which is reduced for both the transverse and the longitudinal mode of propagations and further it is reduced for the axis of rotation parallel and perpendicular to the magnetic field. We found that the stabilizing effects of rotation are decreases for a strong magnetic field which is shown in the graphical representation. We also found that the quantum correction modified the condition of Jeans instability in both modes of propagation. The stabilizing effect of rotation is more increased in the presence of quantum correction.

The problem of radiative instability of homogeneous rotating partially ionized plasma incorporating viscosity, porosity, and electron inertia in the presence of a magnetic field is investigated. A general dispersion relation is obtained using normal mode analysis with the help of relevant linearized perturbation equations of the problem. The modified Jeans criterion of instability is obtained. The conditions of Jeans instabilities are discussed in the different cases of interest. It is found that the simultaneous effect of viscosity, rotation, finite conductivity, and porosity of the medium does not essentially change the Jeans criterion of instability. It is also found that the presence of arbitrary radiative heat-loss function and thermal conductivity modified the conditions of Jeans instability for longitudinal propagation. It is found that, for longitudinal propagation, the conditions of radiative instability are independent of magnetic field, viscosity, rotation, finite electrical resistivity, and electron inertia, but for the transverse mode of propagation it depends upon finite electrical resistivity and strength of magnetic field and is independent of viscosity, electron inertia, and rotation. From the curves we find that viscosity has a stabilizing effect on the growth rate of instability but the thermal conductivity and density-dependent heat-loss function has a destabilizing effect on the instability growth rate.PACS No: 94.20.wf Résumé : Nous étudions le problème de l'instabilité radiative dans un plasma partiellement ionisé, homogène et en rotation, incluant les effets de viscosité, de porosité et d'inertie des électrons, le tout en présence d'un champ magnétique. Nous obtenons une relation de dispersion générale en utilisant l'analyse en modes normaux, avec l'aide des équations de perturbation linéarisées pertinentes au problème. Nous retrouvons le critère modifié de stabilité de Jeans. Nous analysons les instabilités de Jeans pour les différents cas qui nous intéressent. Nous trouvons que les effets simultanés de la viscosité, de la rotation, de la conductivité finie et de la porosité du milieu n'affectent pas de façon significative le critère d'instabilité de Jeans. Plus précisément, nous trouvons que la présence d'une perte de chaleur radiative arbitraire et la conductivité thermique modifient les conditions de l'instabilité de Jeans pour la propagation longitudinale. En effet, nous observons pour la propagation longitudinale, que la condition d'instabilité radiative est indépendante du champ magnétique, de la viscosité, de la rotation, de la conductivité électrique finie et de l'inertie des électrons. Par contre, dans le mode transverse de propagation, la condition d'instabilité dépend de la conductivité électrique finie et du champ magnétique et reste indépendante de la viscosité, de la rotation et de l'inertie des électrons. À partir des courbes de résultats, nous observons que la viscosité a un effet stabilisant sur le taux de croissance de l'instabilité, mais la conductivité thermique et la ...

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