Gravitational Instability of a Rotating Viscous Finitely Conducting Plasma

The gravitational instability of infinite homogeneous plasma has been studied to include simultaneously the effects of rotations, Hall currents, viscosity, finite electrical conductivity and the finite Larmor radius (FLR). Both the longitudinal, and transverse modes of wave propagation have been studied. It is found that the gravitational instability is determined by Jeans' criterion even in the presence of effects of rotation, Hall currents, FLR, viscosity and finite conductivity whether included separately or jointly.     

Gravitational Instability of a Thermally Conducting Plasma in an Oblique Magnetic Field

The combined influence of the effects of Hall currents, magnetic resistivity and viscosity have been studied on the gravitational instability of a thermally conducting homogeneous unbounded plasma in an oblique magnetic field. The solution has been obtained through the normal mode technique and the dispersion relation has been derived. It is shown that the Jeans' criterion for gravitational instability remains unchanged. Solving numerically the dispersion relation, the dependence of the growth rate of the gravitational unstable mode on the considered physical effects has been obtained for an astrophysical situation. For conditions prevailing in the magnetized collapsing clouds, the numerical calculations for the plot of growth rate against wave number has been obtained for several values of the parameters characterizing Hall currents magnetic resistivity viscosity thermal conductivity. It is found that magnetic resistivity and thermal conductivity have destabilizing influence while viscosity has stabilizing influence on the instability of the plasma of disturbance m(ϱ) = 9 × 10⁻³ kg.     

Jeans' gravitational instability of a thermally conducting plasma

The gravitational instability of an infinitely extending homogenous plasma endowed with several physical mechanisms, namely Hall currents, finite conductivity, ion viscosity and thermal conductivity is considered. The main result is that the various parameters play different physical roles in the perturbed problem. Jeans' criterion is analyzed in the framework of Tsallis' statistics for possible modifications due to the presence of nonextensive effects. A simple generalization of the Jeans' criterion is obtained and the standard values are obtained in the limiting case q=1, q being the nonextensive parameter.     

Influence of Finite Larmor Radius with Finite Electrical and Thermal Conductivities on the Gravitational Instability of a Magnetized Rotating Plasma Through a Porous Medium

An infinitely extending homogeneous, self-gravitating rotating magnetized plasma flowing through a porous medium has been considered under the influence of Finite Larmor Radius (FLR) and other transport phenomena. A general dispersion relation has been derived through the linearized perturbation equations. Longitudinal and transverse modes of propagation have been discussed for the rotation with axis parallel and perpendicular to the magnetic field. The joint influence, of the aforesaid parameters, does not essentially change the Jeans' criterion of instability but modifies the same. The adiabatic sonic speed has been replaced by the isothermal one due to the thermal conductivity. It is further observed that the FLR corrections have stabilizing effect for an inviscid, non-rotating plasma, in case of transverse propagation. Rotation decreases the Larmor radius, whereas the porosity reduces the effects of rotation, FLR, and the magnetic field. Viscosity removes the effects of both, the roation, and the FLR corrections.     

Thermally Conducting Partially Ionized Plasma in a Variable Magnetic Field

An infinitely extending homogenous partially ionized plasma endowed with several physical mechanisms and permeated by a variable magnetic field is considered. The combined effect of these parameters, namely, Hall currents, finite conductivity, ion viscosity, collision with neutrals and thermal conductivity on the gravitational instability of the plasma is studied. It is found that the several mechanisms play different physical roles in the perturbed problem. Jeans' Criterion is analyzed in the framework of Tsallis' statistics for possible modifications due to the presence of nonextensive effects. A simple generalization of the Jeans' criterion is obtained and the standard values are obtained in the limiting case q = 1, q being the nonextensive parameter. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Larmor radius and Hall effects on thermal instability of a compressible plasma

The effects of compressibility, finite Larmor radius (FLR) and Hall currents are considered on the thermal instability of a plasma in the presence of a uniform horizontal magnetic field. For stationary convection, the compressibility has a stabilizing effect whereas FLR and Hall currents have stabilizing as well as destabilizing effects. For (C _pβ/g)<1, the system is stable. The magnetic field, FLR and Hall currents introduce oscillatory modes in the system for (C _pβ/g)>1.     

Effects of Hall Currents and Gyroviscosity on the Stability of a Finitely Conducting Rotating Viscous Plasma of Variable Density

The Rayleigh-Taylor instability of an incompressible viscous, finitely conducting, rotating plasma of variable density has been investigated in the presence of the effects of Hall currents and finite ion Larmor radius. The proper solution for a semi-infinité plasma layer having exponentially varying density in the vertical direction has been obtained by making use of a variational principle which is shown to characterize the problem. The dispersion relation has been solved numerically. It is found that gyroviscosity, viscosity and coriolis forces have stabilizing influence whereas Hall currents and resistivity have a destabilizing influence.     

Hall effects on thermosolutal instability of a rotating plasma

Summary The thermosolutal instability of a rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of Hall current. When the instability sets in as stationary convection for the case of no rotation, the Hall effects are found to be destabilizing. The stable solute gradient and rotation are found to have stabilizing effects. In the presence of rotation the Hall currents are found to be stabilizing forT ₁>M(1+x)². the case of overstability is also considered and it is shown that such solutions exist. The variation of the frequency with respect to the wave number at the neutral state is graphically shown. The authors of this paper have agreed to not receive the proofs for correction.     

On the Gravitational Instability of an Ionized Magnetized Rotating Plasma Flowing Through a Porous Medium with other Transport Processes and the Suspended Particles

The effects of suspended particles and the finite thermal and electrical conductivities on the magnetogravitational instability of an ionized rotating plasma through a porous medium have been investigated, under varying assumptions of the rotational axis and the modes of propagation. In all the cases it is observed that the Jeans' criterion determines the condition of instability with some modifications due to various parameters. The effects of rotation, the medium porosity, and the mass concentration of the suspended particles on instability condition have been removed by (1) magnetic field for longitudinal mode of propagation with perpendicular rotational axis, and (2) viscosity for transverse propagation with rotational axis parallel to the magnetic field. The mass concentration reduces the effects of rotation. Thermal conductivity replaces the adiabatic velocity of sound by the isothermal one, whereas the effect of the finite electrical conductivity is to delink the alignment between the magnetic field and the plasma. Porosity reduces the effects of both the magnetic field and the rotation, on Jeans' criterion.     

Stability of a Rotating Compressible Stratified Plasma in the Presence of Hall Currents and Magnetic Resistivity

The dynamic instability in a horizontal layer of a rotaing compressible plasma of variable density has been investigated to examine the influence of the simultaneous presence of the effects of Hall currents and finite magnetic resistivity. The linearized stability analysis has been carried out through the normal mode technique. By making use of the existence of a variational principle which is shown to characterize the problem, proper solutions have been obtained for a semiinfinite plasma in which there is an exponential density gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that both the resistivity and the Hall currents have a destabilizing influence as the growth rate of the unstable disturbances increases with increasing values of the parameters characterizing these effects. On the other hand, the Coriolis forces are found to have a stabilizing influence for in this case the growth rate decreases with increasing rotation.     

Hall Currents and the Rayleigh-Taylor Instability of a Finitely Conducting Plasma in the Presence of Coriolis Forces

We have studied the effect of rotation on the development of Rayleigh-Taylor instability of an incompressible, viscous, Hall, finitely conducting plasma of variable density. The solution is developed, through variational methods, for a semi-infinite plasma in which the density varies exponentially along the vertical. It is found that the system is unstable for all wave numbers when the effects of magnetic resistivity are included. The effects of coriolis forces and viscosity on the growth rate of the unstable system are found to be stabilizing while that of Hall currents is destabilizing. Finite conductivity affects the growth rate of the unstable mode differently for the smaller and larger values of the wave numbers, destabilizing for the waves of large wave length and stabilizing for waves of small wave length.     

Stability of Self-Gravitating Magnetized Hall Plasma with Electrical and Thermal Conductivity through Porous Medium

The problem of stability of a self-gravitating, infinite homogeneous gas in the presence of magnetic field is investigated. The medium is assumed electrically and thermally conducting. The effect of porosity, electrical conductivity, thermal conductivity and Hall current is investigated on the self-gravitating plasma flowing through porous medium. The relevant linearized equations of the problem are stated and dispersion relation is obtained. The effect of Hall current on the condition of the instability of the system is examined for both longitudinal and transverse mode of propagation and found that in longitudinal propagation Hall effect does not change the condition of instability but modifies the Alfvén wave mode. The stability of the system is discussed by applying Routh-Hurwitz criterion and it is found that Jeans criterion determines the stability of the system. Thermal conductivity and porosity have a destabilizing influence on the medium. The general condition for instability of the system is also derived.     

Effects of Hall Currents and Gyroviscosity on the Instability of a Self-Gravitating Stratified Plasma

The instability in a horizontal layer of a partially ionized self gravitating plasma has been studied to include simultaneously the effects of Hall currents, viscosity and finiteness of Larmor radius (FLR). The ambient magnetic field is assumed to be uniform and vertical. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of unstable perturbations decreases with the effects of viscosity, neutral gas friction and FLR. The influence of effects of viscosity, neutral gas friction and FLR are consequently stabilizing. It is found that the Hall currents have a destabilizing influence as the growth rate is found to increase with this effect.     

The Gravitational Instability of a Finitely Conducting Rotating Plasma Through a Porous Medium

The magneto-gravitational instability of an infinite homogeneous, finitely conducting, viscous rotating plasma through porous medium is investigated in view of its relevance to certain stellar atmospheres. The dispersion relation has been obtained from the relevant linearized perturbation equations of the problem and it has been discussed in the case of rotation parallel and perpendicular to the direction of magnetic field separately. The longitudinal and transverse modes of wave propagation are discussed in each case of rotation. It is found that the combined effect of viscosity, finite conductivity, rotation and the medium porosity does not essentially change the Jeans' criterion of gravitational instability. It is also shown that for the propagation transverse to the direction of magnetic field. the finite conductivity destabilizes the wave number band which is stable in the limit of infinite conductivity when the medium is considered inviscid.     

Stability of a Stratified Layer of a Gravitating Partially Ionized Plasma

The instability in a stratified layer of a self-gravitating partially ionized plasma has been studied in the presence of effects of Hall currents. For a plasma permeated by a uniform vertical magnetic field, the dispersion relation has been obtained through variational method. It is found that the Hall currents have a destabilizing effect while the neutral gas frictional effects have a stabilizing influence.     

Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

The effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly-trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.     

Frictional effects with neutrals and Rayleigh-Taylor instability of a compressible Hall plasma

The effect of neutral gas friction is considered on the Rayleigh-Taylor instability of a compressible plasma in the presence of Hall currents. The prevailing magnetic field is assumed to be uniform and horizontal. It is shown that the solution is characterized by a variational principle. Based on the variational principle the dispersion relation is derived for a composite plasma, confined between two horizontal planes at a finite distance, in which the density is stratified in the direction of gravity according to the exponential law. It is found that the effect of collisions with neutrals, Hall currents and compressibility of the medium have destabilizing influence as the wave number range which is stable in their absence, is rendered unstable by their presence.     

Instability of a charged interface of two immiscible viscous liquids with charge relaxation taken into account

On the basis of an analysis of a derived dispersion relation, it is demonstrated that there can be two different types of instability relative to the free charge of a charged, planar interface between two viscous immiscible liquids with finite electrical conductivity in a gravitational field. For large values of the surface charge density, depending on the viscosities and ratio of conductivities of the media, one can observe either an aperiodic (of the Tonks-Frenkel type) or oscillatory instability of the interface. Increasing the viscosity of the lower liquid leads to a substantial drop in the increments of the mentioned instability types and alters the critical conditions for manifestation of the oscillatory instability, whereas varying the viscosity of the upper surface has only a very weak effect on these characteristics. Zh. Tekh. Fiz. 68, 13–19 (September 1998)     

Gravitational Instability of Fluid of Finite Electrical and Thermal Conductivity Flowing through Porous Medium

In view of the importance of porosity in astrophysical context the problem of gravitational instability of fluid of finite electrical and thermal conductivity flowing through porous medium is studied. Equations of the problem are stated and from them linearized perturbation equations are derived. Dispersion relations are obtained and Jeans' criterion of instability is discussed taking properties of the medium in different combinations for parallel and perpendicular directions to the magnetic field. Thermal conductivity modifies the Jeans' expression. Magnetic field and porosity of the medium also modify the Jeans' expression in case of wave propagation in perpendicular direction to the magnetic field but finite electrical conductivity neutralizes the effect of porosity on Jeans' criterion of instability.     

Heat conductivity and Dufour effect in the weakly ionized,magnetized, and kappa-distributed plasma

By using the generalized Boltzmann equation of transport and the first-order approximation of Chapman-Enskog expansion on the κ-distribution function, we study the thermal conductivity and Dufour effect in the weakly ionized and magnetized plasma. We show that the thermal conductivity and Dufour coefficient in the κ-distributed plasma are significantly different from those in the Maxwell-distributed plasma, and the transverse thermal conductivity and Dufour coefficient in the κ-distributed plasma are generally greater than those in the Maxwell-distributed plasma, and the Righi-Leduc coefficient and Hall Dufour coefficient in the κ-distributed plasma are also generally greater than those in the Maxwell-distributed plasma.