Gravitational instability of a Hall plasma in the presence of suspended particles

The gravitational instability of an infinite homogeneous and infinitely conducting selfgravitating gas particle medium in the presence of suspended particles of a Hall plasma is considered. The particular cases of the effects of Hall currents and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. Jeans's criterion determines the gravitational instability.     

Magneto-gravitational instability and suspended particles

The gravitational instability of an infinite homogeneous and infinitely conducting self-gravitating gas-particle medium in the presence of a vertical magnetic field and suspended particles is considered. It is found that in the presence of suspended particles and magnetic field, Jeans' criterion determines the gravitational instability.     

Gravitational instability in the presence of suspended particles and variable magnetic field

The gravitational instability of an infinite homogeneous self-gravitating and infinitely conducting gas-particle medium is considered in the presence of suspended particles and a variable horizontal magnetic field varying in vertical direction. It is found that the Jeans's criterion of instability remains unaffected even if the effects due to suspended particles and variable horizontal magnetic field are included.     

Finite larmor-radius effects on Rayleigh-Taylor instability of a dusty magnetized plasma

This paper discusses the Rayleigh-Taylor (RT) instability of an infinitely conducting medium having an exponential density distribution which includes the effects of finite ion Larmor-radius (FLR) corrections and suspended particles in the presence of a uniform horizontal magnetic field. The relevant equations of the problem are linearized and from the linearized perturbation equations a dispersion relation is obtained, using appropriate boundary conditions. It has been found that the criterion for the stable density stratification remains uninfluenced by the simultaneous inclusion of the FLR corrections and suspended particles. The stability of the medium has been proved for the case of stable stratification when the FLR corrections are not considered in the analysis. The growth rate of unstable RT modes with increasing relaxation frequency of the suspended particles is evaluated analytically. It has been shown that the presence of suspended particles in the medium suppresses the growth rate of the unstable RT modes, thereby implying a stabilizing influence of the particles on the considered configuration.     

Suspended particles and the gravitational instability of a rotating plasma

The gravitational instability of an infinite homogeneous self-gravitating and finitely conducting, rotating gas-particle medium, in the presence of a uniform vertical magnetic field, is studied to include finite Larmor radius and suspended particles effects. The particular cases of the effects of rotation, finite conductivity, finite Larmor radius and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. Jeans's criterion determines the gravitational instability.     

Studies on some properties of coronal mass ejections based on angular width

The paper investigates the effects of thermal conductivity and non-uniform magnetic field on the gravitational instability of a non-uniformly rotating infinitely extending axisymmetric cylinder in a homogeneous heat conducting medium. The non-uniform rotation and magnetic field are supposed to act along θ and z directions of the cylinder. It is found that the gravitational instability of this general problem is determined by the same criterion as obtained by Dhiman and Dadwal (Astrophys. Space Sci. 325(2):195–200, 2010) for the self-gravitating isothermal medium in the presence of non-uniform rotation and magnetic field with the only difference that adiabatic sound velocity is now replaced by the isothermal sound velocity. It is found that the thermal conductivity has stabilizing effect on the onset of gravitational instability. Further, the stabilizing/destabilizing effect of the non-uniform magnetic field on the gravitational instability of heat conducting medium has been discussed and is illustrated by considering some special forms of the basic magnetic fields.     

The gravitational instability of a rotating plasma in the presence of finite Larmor radius,Hall currents and suspended particles

The gravitational instability of an infinite homogeneous self-gravitating and finitely conducting, rotating gas-particle medium, in the presence of finite Larmor radius, Hall currents and suspended particles effects is considered. The particular cases of the effects of rotation, finite conductivity, finite Larmor radius, Hall currents, and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. It is found that Jeans's criterion remains unchanged in the presence of rotation, finite conductivity, finite Larmor radius, Hall currents, and suspended particles.     

Effect of rotation and finite Larmor radius on magneto-gravitational instability of Hall plasma in the presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetized Hall plasma is considered with the inclusion of finite Larmor radius corrections and the effect of suspended particles. A general dispersion relation is obtained from the linearized set of equations. The particular cases of the effect of rotation along and perpendicular to the direction of the magnetic field are considered. The effects of Hall current, finite Larmor radius, and suspended particles on the waves propagated parallel and perpendicular to the uniform magnetic field are investigated along with the uniform rotation of the medium. It is found that in the presence of suspended particles, magnetic field, Hall current, rotation and finite Larmor radius, the Jeans criterion determines the condition of gravitational instability of a gas-particle medium.     

Effect of thermal conductivity on the gravitational instability of a magnetized rotating plasma through a porous medium in the presence of suspended particles

The self-gravitational instability of an ionized, thermally-conducting, magnetized, rotating plasma flow through a porous medium has been studied in the presence of suspended particles. The ionized gas-particle medium has been considered rotating along and perpendicular to the vertical magnetic field. Propagation of the plasma waves has been studied for the longitudinal and the transverse modes for both the cases of rotation. A general dispersion relation has been derived with the help of relevant perturbation equations, using the method of normal mode analysis. The Jeans criterion determines the condition of gravitational instability in all the cases with some modifications introduced by the various parameters considered. Thermal conductivity replaces the adiabatic sonic speed by the isothermal one. Considering the longitudinal mode of propagation with perpendicular rotational axis, for an inviscid plasma with adiabatic behaviour the effect of both, the rotation and the suspended particles has been removed by the magnetic field. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the viscosity removes the effect of both, the rotation and the suspended particles. Porosity reduces the effect of both, the rotation and the magnetic field, whereas the concentration of the suspended particles reduces the rotational effect.     

Magnetogravitational stability of self-gravitating plasma with thermal conduction and finite Larmor radius through porous medium

The problem of incipient fragmentation of interstellar matter to form condensation is investigated taking into account the porosity, viscosity, thermal conductivity, and effect of finite ion-Larmor radius (FLR) on the self-gravitating plasma having a uniform magnetic field acting in vertical direction. Relevant linearized equations are stated and dispersion relation is obtained. Wave propagation in longitudinal and transverse direction to the magnetic field is considered. Stability and instability of the medium is discussed. It is found that if the Jeans's instability condition is not fulfilled the medium must remain stable. Magnetic field, FLR and porosity do not affect the Jeans's criterion of instability in longitudinal direction but in transverse direction, the magnetic field and FLR have stabilizing effect which is reduced due to porosity of the medium. Thermal conductivity destabilizes the medium in both the directions. In transverse direction contribution of FLR on the Jeans's expression for instability is not observed in thermally conducting medium.     

The gravitational instability of flow through porous medium for some systems of astrophysical interest

The gravitational instability of flow through porous medium for some hydrodynamical and hydromagnetical systems of astrophysical interest is investigated. The effects of rotation, magnetic field, viscosity and finite electrical conductivity are studied for the gravitational instability through porous medium. The effect of suspended particles on the instability is also considered. It is found that Jean's criterion remains unchanged in the presence of porosity, viscosity, finite conductivity, rotation, magnetic field and suspended particles in the medium.     

Magnetogravitational instability of a finitely-conducting medium with variable streaming motion

A discussion of gravitational instability of a finitely conducting medium with streams of variable velocity distribution is made in the presence of a uniform magnetic field. It is found that the variable streaming motion shows a destabilizing effect and affects the instability criterion only in the case of general wave propagation. For purely parallel propagation to the direction of the magnetic field and the streaming motion, the criterion is independent of the variation in the streaming motion and further the Jeans's criterion is found to remain unaffected in this case. For purely transverse propagation, the criterion is independent of any streaming motion and the Jeans's criterion remains unaffected. The criterion is further independent of the magnetic field and the finite conductivity except in the case of transverse propagation where the magnetic field exhibits a stabilizing influence in case of an infinitely conducting medium.     

Thermosolutal-convective instability of a stellar atmosphere in the presence of suspended particles

Thermosolutal-convective instability of a stellar atmosphere is considered in the presence of suspended particles. The criteria for monotonic instability are derived which are found to hold good in the presence of uniform rotation and uniform magnetic field, separately, on the thermosolutal-convective instability in the presence of suspended particles.     

Effect of rotation on magnetogravitational instability of finite conducting gas in presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetised gas-particle medium in the presence of suspended particles is investigated. The conductivity of the medium is assumed to be finite. The equations of the problem are linearized and the general dispersion relation is obtained. The rotation is assumed along two different directions separately and separate dispersion relation for each case is obtained. The dispersion relation for propagation parallel and perpendicular to the uniform magnetic field along with rotation is derived. It is found that in presence of suspended particles, magnetic field, finite conductivity, rotation and viscosity, Jeans's criterion determines the condition of gravitational instability of gas-particle medium.     

Thermosolutal-convective instability in a stellar atmosphere

The thermosolutal-convective instability of a stellar atomsphere is studied in the presence of suspended particles. The criteria for monotonic instability are derived and are found to hold good also in the presence of uniform rotation and uniform magnetic field on the thermosolutal-convective instability. The thermosolutal-convective instability of a stellar atmosphere is also studied in the presence of suspended particles and radiative transfer effects and the criteria for monotonic instability are obtained in terms of source function.     

On the Jeans Criterion of a Stratified Heat Conducting Gaseous Medium in the Presence of Non-uniform Rotation and Magnetic Field

The problem of self-gravitational instability of an infinite, homogeneous stratified gaseous medium with finite thermal conductivity and infinite electrical conductivity, in the presence of non-uniform rotation and magnetic field in the Chandrasekhar’s frame of reference, is studied. It is found that the magnetic field, whether uniform or non-uniform, has no effect on the Jeans’ criterion for gravitational instability and remains essentially unaffected. However, the thermal conductivity has the usual stabilizing effect on the criterion that the adiabatic sound velocity occurring in the Jeans criterion is replaced by the isothermal sound velocity. Thus, the present analysis extends the results of Chandrasekhar for the case of heat conducting medium and for non-uniform rotation and magnetic field.     

Gravitational instability for some astrophysical systems

The gravitational instability of an infinite homogeneous self-gravitating mixture through porous medium in the presence of a variable horizontal magnetic field varying in vertical directions has been considered to include, separately, the effects due to suspended particles and collisions between ionized and neutral components. The dispersion relations in both cases have been obtained. It has been found that Jeans's criterion of instability holds good even if the effects due to suspended particles, collisions, porosity, and variable magnetic field are considered.     

Magneto-gravitational instability of a fluid through porous medium including finite ion Larmor radius

The magneto-gravitational instability of an infinite, homogenous, and infinitely conducting plasma flowing through a porous medium is studied. The finite ion Larmor radius (FLR) effects and viscosity are also incorporated in the analysis. The prevalent magnetic field is assumed to be uniform and acting in the vertical direction. A general dispersion relation has been obtained from the relevant linearized perturbation equations of the problem. The wave propagation parallel and perpendicular to the direction of the magnetic field have been discussed. It is found that the condition of the instability is determined by the Jeans criterion for a self-gravitating, infinitely conducting, magnetized fluid through a porous medium. Furthermore, for transverse perturbation FLR is found to have stabilizing influence when the medium is considered inviscid.     

Stability of a compressible fluid cylinder ambient with a bounded conducting medium under general varying magnetic fields

The stability of a compressible fluid cylinder pervaded by a longitudinal uniform magnetic field-ambient with a bounded conducting medium of negligible inertia penetrated with general varying vacuum magnetic fields has been developed. The stability criterion describing the stability characteristics of that model is derived and discussed analytically in general terms. The axial fields have always stabilizing influences. The azimuthal vacuum field has a destabilizing effect, however, it becomes minimal if the perturbed and the unperturbed vacuum fields are not orthogonal. The magnetodynamic instability of the fluid jet is modified in the presence of the fluid compressibility. The stabilizing influence due to the latter may be realized more clearly on utilizing the numerical methods for investigating the eigenvalue relation.Several reported works can be recovered as limiting cases with appropriate simplifications.     

Rayleigh-Taylor instability of magnetized partially-ionized superposed fluids with rotation and surface tension in porous medium

The Rayleigh-Taylor instability of the plane interface separating the two partially-ionized superposed fluids through porous medium is analysed. The effect of variable horizontal magnetic field, surface tension and rotation along the vertical axis are also incorporated. The relevant linearized perturbation equations are taken and using normal mode analysis the general relation is obtained from which the dispersion relation for two superposed fluids of different densities is derived. It is found that the surface tension and horizontal magnetic field have the stabilizing effect on the R-T-instability. The condition of instability remains unaffected by the permeability of porous medium, presence of neutral particles in the fluids and rotation.It is concluded that the system is unstable only for those positive wave numbers which are less than certain critical value in case of an adverse density gradient.