Magneto-gravitational instability of a rotating and finitely-conducting fluid

The gravitational instability of an infinite homogeneous finitely conducting viscid fluid through porous medium is studied in the presence of a uniform vertical magnetic field and finite ion Larmor radius (FLR) effects. The medium is considered uniformly rotating along and perpendicular to the direction of the prevalent magnetic field. A general dispersion relation is obtained from the relevant linearized perturbation equations of the problem. Furthermore, the wave propagation along and perpendicular to the direction of existing magnetic field has been discussed for each direction of the rotation. It is found that the simultaneous presence of viscosity finite conductivity, rotation, medium porosity, and FLR corrections does not essentially change the Jeans's instability condition. The stabilizing influence of FLR in the case of transverse propagation is reasserted for a non-rotating and inviscid porous medium. It is shown that the finite conductivity has destabilizing influence on the transverse wave propagation whereas for longitudinal propagation finite conductivity does not affect the Jean's criterion.     

Larmor radius effects on the instability of a rotating layer of a self-gravitating plasma

The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.     

Gravitational instability of a thermally-conducting plasma flowing through a porous medium in the presence of suspended particles

Magnetogravitational instability of a thermally-conducting, rotating plasma flowing through a porous medium with finite conductivity and finite Larmor radius in the presence of suspended particles has been investigated. The wave propagation has been considered for both parallel and perpendicular axes of rotation. Magnetic field is being taken in the vertical direction. A general dispersion relation has been derived through relevant linearized perturbation equations. It has been observed that the condition of instability is determined by the Jeans's criterion in its modifed form. Thermal conductivity replaces the adiabatic velocity of sound by the isothermal one. Rotation decreases the Larmor radius. Porosity decreases the Alfvén velocity. In case of a viscous medium the effects of FLR, rotation, and suspended particles are not observed in the Jeans's condition, for transverse propagation for rotational axis parallel to the magnetic field. The effects of rotation and FLR are decreased by the porosity and the suspended particles. Finite conductivity removes the Alfvén velocity from Jeans's condition.     

Effect of Hall Current and Finite Larmor Radius Corrections on Thermal Instability of Radiative Plasma for Star Formation in Interstellar Medium (ISM)

The effects of finite ion Larmor radius (FLR) corrections, Hall current and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effects of finite electrical resistivity, thermal conductivity and permeability for star formation in interstellar medium have been investigated. A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instability criterion gets modified into radiative instability criterion. The finite electrical resistivity removes the effect of magnetic field and the viscosity of the medium removes the effect of FLR from the condition of radiative instability. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. Numerical calculation shows stabilizing effect of viscosity, heat-loss function and FLR corrections, and destabilizing effect of finite resistivity and permeability on the thermal instability. The outcome of the problem discussed the formation of star in the interstellar medium.     

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.     

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.     

Kelvin-Helmholtz instability of two viscous superposed rotating and conducting fluids

Kelvin-Helmholtz instability of the interface separating two viscous rotating-conducting fluids has been studied in the presence of finite ion-Larmor radius (FLR) effects. Emloying the normal mode technique, the solutions have been obtained when the fluids are assumed to be permeated by a uniform horizontal magnetic field. For the case of two highly viscous fluids, the dispersion relation has been derived and solved numerically. It is found that the streaming velocity has a stabilizing influence on the potentially unstable arrangement of the fluids. The viscosity and FLR effects are also found to have a stabilizing influence while the Coriolis forces have a destabilizing influence on the system.     

On thermosolutal-convective instability in a stellar atmosphere

Thermosolutal-convective instability of a stellar atmosphere in the presence of a stable solute gradient is considered to include the effects, separately, due to finite Larmor radius (FLR) and Hall currents in the presence of a uniform horizontal magnetic field. The criteria derived for monotonic instability are found to hold true in the presence of FLR and Hall effects.     

Thermosolutal-convective instability of a composite plasma in a stellar atmosphere including the effects of finite larmor radius and Hall currents

Thermosolutal-convective instability of a composite plasma in a stellar atmosphere is considered to include the effects, separately, due to finite Larmor radius (FLR) and Hall currents in the presence of a uniform horizontal magnetic field. The sufficient conditions for the existence of monotonic instability are derived and are found to hold good both in the presence, separately, of FLR and Hall current effects.     

Effect of self-gravitation or finite ion mass on the stability of anisotropic plasma

The problem of stability of an unbounded anisotropic plasma characterized by different temperatures along and transverse to the magnetic field is investigated for an arbitrary direction of propagation. Chewet al (1956) equations modified to incorporate self-gravitation, finite ion Larmor radius (FLR) and Hall current are used. Uniform rotation (of an order of interest in astrophysics) is also considered. Extensive numerical treatment of the dispersion relation leads to several interesting results.Inclusion of FLR, or Hall current or both together introduces pulsational instability for prepagation parallel to the magnetic field. The aperiodic growth rate of the mirror instability is only slightly altered due to FLR or Hall current effects. In the absence of rotation, self-gravitation, FLR and Hall current, the growth rate decreases for the mirror region as the direction of propagation approaches the field direction, while the fire hose instability persists for arbitrary propagation, even in the limiting case (the mirror limit) where the propagation is nearly transverse to the magnetic field. Uniform rotation altogether stabilizes the fire hose instability for a sufficiently strong pressure (or temperature) anisotropy. Pulsational instability is introduced when both ratation and self-gravitation effects are present. Either FLR or Hall current depresses the growth rate of the fire hose instability and introduces pulsational instability for the general case of arbitrary propagation. When FLR and Hall current effects are present simultaneously, the interaction terms due to these effects may be strongly destabilizing in nature for arbitrary propagation.     

Gravitational instability of a rotating partially-ionized plasma carrying a uniform magnetic field with hall effect

The problem of gravitational instability of an infinite homogeneous self-gravitating medium carrying a uniform magnetic field in the presence of Hall effect has been investigated to include the effect due to rotation. The dispersion relation has been obtained. It has been found that the Jeans's criterion for the instability remains unaffected even when the effect due to rotation is considered in the presence of Hall effect carrying a uniform magnetic.     

Magnetogravitational instability of an infinite homogeneous rotating plasma through a porous medium with finite electrical and thermal conductivities

The gravitational instability of an infinite homogenous rotating plasma through a porous medium in the presence of a uniform magnetic field with finite electrical and thermal conductivities has been studied. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained, which is further reduced for the special cases of rotation, parallel and perpendicular to the megnetic field acting in the vertical direction. Longitudinal and transverse modes of propagation are discussed separately. It is found that the joint effect of various parameters is simply to modify the Jeans's condition of instability. The effect of finite electrical conductivity is to remove the effect of magnetic field where as the effect of thermal conductivity is to replace the adiabatic velocity of sound by the isothermal one. Rotation has its effect only along the magnetic field in the transverse mode of propagation for an inviscid plasma, thereby stabilizing the system. Porosity reduces the effect of both, the magnetic field and the rotation, in the transverse mode of propagation in both the cases of rotation. The effect of viscosity is to remove the rotational effects parallel to the magnetic field in the transverse mode of propagation.     

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.     

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.     

Gravitational instability of a non-linear magnetic fluid

The problem of gravitational instability of an infinite homogenous fluid has been considered in the presence of a non-vertical magnetic field. A non-linear relation between the magnetic field and the magnetic induction proposed by P.H. Roberts (1981) in the context of neutron stars has been used. The dispersion relations have been obtained. It has been found that Jeans's criterion for instability is unaffected by this non-linear relationship even if the effect due to rotation is considered in the presence of a non-vertical magnetic field.     

Infrared spectra of carbonaceous chondrites and the composition of intertellar grains

Gravitational instability of an infinitely conducting hydromagnetic composite rotating plasma is considered to include simultaneously the finite Larmor radius effects and the frictional effects with neutrals. It is found that Jeans' criterion of instability holds good in the presence of rotation, finite Larmor radius and collisions with neutrals. The particular cases of the above effects on the waves propagated along and perpendicular to the magnetic field have been discussed. The effect of rotation is to decrease the Larmor radius by an amount depending upon the wave number of perturbation.     

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.     

On thermosolutal-convective instability in a stellar atmosphere

Thermosolutal-convective instability of a stellar atmosphere is considered. The criteria for monotonic instability are derived. The effects of a variable horizontal magnetic field and the simultaneous presence of a uniform rotation and a uniform horizontal magnetic field have been considered on the thermosolutal-convective instability. The criteria derived for monotonic instability are found to hold good in the presence of a variable horizontal magnetic field as well as in the presence of a uniform rotation and a uniform horizontal magnetic field.     

Self-gravitational instability of rotating viscous Hall plasma with arbitrary radiative heat-loss functions and electron inertia

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 heat-loss 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 density-dependent 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 heat-loss functions is also studied on the growth rate of a radiative instability.     

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.