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.     

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.     

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.     

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.     

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.     

On thermal-convective instability in a stellar atmosphere with finite Larmor radius and Hall effects

The thermal-convective instability of a stellar atmosphere is considered to include rotation, finite Larmor radius and Hall effects in the presence of a uniform vertical magnetic field. The criterion for monotonic instability is found to be the same even if the above effects are included.     

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 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.     

Gravitational instability of a rotating plasma

The gravitational instability of an infinite homogeneous self-gravitating rotating plasma in the presence of a uniform vertical magnetic field has been studied to include the FLR effects. It has been found that the Jeans' criterion of instability remains unaffected even if rotation and FLR effects are included. The effect of rotation is to decrease the Larmor radius by an amount-depending upon the wavenumber of perturbation. The particular cases of the effect of FLR and rotation on the waves propagated along and perpendicular to the magnetic field have been discussed.     

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.     

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.     

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.     

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.     

Finite Larmor radius effect on thermal instability of a compressible rotating plasma

Thermal instability of a compressible rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of finiteness of the ion-Larmor radius. When the instability sets in as stationary convection, the compressibility is found to have stabilizing effect. It is found that finite Larmor radius effects are always stabilizing forx greater than two and forx less than two they have a destabilizing influence in the presence of rotation. The stabilizing effect of coriolis force is observed and for the case of no rotation, finite Larmor radius effects are always stabilizing. The sufficient conditions for the nonexistence of overstability are investigated.     

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.     

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.     

Finite larmor radius and hall effects on thermosolutal instability of a rotating plasma

Thermosolutal instability of a rotating plasma with finite Larmor radius and Hall effects is studied. When the instability sets in as stationary convection, the Hall currents and the stable solute gradient are found to have destabilizing and stabilizing effects, respectively. For the case of no rotation, finite Larmor radius effects are always stabilizing forx greater than two and forx less than its critical valueN _cr. In the limit of vanishing Hall current, the stabilizing effect of Coriolis force is observed. The question of onset of instability as overstability is also discussed.     

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.     

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.     

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.