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.     

Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the presence of a two-dimensional horizontal uniform magnetic field. The streaming motion is also assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluids of uniform densities. It is found that the streaming motion has dual influence on the unstable system, destabilizing for low values of streaming velocity and stabilizing for high values of streaming velocity. The effect of viscosity is, however, found to be stabilizing as the growth rate of the unstable configuration decreases on increasing the viscosity.     

Larmor radius effects on the instability of a stratified partially-ionized plasma in the presence of Hall currents and magnetic resistivity

Instability of a stratified layer of a partially-ionized plasma has been investigated in the simultaneous presence of the effects of Hall currents, magnetic resistivity, finite Larmor radius (FLR), and viscosity. The ambient magnetic field is assumed to be uniform and acting along the vertical direction. The solution is shown to be characterized by a variational principle, based on it the solution has been obtained for a plasma in which the density is stratified exponentially along the vertical. It is found that the viscosity, friction with neutrals, and FLR have all stabilizing influence on the growth rate of the unstable mode of disturbance. Magnetic resistivity and Hall currents are, however, found to have a destabilizing influence.     

Finite Larmor radius effects on the Rayleigh-Taylor instability of a rotating plasma of variable density

The Rayleigh-Taylor instability in a rotating plasma of variable density has been investigated to include simultaneously the effects of viscosity and the finiteness of the ion Larmor radius. It is shown that, for a plasma in which the density is stratified along the vertical, the solution is characterized by a variational principle. Making use of this, proper solutions have been otained for a semiinfinite plasma in which the density varies exponentially. The dispersion relation has been solved numerically and it is found that the influence of the effects of both FLR and viscosity is stabilizing. The Coriolis forces are found to have a dual role, stabilizing for small wave numbers and destabilizing for large wave numbers. The range of the small wave numbers, over which the Coriolis forces have a stabilizing influence, is found to increase with Coriolis forces.     

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.     

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.     

Instability of rotating isotropic and anisotropic plasmas

The instability in a horizontal layer of stratified compressible isotropic and anisotropic plasmas has been studied to include simultaneously the effects of Coriolis forces and the finiteness of the ion Larmor radius. Using an integral approach, the dispersion relation has been derived in both cases for plasmas having density stratified exponentially along the vertical. The dispersion, relation has been solved numerically and it is found that both the FLR and Coriolis forces have stabilizing influence on the instability in the isotropic plasmas. The same result is obtained for the case of anisotropic plasmas where also the dispersion relation has been evaluated numerically.     

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 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.     

Finite Larmor radius effects on the stability of a stratified plasma

The hydromagnetic stability of a cosmical plasma interacting with neutral gas has been studied to include the effects of ion viscosity and the finiteness of the ion Larmor radius. It is first shown that the system is characterized by a variational principle. The explicit solution has then been obtained, by making use of the existence of the variational principle, for a semi-infinite plasma in which the density is stratified, exponentially, along the vertical. It is found that FLR, ion viscosity as well as neutral gas friction have all a stabilizing influence.     

The Rayleigh Taylor instability of superposed partially-ionized plasmas

The Rayleigh-Taylor instability of the plane interface separating two superposed, partiallyionized, viscous plasmas of different densities has been studied to include the effects of finite Larmor radius. The solution of the relevant linearized perturbation equations has been developed by the Normal mode technique, taking the prevalent magnetic field to be uniform and horizontal. The potentially unstable case of a dense fluid superimposed on a lighter one has been considered. It is found that neutral gas friction, viscosity as well as finite Larmor radius all have stabilizing influence.On leave of absence from Department of Mathematics, University of Jodhpur, India.     

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.     

Instability of partially-ionized superposed plasmas

The stability of the plane interface separating two viscous superposed partially-ionized plasmas of uniform densities has been studied. The whole system is assumed to be immersed in a uniform two-dimensional horizontal magnetic field and the stability analysis has been carried out through the normal mode technique. The dispersion relation has been derived for the case of two superposed plasmas of equal kinematic viscosities. The dispersion relation has been solved numerically for different values of the physical parameters involved. It is found that viscosity and collision frequency of ionized plasmas both have stabilizing influence on the growth rate of the unstable mode of disturbance.     

Rayleigh-Taylor instability of ionized viscous fluids with FLR-corrections and surface-tension

The problem of Rayleigh-Taylor instability of superposed viscous magnetized fluids through porous medium is investigated in a partially-ionized medium. The fluid has ionized and neutralized particle components interacting with collisions. The effect of surface tension on R-T instability is also included in the present problem. The magnetohydrodynamic equations are modified for finite-Larmor radius corrections which is in the form of tensor. The equations of problem are linearized and using appropriate boundary condition, general dispersion relation is derived for two superposed fluids separated by horizontal boundary. The first part of the dispersion relation gives stable mode and condition is investigated using Hurwitz conditions. The second part of the dispersion relation shows that the growth rate of unstable system is reduced due to FLR corrections, viscosity, and collisional frequency of the neutrals. The role of surface tension on the system is also discussed.     

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.     

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.     

Rayleigh-Taylor instability of a viscous compressible plasma of variable density

A study has been made of the problem of the Rayleigh-Taylor instability of a hydromagnetic plasma of varying density to investigate the influence of the simultaneous presence of the effects of compressibility and viscosity. The solution is shown to be characterized by a variational principle. Based on the variational principle proper solutions have been obtained for a semi-infinite plasma, in which the density has a one-dimensional gradient along the direction of a uniform vertical magnetic field, confined between two planes. Both the viscosity and magnetic field are found to have a stabilizing influence. The effect of compressibility is found to be destabilizing.     

Effect of quantum corrections on the Jeans instability of self-gravitating viscoelastic dusty fluid

In this paper we investigate the effects of quantum correction on the Jeans instability of self-gravitating viscoelastic dusty electron-ion quantum fluids. The massive self-gravitating dust grains are assumed to be strongly coupled and non-degenerate having both viscous and elastic behavior while the inertialess electrons and ions are considered as weakly coupled and Fermi degenerate. The hydrodynamic model is modified and a linear dispersion relation is derived employing the plane wave solutions on the linearized perturbation equations for the considered system. It is observed that the dispersion properties are affected due to the presence of viscoelastic effects and quantum statistical corrections. The modified condition of Jeans instability and expression of critical Jeans wavenumber are obtained. Numerically it is shown that viscoelastic effects, dust plasma frequency and quantum statistical effects all have stabilizing influence on the growth rate of gravitationally Jeans mode. The growth rates are also compared in kinetic and hydrodynamic limits and it is found that decay in the growth of unstable Jeans mode is larger under the kinetic limits than the hydrodynamic limits. The results are discussed for the understanding of formation of dense degenerate dwarf star through gravitational collapsing which is assumed to be strongly coupled dusty quantum fluid where the strongly coupled dust provides inertia and Fermi degenerate electron and ions provide quantum statistical effects.     

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.     

Effects of gyroviscosity and hall currents on the stability of a stratified rotating self-gravitating plasma

Instability in a horizontal layer of a stratified rotating self-gravitating plasma is studied to include simultaneously the effects of Hall currents and the finiteness of the ion Larmor radius. 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 the unstable perturbations decreases with both coriolis forces and gyroviscous effects. The influence of the effects of gyroviscosity as well as of Coriolis forces is consequently stabilizing. Hall currents are found to have a destabilizing influence as the growth rate is found to increase with this effect.