Search

The effect of radiative heat-loss function and finite ion Larmor radius (FLR) corrections on the self-gravitational instability of infinite homogeneous viscous plasma has been investigated incorporating the effects of thermal conductivity and finite electrical resistivity for the formation of a star in astrophysical plasma. The general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. Furthermore the wave propagation along and perpendicular to the direction of external magnetic field has been discussed. Stability of the medium is discussed by applying Routh Hurwitz’s criterion. We find that the presence of radiative heat-loss function and thermal conductivity modify the fundamental Jeans criterion of gravitational instability into radiative instability criterion. From the curves we see that temperature dependent heat-loss function, FLR corrections and viscosity have stabilizing effect, while density dependent heat-loss function has destabilizing effect on the growth rate of self-gravitational instability. Our result shows that the FLR corrections and radiative heat-loss functions affect the star formation.

The Rayleigh–Taylor instability of two superposed incompressible fluids of different densities in the presence of small rotation, surface tension and suspended dust particles is investigated. The linearized equations of the problem are constructed and the general dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The effects of surface tension, the Atwood number, small rotation and suspended dust particles are studied on both conditions of Rayleigh–Taylor instability and growth rate of the unstable Rayleigh–Taylor mode. The numerical calculations have been performed to see the effect of rotation, the Atwood number, relaxation frequency and mass concentration of suspended dust particles. It is found that the growth rate of Rayleigh–Taylor instability depends upon the mass concentration and relaxation frequency of suspended dust particles. The uniform small rotation, relaxation frequency and mass concentration of suspended dust particles all have stabilizing influence on the growth rate of Rayleigh–Taylor instability. It is also found that the Atwood number has destabilizing influence on the growth rate of the considered Rayleigh–Taylor configuration.

The effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

The Rayleigh-Taylor (R-T) instability of two superposed plasmas, consisting of interacting ions and neutrals, in a horizontal magnetic field is investigated. The usual magnetohydrodynamic equations, including the permeability of the medium, are modified for finite Larmor radius (FLR) corrections. From the relevant linearized perturbation equations, using normal mode analysis, the dispersion relation for the two superposed fluids of different densities is derived. This relation shows that the growth rate unstability is reduced due to FLR corrections, rotation and the presence of neutrals. The horizontal magnetic field plays no role in the R-T instability. The R-T instability is discussed for various simplified configurations. It remains unaffected by the permeability of the porous medium, presence of neutral particles and rotation. The effect of different factors on the growth rate of R-T instability is investigated using numerical analysis. Corresponding graphs are plotted for showing the effect of these factors on the growth of the R-T instability.

The thermal instability of an infinite homogeneous, thermally conducting, and rotating plasma, incorporating finite electrical resistivity, finite electron inertia, and an arbitrary radiative heat-loss function in the presence of finite Larmor radius corrections and Hall current, has been studied. Analysis has been made with the help of linearized magnetohydrodynamics (MHD) equations. A general dispersion relation is obtained using the normal mode analysis method, and the dispersion relation is discussed for longitudinal propagation and transverse propagation separately. The dispersion relation has been solved numerically to obtain the dependence of the growth rate on the various parameters involved. The conditions of modified thermal instability and stability are discussed in the different cases of interest.

A linear analysis of the combined influence of a finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be uniform and transverse to the direction of streaming. The medium is assumed to be incompressible. Certain simplifying assumptions are made for the motion of the suspended particles. A dispersion relation for such a medium has been obtained using appropriate boundary conditions. The stabilizing effect of a finite Larmor radius has been reasserted in the absence of the suspended particles. A stability criterion for the medium is derived, which is found to be independent of the presence of the suspended particles. Similarly a condition of instability of the system is also derived. Numerical analysis is presented in a few limiting cases of interest. Furthermore, growth rates of unstable modes of the configuration with increasing relaxation fre­quency of the particles and finite Larmor radius have been evaluated analytically. It is shown that the finite Larmor radius in the presence of the suspended particles destabilizes a certain wave number band which is stable otherwise. Implications of the suspended particles on the growth rate of unstable modes are discussed in the limit of vanishing ion Larmor radius.

The linear Rayleigh Taylor instability of two superposed compressible Newtonian fluids is discussed with the effect of surface tension which can play important roles in space plasma. As in both the superposed Newtonian fluids, the system is stable for potentially stable case and unstable for potentially unstable case in the present problem also. The equations of the problem are solved by normal mode method and a dispersion relation is obtained for such a system. The behaviour of growth rate is examined in the presence of surface tension and it is found that the surface tension has stabilizing influence on the Rayleigh Taylor instability of two superposed compressible fluids. Numerical analysis is performed to show the effect of sound velocity and surface tension on the growth rate of Rayleigh Taylor instability. It is found that both parameters have stabilizing influence on the growth rate of Rayleigh Taylor instability.

The problem of Jeans instability is investigated for a self-gravitating, rotating, radiative plasma with finite Larmor radius corrections, which has connection in astrophysical condensation. A general dispersion relation is derived using normal mode analysis method with the help of relevant linearized perturbation equations of the problem. We find that the classical Jeans result regarding the size of initial break-up is considerably modified due to rotation, finite Larmor radius corrections and radiative heat-loss function. Numerical calculations have been performed to discuss the effect of various physical parameters on the growth rate of the Jeans gravitational instability.

The effect of the magnetic field on the Jeans instability of self-gravitating strongly coupled dusty plasma is investigated. The medium consists of extremely massive, negatively charged strongly correlated dust grains and weakly correlated Boltzmann distributed electrons and ions. The basic equations of the problem are constructed using generalized hydrodynamic model. In deriving dispersion relation the plane wave solutions are used on the linearized perturbation equations. The analysis is done by normal mode analysis theory. The dispersion relation is found to be affected due to the presence of viscoelastic effects and magnetic field. The dispersion relation is further reduced for hydrodynamic and kinetic regime of propagation. The condition of Jeans instability is also obtained for both the regimes of propagation. Numerical results are presented to show the effect of magnetic field and time relaxation parameter which is found to have stabilizing influence on growth rate of Jeans instability in strongly coupled dusty plasma. The condition of Jeans instability are compared in kinetic and hydrodynamic regime.

In the present work, the self-gravitational instability of quantum plasma is investigated including the effects of finite Larmor radius corrections (FLR) and rotation. The formulation is done employing quantum magnetohydrodynamic (QMHD) model. The plane wave solutions are employed on the linearized perturbed QMHD set of equations to obtain the general dispersion relation. The rotation is assumed only along the z- direction. The general dispersion relation is further reduced for transverse and longitudinal directions of propagation. It is found that in transverse direction of propagation the Jeans criterion is modified due to the rotation, FLR and quantum corrections while in longitudinal direction of propagation it is observed that the Jeans criterion is modified by quantum corrections only. The growth rate of perturbation is discussed numerically including the considered parameters FLR and quantum corrections. The growth rate is observed to be modified significantly due to the quantum correction and FLR effects.

The problem of thermal instability and gravitational instability is investigated for a partially ionized self-gravitating plasma which has connection in astrophysical condensations. We use normal mode analysis method in this problem. The general dispersion relation is derived using linearized perturbation equations of the problem. Effects of collisions with neutrals, radiative heat-loss function, viscosity, thermal conductivity and magnetic field strength, on the instability of the system are discussed. The conditions of instability are derived for a temperature-dependent and density-dependent heat-loss function with thermal conductivity. Numerical calculations have been performed to discuss the effect of various physical parameters on the growth rate of the gravitational instability. The temperature-dependent heat-loss function, thermal conductivity, viscosity, magnetic field and neutral collision have stabilizing effect, while density-dependent heat-loss function has a destabilizing effect on the growth rate of the gravitational instability. With the help of Routh-Hurwitz's criterion, the stability of the system is discussed.

The effect of radiative heat-loss function and finite ion Larmor radius (FLR) corrections on the gravitational instability of infinite homogeneous viscous plasma has been investigated incorporating the effects of thermal conductivity and finite electrical resistivity. We find that radiative heat-loss function and thermal conductivity modify the Jeans criterion into radiative instability criterion. Numerical calculations have been performed to show the effect of various parameters on the growth of the gravitational instability.

The effect of two dimensional magnetic field on the Rayleigh-Taylor (R-T) instability in an incompressible plasma is investigated to include simultaneously the effects of suspended particles and the porosity of the medium. The relevant linearized perturbation equations have been solved. The explicit expression of the linear growth rate is obtained in the presence of fixed boundary conditions. A stability criterion for the medium is derived and discussed the Rayleigh Taylor instabilities in different configurations. It is found that the basic Rayleigh-Taylor instability condition is modified by the presence of magnetic field, suspended particles and porosity of the medium. In case of an unstable R-T configuration, the magnetic field has a stabilizing effect on the system. It is also found that the growth rate of an unstable R-T mode decreases with increasing relaxation frequency thereby showing a stabilizing influence on the R-T configuration.

We investigate the Jeans instability of self-gravitating magnetized strongly coupled plasma. The equations of the problem are formulated using the generalized hydrodynamic model and a general dispersion relation is obtained using the normal mode analysis. This dispersion relation is discussed for transverse and longitudinal mode of propagations. The modified condition of Jeans instability is obtained for magnetized strongly coupled plasma. We find that strong coupling of plasma particles modify the fundamental criterion of Jeans gravitational instability. In transverse mode it is found that Jeans instability criterion gets modified due to the presence of magnetic field, shear viscosity and fluid viscosity but in longitudinal mode it is unaffected due to the presence of magnetic field. From the curves we found that all these parameters have stabilizing influence on the growth rate of Jeans instability.

We investigate the linear Kelvin-Helmholtz (K-H) instability of two streaming magnetized plasmas considering the effects of surface tension and suspended dust particles. The usual magnetohydrodynamic (MHD) equations are considered for the present configuration including the effects of suspended dust particles and surface tension. The general dispersion relation is obtained using the normal mode analysis by applying the appropriate boundary conditions. The dispersion relation is modified due to the presence of surface tension, magnetic field and suspended dust particles for three-dimensional perturbations. It is found that the effect of magnetic field appears in the dispersion relation due to consideration of three- dimensional perturbations of the present problem of K-H instability with suspended dust particles and surface tension. It is also found that the condition of K-H instability is affected by the presence of suspended dust particles, surface tension and magnetic field. Numerical calculations have been performed to show the effect of magnetic field, mass concentration and relaxation frequency of suspended dust particles on the growth rate of K-H instability. It is found that magnetic field, mass concentration and relaxation frequency of suspended dust particles have stabilizing influence on the growth rate of K-H instability.

The gravitational instability of two-component plasma is discussed to investigate the effect of the radiative heat-loss function, thermal conductivity, collision frequency of neutrals, finite electrical resistivity and viscosity of the medium on the Jeans instability. The usual Magnetohydrodynamics (MHD) equations are used for the present configuration with radiative heat-loss function and thermal conductivity. A general dispersion relation is obtained from perturbation equations using the normal mode analysis method. We find that the Jeans condition of self-gravitational instability is modified due to the presence of radiative heat-loss function and thermal conductivity. Numerical calculations have been performed to show the effect of the various parameters on the growth rate of the self-gravitational instability.

The hydromagnetric Rayleigh-Taylor instability of a composite medium has been studied in the presence of suspended particles for an exponentially varying density distribution. The prevalent horizontal magnetic field and viscosity of the medium are assumed to be variable. The dispersion relation is derived for such a medium. It is found that the stability criterion is independent of both viscosity and suspended particles. The system can be stabilized for an appropriate value of the magnetic field. It is found that the suspended particles can suppress as well as enhance the growth rate of the instability in certain regions. The growth rates are obtained for a viscid medium with the inclusion of suspended particles and without it. It has been shown analytically that the growth rate is modified by the inclusion of the relaxation frequency parameter of the suspended particles.

The Rayleigh-Taylor (RT) instability of a stratified and viscid magnetoplasma including the effects of "finite-resistivity and suspended particles is investigated using normal mode analysis. The horizontal magnetic field and the viscosity of the medium are assumed to be variable. The dispersion relation, which is obtained for the general case on employing boundary conditions appropriate to the case of two free boundaries, is then specialized for the longitudinal and transverse modes. It is found that the criterion of stable stratification remains essentially unchanged and that the unstable stratification for the longitudinal mode can be stabilized for a certain wave number band, whereas the transverse mode remains unstable or all wave numbers which can be stabilized by a suitable choice of the magnetic field for vanishing resistivity. Thus, resistivity is found to have a destabilizing influence on the RT configuration. The growth rates of the unstable RT modes with the kinematic viscosity and the relaxation frequency parameter of the suspended particles have been analytically evaluated. Dust (suspended particles) tends to stabilize the configuration when the medium is considered viscid with infinite conductivity. The kinematic viscosity has a stabilizing influence on the ideal plasma modes.

The self gravitational instability of an infinite homogeneous magnetized gas-particle medium in the presence of suspended particles is investigated. The conductivity of the medium is assumed to be finite. The dispersion relation is obtained for such a medium. It is found that in the presence of suspended particles a sufficient condition of instability is obtained by Jeans’ criterion for a self gravitating magnetized conducting gas-particle medium.

The effect of Hall current, finite conductivity, and rotation on magnetogravitational instability of a medium in the presence of suspended particles using a linear analysis of magnetohydrodynamic equations is investigated. Separate dispersion relations are obtained for rotation along and perpendicular to the direction of magnetic field considering the propagation of modes parallel and perpendicular to magnetic field. The instability of the system is discussed separately for each case. It is found that, in the presence of suspended particles, magnetic field, finite conductivity, Hall current, and rotation, Jeans's criterion determines the condition of instability of the gas particle medium. The effect of presence of suspended particles in the self-gravitating medium is also investigated.