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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.

The linear self-gravitational instability of finitely conducting, magnetized viscoelastic fluid is investigated using the modified generalized hydrodynamic (GH) model. A general dispersion relation is obtained with the help of linearized perturbation equations using the normal mode analysis and it is discussed for longitudinal and transverse modes of propagation. In longitudinal propagation, we find that Alfven mode is uncoupled with the gravitating mode. The Jeans criterion of instability is determined which depends upon shear viscosity and bulk viscosity while it is independent of magnetic field. The viscoelastic effects modify the fundamental Jeans criterion of gravitational instability. In transverse mode of propagation, the Alfven mode couples with the acoustic mode, compressional viscoelastic mode and gravitating mode. The growth rate of Jeans instability is compared in weakly coupled plasma (WCP) and strongly coupled plasma (SCP) which is larger for SCP in both the modes of propagations. The presence of finite electrical resistivity removes the effect of magnetic field in the condition of Jeans instability and expression of critical Jeans wavenumber. It is found that Mach number and shear viscosity has stabilizing while finite electrical resistivity has destabilizing influence on the growth rate of Jeans instability.

The problem of Jeans gravitational instability and radiative instability is investigated for partially ionized self-gravitating plasma which has connection in astrophysical condensations and formation of objects. A general dispersion relation has been derived with the help of relevant linearized perturbation equations, using the normal mode analysis method. Effects of FLR corrections, radiative heat-loss function and collisions with neutrals on the Jeans criterion of self-gravitational 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 and FLR corrections for some special case. The stability of the system is discussed by using Routh-Hurwitz’s criterion. Numerical calculations have been performed to discuss the dependence of the growth rate of the Jeans gravitational instability on the various physical parameters. The FLR corrections, viscosity, porosity, magnetic field, and neutral collision have stabilizing influence while finite electrical resistivity and permeability have a destabilizing influence on the growth rate of the gravitational instability. Our results are helpful for understanding the formation of dense molecular clouds.

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 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.

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.

In the present paper the Rayleigh Taylor instability of two superposed conducting incompressible viscous fluids including the effect of finite Larmor radius and rotation has been investigated. The relevant MHD equations are solved by using normal mode method and a general dispersion relation is derived with the help of appropriate boundary conditions for the considered medium. The general dispersion relation of the medium is discussed for the stable and unstable configuration of Rayleigh Taylor instability. The growth rate of Rayleigh Taylor instability is analysed in the presence of finite Larmor radius and rotation and their influence are studied on the Rayleigh Taylor instability.

The Jeans self-gravitational instability is studied for dense quantum viscous plasma with Hall term and intrinsic magnetization generated by collective electron spin. The quantum magnetohydrodynamic model is employed to formulate the basic equations of the problem. The dispersion relation is obtained using the normal mode analysis, and further reduced for both transverse and longitudinal modes of propagation. The transverse mode of propagation is found to be unaffected by the Hall term but affected by quantum effect, viscosity, and magnetization parameters. The Jeans criterion of instability in the transverse direction is modified by Alfven velocity, magnetization parameter, and quantum effect. The non-gravitating magnetized mode is obtained in the longitudinal direction, which is modified by Hall parameter and is not affected by quantum term, whereas the gravitational mode is unaffected by the magnetization parameter but affected by viscosity and quantum parameters. It is observed that the Jeans condition of instability is affected by the quantum term. The growth rate of Jeans instability is plotted for various values of magnetization, quantum, and viscosity parameters of the quantum plasma medium.

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 gravitational instability of an infinite homogeneous, finitely conducting, rotating, collisionless, anisotropic-pressure plasma in the presence of a uniform magnetic field with finite-ion-Larmor-radius (FLR) corrections and generalized polytropic laws is investigated. The polytropic laws are considered for the pressure components in directions parallel and perpendicular to the magnetic field. The method of normal-mode analysis is applied to derive the dispersion relation. Wave propagation is considered for both parallel and perpendicular axes of rotation. Longitudinal and transverse modes of propagation are discussed separately. The effects of rotation, finite electrical resistivity, FLR corrections and polytropic indices on the gravitational, firehose and mirror instabilities are discussed. The stability of the system is discussed by applying the Routh–Hurwitz criterion. Extensive numerical treatment of the dispersion relation leads to several interesting results. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, it is observed that rotation stabilizes the system by decreasing the critical Jeans wavenumber. It is also seen that the region of instability and the value of the critical Jeans wavenumber are larger for the Chew–Goldberger–Low (CGL) set of equations in comparison with the magnetohydrodynamic (MHD) set of equations. It is found that the effect of FLR corrections is significant only in the low-wavelength range, and produces a stabilizing influence. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the finite electrical resistivity removes the polytropic index [nu] from the condition for instability. The inclusion of rotation alone or FLR corrections alone or both together does not affect the condition for mirror instability. The growth rate of the mirror instability is modified owing to uniform rotation or FLR corrections or both together. We note that the condition of mirror instability depends upon the polytropic indices. We also note that neither the mirror instability nor the firehose instability can be observed for the isotropic MHD set of equations.

The Kelvin–Helmholtz (K–H) instability of two fluids of plasma streaming in opposite directions with the same velocity and in the presence of an external magnetic field is investigated. The usual magnetohydrodynamic equations with anisotropic pressure are considered. In the present problem, the two pressures parallel and perpendicular to the direction of the magnetic field are defined by polytropic pressure laws. The generalized pressure relations are used, and two equations of state for two pressures are assumed. The equations are linearized, and initially two different flow velocities are taken for the system. The flow is assumed to be in the direction perpendicular to the magnetic field. The problem is solved and a dispersion relation is obtained. From the dispersion relation, the K–H instability condition is obtained. It is found that the instability condition depends upon the polytropic indices of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low systems. It is also found that the growth rate of the instability depends upon various polytropic indices.

The study of the Rayleigh–Taylor (RT) instability of two superposed conducting fluids acted upon by a uniform horizontal magnetic field is discussed. The usual magnetohydrodynamic (MHD) equations, with modifications to include the effect of finite Larmor radius corrections (FLR) and rotation, are taken for the description of the problem. The fluid is assumed to be dusty, and dust in the form of suspended particles is considered. The equations of the problem are linearized, and using necessary boundary conditions, a general dispersion relation for the RT instability of two superposed plasma is obtained. The dispersion relation shows no contribution of the magnetic field on the condition of the RT instability. It is also found that rotation, FLR, and suspended particles do not affect the condition of the RT instability. The different special cases are discussed to find the effect of different parameters on the growth and condition of the RT instability.

The Kelvin–Helmholtz (K-H) instability of two fluids of a plasma, streaming in opposite directions with the same velocity and in the presence of an external magnetic field, is investigated. The external magnetic field in both fluids are in different directions. The usual magnetohydrodynamic (MHD) equations with anisotropic pressures are considered. The generalized pressure relation is used and two equations of state for two pressures are taken up in the problem. The equations are linearized and initially two different flow velocities are taken for the system. The problem is solved and a dispersion relation is obtained. It is found that the instability condition for the static configuration depends on the polytropic index of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low (CGL) systems. For the nonstatic streaming configuration it is also found that growth rate of K-H instability depends on various polytropic indices and magnetic field.

The Jeans instability of partially ionized self gravitating plasma is discussed to investigate the effect of the Hall current, radiative heat-loss function, thermal conductivity, collision frequency of neutrals, porosity, finite electrical resistivity and viscosity for the formation of stars in HI and HII regions. The standard Magnetohydrodynamics (MHD) set of equations is 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 neutral particle, radiative heat-loss functions and thermal conductivity. Presence of Hall current, porosity and collision frequency have no effect on Jeans criterion.

We investigate the effect of different dust flow velocities and two dimensional magnetic fields on the combined Kelvin-Helmholtz instability (KHI) and Rayleigh-Taylor instability (RTI) of two superimposed incompressible dusty fluids. A single fluid reduced dusty magnetohydrodynamic model is obtained for the three component magnetized incompressible dusty plasma, and it is assumed that a plane interface of infinite boundaries separates heavy and light dusty fluids at z = 0. The general dispersion relations for RT and KH configurations are obtained using appropriate boundary conditions and discussed in the case of equal and different dust fluid flow velocities. In the case of the stable RT configuration, we find that the condition of RTI depends upon both longitudinal and transverse magnetic field components and relative dust flow velocity. In the case of the KH configuration, the effect of magnetic field and relative dust flow velocity is observed and it is shown that dust flow velocity must be larger than...

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.

The influence of dust-neutral collisions, polarization force, and electron radiative condensation is analysed on the Jeans (gravitational) instability of partially ionized strongly coupled dusty plasma (SCDP) using linear perturbation (normal mode) analysis. The Boltzmann distributed ions, dynamics of inertialess electrons, charged dust and neutral particles are considered. Using the plane wave solutions, a general dispersion relation is derived which is modified due to the presence of dust-neutral collisions, strong coupling effect, polarization force, electron radiative condensation, and Jeans dust/neutral frequencies. In the long wavelength perturbations, the Jeans instability criterion depends upon strong coupling effect, polarization interaction parameter, and thermal loss, but it is independent of dust-neutral collision frequency. The stability of the considered configuration is analysed using the Routh–Hurwitz criterion. The growth rates of Jeans instability are illustrated, and stabilizing influence of viscoelasticity and dust-neutral collision frequency while destabilizing effect of electron radiative condensation, polarization force, and Jeans dust-neutral frequency ratio is observed. This work is applied to understand the gravitational collapse of SCDP with dust-neutral collisions.

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 effect of finite ion Larmor radius corrections on the propagation of small perturbations through self gravitating, anisotropic system with generalized polytrope law is investigated. The polytrope laws are considered for the pressure components in parallel and perpendicular directions to the magnetic field. The polytrope model proposed by Abraham-Shranuer can be reduced to CGL equations with double adiabatic equations of state and MHD set of equations with isothermal equation of state. The effects of FLR and polytrope indices are discussed on the gravitational, firehose and mirror instability. The critical Jeans wave numbers are found to depend on polytropic indices and derived for CGL and MHD cases. The FLR corrections are found effective in shorter wave length region and produce stabilizing influence. The condition of mirror instability is uninfluenced by FLR but dependent on polytropic indices.

The gravitational instability of infinite homogeneous magnetized dusty plasma with radiative process is studied with the help of relevant dusty magnetohydrodynamic (MHD) equations using normal mode analysis. The dispersion relation is obtained with radiative pressure and magnetic field, which is discussed for the transverse and longitudinal mode of propagations. The improvement in the Jeans condition of instability due to dust, magnetic field and radiative pressure is discussed. We find that in transverse mode of propagation the condition of Jeans instability of dusty plasma is modified by magnetic field and radiative pressure. In case of longitudinal mode it is unaffected by magnetic field as this mode provides the Alfven mode separately with the gravitational mode.

We investigate the Jeans instability of self‐gravitating magnetized dusty plasma including the effect of polarization force on the massive charged dust grains. The basic dusty magnetohydrodynamic (MHD) equations are constructed considering the effect of magnetic field, gravitational force and polarization force. A general dispersion relation and condition of Jeans instability is obtained using normal mode analysis. It is found that polarization force modifies the condition of Jeans instability but it is unaffected due to magnetic field. The polarization force has destabilizing while magnetic field has stabilizing influence on the growth rate of Jeans instability.

Kelvin-Helmholtz instability of two superimposed fluids has been studied. One of the fluids is non-conducting and the other is conducting with finite resistivity. The fluids are assumed rotating and slipping past each other with a relative velocity. The neutral particles are also incorporated in one of the fluids of the system. A general dispersion relation has been derived and discussed under different conditions. The effect of rotation and the neutral particles, considering an infinitely-conducting system has also been analyzed and it is observed that small rotation and the presence of neutral particles destabilize the system. The effect of neutral particles is to decrease the effect of magnetic field, angular velocity, and the gravitational field. It has been found that an otherwise stable mode becomes overstable and grows exponentially in the presence of finite resistivity.

The hydromagnetic K-H instability of two (one finitely conducting and another non-conducting) super-imposed fluids slipping past each other, with a relative velocity, in the presence of neutral particles for density discontinuity has been analyzed. The magnetic field is taken oblique to the interface. A general dispersion relation has been derived through proper boundary conditions. The general condition is discussed separately for the horizontal (parallel and perpendicular to the streaming) and the vertical magnetic field. The static fluid is considered as both finitely and infinitely conducting whereas the streaming fluid is non-conducting. It is observed that the presence of the neutral particles modifies the conditions of the ideal-plasma modes for both the horizontal and the vertical magnetic field. Furthermore, it is observed that the growth rate varies as the one-third power of the resistivity whereas the neutral particles merely change the constant of proportionality.

An infinitely extending homogeneous, self-gravitating rotating magnetized plasma flowing through a porous medium has been considered under the influence of Finite Larmor Radius (FLR) and other transport phenomena. A general dispersion relation has been derived through the linearized perturbation equations. Longitudinal and transverse modes of propagation have been discussed for the rotation with axis parallel and perpendicular to the magnetic field. The joint influence, of the aforesaid parameters, does not essentially change the Jeans' criterion of instability but modifies the same. The adiabatic sonic speed has been replaced by the isothermal one due to the thermal conductivity. It is further observed that the FLR corrections have stabilizing effect for an inviscid, non-rotating plasma, in case of transverse propagation. Rotation decreases the Larmor radius, whereas the porosity reduces the effects of rotation, FLR, and the magnetic field. Viscosity removes the effects of both, the roation, and the FLR corrections.

The gravitational instability of a two component plasma is studied to include the simultaneous effects of collisions, gyroviscosity, finite conductivity, viscosity and porosity of the medium within the framework of two-fluid theory. From linearized equations of the system, using normal mode analysis, the dispersion relations for parallel and perpendicular directions to the magnetic field are derived and discussed. For longitudinal wave propagation it is found that the value of critical JEANS' wave number increases with increasing density and decreasing temperature of the neutral component. For transverse wave propagation the value of critical JEANS' wave number depends on gyroviscosity, ALFVEN number, ratio of sonic speeds and densities of the two component and porosity of the medium. It is observed that the effect of magnetic field and porosity is suppressed by finite condutivity of the plasma and similarly the effect of gyroviscosity is removed by viscosity from JEANS' expression of instability. For both the directions instability is produced when the velocity perturbations are considered parallel to wave vector. The damping effect is produced due to collisional frequency, permeability of the porous medium and viscosity. The density of the neutral component and porosity of the medium tends to destabilize the system while an increased value of FLR corrections leads the system towards stabilization.

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 effect of spin induced magnetization and electrical resistivity incorporating the viscosity of the medium is examined on the Jeans instability of quantum magnetoplasma. Formulation of the system is done by using the quantum magnetohydrodynamic model. The analysis of the problem is carried out by normal mode analysis theory. The general dispersion relation is derived from set of perturbed equations to analyse the growth rate and condition of self-gravitational Jeans instability. To discuss the influence of resistivity, magnetization, and viscosity parameters on Jeans instability, the general dispersion relation is reduced for both transverse and longitudinal mode of propagations. In the case of transverse propagation, the gravitating mode is found to be affected by the viscosity, magnetization, resistivity, and magnetic field strength whereas Jeans criterion of instability is modified by the magnetization and quantum parameter. In the longitudinal mode of propagation, the gravitating mode is found to be modified due to the viscosity and quantum correction in which the Jeans condition of instability is influenced only by quantum parameter. The other non-gravitating Alfven mode in this direction is affected by finite electrical resistivity, spin induced magnetization, and viscosity. The numerical study for the growth rate of Jeans instability is carried out for both in the transverse and longitudinal direction of propagation to the magnetic field. The effect of various parameters on the growth rate of Jeans instability in quantum plasma is analysed.The effect of spin induced magnetization and electrical resistivity incorporating the viscosity of the medium is examined on the Jeans instability of quantum magnetoplasma. Formulation of the system is done by using the quantum magnetohydrodynamic model. The analysis of the problem is carried out by normal mode analysis theory. The general dispersion relation is derived from set of perturbed equations to analyse the growth rate and condition of self-gravitational Jeans instability. To discuss the influence of resistivity, magnetization, and viscosity parameters on Jeans instability, the general dispersion relation is reduced for both transverse and longitudinal mode of propagations. In the case of transverse propagation, the gravitating mode is found to be affected by the viscosity, magnetization, resistivity, and magnetic field strength whereas Jeans criterion of instability is modified by the magnetization and quantum parameter. In the longitudinal mode of propagation, the gravitating mode is found to b...

The influence of finite Larmor radius (FLR) effects on the Jeans instability of infinitely conducting homogeneous quantum plasma is investigated. The quantum magnetohydrodynamic (QMHD) model is used to formulate the problem. The contribution of FLR is incorporated to the QMHD set of equations in the present analysis. The general dispersion relation is obtained analytically using the normal mode analysis technique which is modified due to the contribution of FLR corrections. From general dispersion relation, the condition of instability is obtained and it is found that Jeans condition is modified due to quantum effect. The general dispersion relation is reduced for both transverse and longitudinal mode of propagations. The condition of gravitational instability is modified due to the presence of both FLR and quantum corrections in the transverse mode of propagation. In longitudinal case, it is found to be unaffected by the FLR effects but modified due to the quantum corrections. The growth rate of Jeans instability is discussed numerically for various values of quantum and FLR corrections of the medium. It is found that the quantum parameter and FLR effects have stabilizing influence on the growth rate of instability of the system.

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.

The effect of pressure anisotropy and flow velocity on the Kelvin–Helmholtz (KH) instability of two magnetized anisotropic pressure plasmas flowing relative to each other is investigated using generalized polytrope laws. The anisotropic pressure with the generalized polytrope laws is considered with three-dimensional perturbations in the description of plasma using relevant magnetohydrodynamic (MHD) set of equations. The magnetic field is assumed in the x-direction and parallel to the direction of the flow of plasma streams. A complete polytrope model is given for the considered system in terms of pressure components, magnetic field, and density of the fluids to discuss the condition of KH instability, stability, and overstability. The problem is solved using the normal mode analysis and the general dispersion relation is obtained by applying the appropriate boundary conditions. The case of nonvanishing wavenumber transverse to the direction of the stream is obtained, which represents the stationery confi...

The effect of Hall current on the Jeans instability of an infinitely conducting, homogeneous, viscous quantum plasma is investigated. The basic equations of the problem are constructed and linearized by using the quantum magnetohydrodynamic model. The contributions of Hall current and viscosity of the medium are incorporated into the present analysis because of their astrophysical importance. The general dispersion relation is obtained using the normal mode analysis technique, which is reduced for both the transverse and the longitudinal mode of propagation. The longitudinal mode is found to be modified by Hall current, while the transverse mode is unaffected by the presence of the Hall parameter. The Jeans criterion of instability is obtained, which is modified by Alfven velocity and quantum corrections but is unaffected by the presence of the Hall parameter and viscosity. The longitudinal mode is found to be modified by Alfven speed and the Hall parameter and is independent of quantum corrections. Viscosity, magnetic field and quantum corrections all have a stabilizing influence on the growth rate of the Jeans instability.

The problem of radiative condensation instability of self-gravitating dusty plasma, including the effects of dust temperature and the magnetic field, is investigated. The medium consists of extremely massive, negatively charged hot dust grains and Boltzmann distributed ions where the electrostatic force is much smaller than the gravitational one. We assume a three-component plasma having electrons, ions and charged dust grains, in which ions are inertialess having infinite thermal conductivity and electrons are inertialess having finite thermal conductivity. Quasi-neutral equilibrium is considered in which there is no electric field and free energy due to the gravitation field of dust grains. The basic equations of the problem are constructed and linearized. A linear dispersion relation is obtained using the normal mode analysis. The Jeans criterion of instability is determined, which depends on dust temperature and radiative cooling effects. The presence of magnetic field has no effect on the condition of Jeans instability. Numerical calculations have been performed to show the effects of various parameters on the growth rate of radiative condensation instability. It is observed that radiation cooling, magnetic field and dust temperature increase the acoustic stabilization of Jeans instability. The presence of magnetic field and dust temperature stabilizes the growth rate of the system under consideration.

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 effects of uniform rotation, finite electrical resistivity, electron inertia, and Hall current on the self-gravitational instability of anisotropic pressure plasma with generalized polytrope laws have been studied. A general dispersion relation is obtained with the help of the relevant linearized perturbed magnetohydrodynamic (MHD) equations incorporating the relevant contributions of various effects of the problem using the method of normal mode analysis. The general dispersion relation is further reduced for the special cases of rotation; i.e., parallel and perpendicular to the direction of the magnetic field. The longitudinal and transverse modes of propagation are discussed separately for investigation of condition of instability. The effects of rotation, Hall current, finite electron inertia, and polytropic indices are discussed on the gravitational, “firehose,” and “mirror” instabilities. The numerical calculations have been performed to obtain the dependence of the growth rate of the gravitatio...

The self-gravitational instability of rotating anisotropic heat-conducting plasma with modified Chew–Goldberger–Low equations is investigated. The general dispersion relation is obtained using normal mode analysis by constructing the linearized set of equations. This dispersion relation is further reduced for propagation parallel and perpendicular to the direction of magnetic field. These conditions are discussed for axis of rotation along and perpendicular to the magnetic field. It is found that the heat flux vector does not influence the transverse mode of propagation for both cases of rotation and Jeans condition remains unchanged. In case of propagation parallel to the magnetic field with axis of rotation perpendicular to the magnetic field, we get the dispersion relation, which shows the joint effect of rotation and heat flux vector. The two separate modes of propagation are obtained in terms of rotation and heat flux vector for rotation parallel to the magnetic field. It is demonstrated that the Alfven wave and the associated firehose instability are not affected by the presence of heat flux corrections and rotation also. The numerical analysis is performed to show the effect of rotation, pressure anisotropy, and heat flux parameter on the condition of instability in the spiral arms of galaxy. The Jeans condition of gravitational instability is obtained for both the cases of propagation.