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

The effects of arbitrary radiative heat-loss functions and Hall current on the self-gravitational instability of a homogeneous, viscous, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, finite electron inertia and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis with the help of relevant linearized perturbation equations of the problem, and a modified Jeans criterion of instability is obtained. The conditions of modified Jeans instabilities and stabilities are discussed in the different cases of our interest. We find that the presence of arbitrary radiative heat-loss functions and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. For longitudinal propagation, it is found that the condition of radiative instability is independent of the magnetic field, Hall parameter, finite electron inertia, finite electrical resistivity, viscosity and rotation; but for the transverse mode of propagation it depends on the finite electrical resistivity, the strength of the magnetic field, and it is independent of rotation, electron inertia and viscosity. From the curves we find that the presence of thermal conductivity, finite electrical resistivity and density-dependent heat-loss function has a destabilizing influence, while viscosity and magnetic field have a stabilizing effect on the growth rate of an instability. The effect of arbitrary heat-loss functions is also studied on the growth rate of a radiative instability.     

Effect of rotation 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.     

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

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

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.     

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.     

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.     

Gravitational instability of partially-ionized plasma in an oblique magnetic field

The effects of Hall currents, finite conductivity, and collision with neutrals have been studied on the gravitational instability of a partially-ionized plasma. It is assumed that plasma is permeated by an oblique magnetic field. The dispersion relation has been obtained and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitationally unstable mode on the various physical parameters involved. It is found that Jeans's criterion remains unchanged in the presence of Hall currents, finite conductivity, and collisions. The Hall currents, finite conductivity, and collisions have destabilizing influence on the unstable mode of wave propagation of a gravitational instability of partially-ionized plasma.     

Possible Role of mhd Waves in Heating the Solar Corona

Heating of the solar corona by MHD waves has been investigated. Taking account of dissipation mechanisms self-consistently, a new general dispersion relation has been derived for waves propagating in a homogeneous plasma. Solution of this sixth-order dispersion relation provides information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. Wave quantities with and without dissipation are presented. In particular, we consider one of the most important clues from space observations that viscosity of coronal plasma may be orders of magnitude different from its classical value in heating of the corona by MHD waves.     

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.     

Studies on some properties of coronal mass ejections based on angular width

The paper investigates the effects of thermal conductivity and non-uniform magnetic field on the gravitational instability of a non-uniformly rotating infinitely extending axisymmetric cylinder in a homogeneous heat conducting medium. The non-uniform rotation and magnetic field are supposed to act along θ and z directions of the cylinder. It is found that the gravitational instability of this general problem is determined by the same criterion as obtained by Dhiman and Dadwal (Astrophys. Space Sci. 325(2):195–200, 2010) for the self-gravitating isothermal medium in the presence of non-uniform rotation and magnetic field with the only difference that adiabatic sound velocity is now replaced by the isothermal sound velocity. It is found that the thermal conductivity has stabilizing effect on the onset of gravitational instability. Further, the stabilizing/destabilizing effect of the non-uniform magnetic field on the gravitational instability of heat conducting medium has been discussed and is illustrated by considering some special forms of the basic magnetic fields.     

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

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

Magnetogravitational 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 Cylindrical Viscoelastic Medium Permeated with Non Uniform Magnetic Field and Rotation

The self-gravitating instability of an infinitely extending axisymmetric cylinder of viscoelastic medium permeated with non uniform magnetic field and rotation is studied for both the strongly coupled plasma (SCP) and weakly coupled plasma (WCP). The non uniform magnetic field and rotation are considered to act along the axial direction of the cylinder. The normal mode method of perturbations is applied to obtain the dispersion relation. The condition for the onset of gravitational instability has been derived from the dispersion relation under both strongly and weakly coupling limits. It is found that the Jeans criterion for gravitational collapse gets modified due to the presence of shear and bulk viscosities for the SCP, however, the magnetic field and rotation whether uniform or non uniform has no effect on the Jeans criterion of an infinitely extending axisymmetric cylinder of a self-gravitating viscoelastic medium.     

Gravitational instability of a composite and rotating plasma in the presence of a variable magnetic field through a porous medium

The gravitational instability of an infinite homogeneous self-gravitating plasma through porous medium is considered to include, separately, the effects due to rotation and collisions between ionized and neutral components. The dispersion relations are obtained in both cases. It is found that the gravitational instability of a composite and rotating plasma in the presence of a variable horizontal magnetic field through porous medium is determined by the Jeans's criterion.     

On the Jeans Criterion of a Stratified Heat Conducting Gaseous Medium in the Presence of Non-uniform Rotation and Magnetic Field

The problem of self-gravitational instability of an infinite, homogeneous stratified gaseous medium with finite thermal conductivity and infinite electrical conductivity, in the presence of non-uniform rotation and magnetic field in the Chandrasekhar’s frame of reference, is studied. It is found that the magnetic field, whether uniform or non-uniform, has no effect on the Jeans’ criterion for gravitational instability and remains essentially unaffected. However, the thermal conductivity has the usual stabilizing effect on the criterion that the adiabatic sound velocity occurring in the Jeans criterion is replaced by the isothermal sound velocity. Thus, the present analysis extends the results of Chandrasekhar for the case of heat conducting medium and for non-uniform rotation and magnetic field.     

Multicomponent theory of buoyancy instabilities in magnetized plasmas: the case of magnetic field parallel to gravity

We investigate electromagnetic buoyancy instabilities of the electron-ion plasma with the heat flux based on not the magnetohydrodynamic (MHD) equations, but using the multicomponent plasma approach when the momentum equations are solved for each species. We consider a geometry in which the background magnetic field, gravity, and stratification are directed along one axis. The nonzero background electron thermal flux is taken into account. Collisions between electrons and ions are included in the momentum equations. No simplifications usual for the one-fluid MHD-approach in studying these instabilities are used. We derive a simple dispersion relation, which shows that the thermal flux perturbation generally stabilizes an instability for the geometry under consideration. This result contradicts to conclusion obtained in the MHD-approach. We show that the reason of this contradiction is the simplified assumptions used in the MHD analysis of buoyancy instabilities and the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. Our dispersion relation also shows that the medium with the electron thermal flux can be unstable, if the temperature gradients of ions and electrons have the opposite signs. The results obtained can be applied to the weakly collisional magnetized plasma objects in laboratory and astrophysics.     

Effect of rotation and finite Larmor radius on magneto-gravitational instability of Hall plasma in the presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetized Hall plasma is considered with the inclusion of finite Larmor radius corrections and the effect of suspended particles. A general dispersion relation is obtained from the linearized set of equations. The particular cases of the effect of rotation along and perpendicular to the direction of the magnetic field are considered. The effects of Hall current, finite Larmor radius, and suspended particles on the waves propagated parallel and perpendicular to the uniform magnetic field are investigated along with the uniform rotation of the medium. It is found that in the presence of suspended particles, magnetic field, Hall current, rotation and finite Larmor radius, the Jeans criterion determines the condition of gravitational instability of a gas-particle medium.     

Gravitational instability of a non-linear magnetic fluid

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

Skinning process stability of the magnetic field in the solar active regions

Skinning process stability of the magnetic field in homogeneous plasma is studied. A set of magnetohydrodynamic equations is used. Dependence of electrical conductivity on the plasma parameters and radiation intensity in grey-body approximation are taken into account. The investigation is carried out on the model problems in linear approximation and by means of numerical solution of MHD equations. Threshold of stability and critical gradient of magnetic field in skin-layer are obtained. The model of the phenomenon proposed in the paper indicates on overheating instability of plasma with electric current in large gradient magnetic field zones as a possible trigger mechanism of solar flare origin.     

Gravitational instability for some astrophysical systems

The gravitational instability of an infinite homogeneous self-gravitating mixture through porous medium in the presence of a variable horizontal magnetic field varying in vertical directions has been considered to include, separately, the effects due to suspended particles and collisions between ionized and neutral components. The dispersion relations in both cases have been obtained. It has been found that Jeans's criterion of instability holds good even if the effects due to suspended particles, collisions, porosity, and variable magnetic field are considered.