The gravitational instability of a rotating plasma in the presence of finite Larmor radius,Hall currents and suspended particles

The gravitational instability of an infinite homogeneous self-gravitating and finitely conducting, rotating gas-particle medium, in the presence of finite Larmor radius, Hall currents and suspended particles effects is considered. The particular cases of the effects of rotation, finite conductivity, finite Larmor radius, Hall currents, and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. It is found that Jeans's criterion remains unchanged in the presence of rotation, finite conductivity, finite Larmor radius, Hall currents, and suspended particles.     

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.     

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.     

Nonlinear Kelvin-Helmholtz magnetohydrodynamic instability of a rotating plasma

Nonlinear analysis for Kelvin-Helmholtz instability of an incompressible, inviscid, rotating fluid with infinite conductivity in the presence of gravity and surface tension has been discussed. The unperturbed magnetic field on two sides of the interface is taken to be uniform. The nonlinear Schrödinger equation for the time variation of amplitude of small perturbations with wave number around the neutral stability is derived. It is found that stability of a magnetised K-H rotating configuration depends on the density ratio, surface tension, and discontinuity of velocity and magnetic field. The effect of an aligned magnetic field and rotation on the non-linear instability of a rotating conducting plasma has been discussed in certain important limiting cases.     

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.     

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

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

Gravitational instability of a Hall plasma in the presence of suspended particles

The gravitational instability of an infinite homogeneous and infinitely conducting selfgravitating gas particle medium in the presence of suspended particles of a Hall plasma is considered. The particular cases of the effects of Hall currents and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. Jeans's criterion determines the gravitational instability.     

Thermal-convective instability of a rotating plasma in stellar atmospheres with Hall effect

Thermal-convective instability of a hydromagnetic, composite, rotating, inviscid, and infinitely conducting plasma in a stellar atmosphere has been studied in the presence of Hall currents. It is found that the criterion for monotonic instability holds good in the presence of the effects due to rotation and Hall currents.     

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.     

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.     

Kelvin-Helmholtz instability of superimposed magnetized,rotating fluids with neutral particles and resistivity

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.     

Wave-wave interactions and gravitational instability

The instability of gravitational waves withk>k _Jeans in a weakly turbulent gas is discussed. Basic features of the processes leading to amplification or damping of gravitational waves are described. Growth rates of the amplitudes are calculated.     

Thermal-convective instability of a composite rotating plasma in a stellar atmosphere with finite larmor radius

Thermal-convective instability of a hydromagnetic, composite, rotating, inviscid and infinitely conducting plasma in a stellar atmosphere has been studied in the presence of finite Larmor radius. It is found that the criterion for monotonic instability holds good in the presence of the effects due to rotation and finite Larmor radius.     

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.     

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.     

Properties of motion in the gravitational field of a rotating bar

A qualitative study of the properties of motion (equilibrium points, regions of motion, periodic orbits) of a test particle in the gravitational field of a uniformly rotating solid bar is made. Two different models are used for the bar, a homogeneous ellipsoid and a homogeneous rectangular parallelepiped, and the dependence of the properties of motion on the specific choice of the model is investigated. It is found that stability properties, especially those of the equilibrium points on the long axis of the bar, are more pronounced in the case of the parallelepiped.     

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 gravitational instability of the interstellar gas

In the galaxy, Jeans' critical length for the interstellar gas is appreciably smaller than the critical length for the stars, a necessary condition for the gravitational instability of the former to have a local character. An accurate discussion of the orders of magnitude involved leads to the establishment of a well defined limiting procedure and to simplified equations in which the effect of stars occurs only through the equilibrium, but disappears from the perturbations. The equations are spatially local, but their coefficients are time-dependent, in that they describe the evolution of a small wave packet dragged along by the supersonic gas motion. They have been solved in several interesting cases by the introduction of an effective, time-dependent wave vector, which describes the deformation of a wave profile due to the velocity gradients. The ordinary Jeans' instability is recovered only when the velocity gradient is a skew tensor; otherwise we find a stabilizing effect in accelerated and sheared flows, a destabilizing effect in a decelerated flow. Possible connections of this model with the observed turbulent structure of the interstellar gas are discussed.     

The multipolar structure of the gravitational radiation from a rotating body

We give the metric coefficients of the retarded field of non-plane gravitational waves from a multipolar source at infinity, and hence the expression for the power of the multipole radiation from a slowly rotating body. When specific calculations are made for the quadrupole radiation, we find that the radiation from a rotating body has a strong directivity. Our calculated results for the total power of two pulsars are in good agreement with previous estimates.     

Gnetic wave instability in a plasma ith relativistic particles in a random magnetic field

A new mechanism, which accounts for the direct excitation of electromagnetic waves by relativistic particles moving in random magnetic fields, is considered. We are then able to study maser-type wave excitations by slightly anisotropic particle distribution functions as well as electromagnetic wave emissions in beam-plasma interactions