Rayleigh-Taylor instability of a plasma with finite ion Larmor radius effects

The stability of an infinitely conducting plasma of variable density has been investigated taking into account the finiteness of the ion Larmor radius. The perturbations propagating along the ambient magnetic field are considered. It is established that, in general,n ² is necessarily real, wheren is the growth rate of disturbance, thus ruling out the possibility of overstability or damped oscillations. The solution is shown to be characterized by a variational principle, which provides the basis for obtaining an approximate solution of the problem. Two density distributions are considered: (i) a continuously stratified plasma layer and (ii) two semi-infinitely extending plasmas of constant densities separated by a horizontal interface. In both cases it has been shown that for the said disturbances the stability criterion remains unaffected by the inclusion of finite Larmor radius effects, though the amplified motion is strongly inhibited due to their inclusion.     

Filamentation instability of Alfvén waves

The filamentation instability of finite amplitude left-hand circularly polarized Alfvén waves has been investigated taking into account the second-order density and magnetic field perturbations that are created by the Alfvén wave pressure. The minimum scale length and time over which the filamentation occurs, are found. Our results are applied to Alfvén waves that should scatter cosmic rays in the interstellar medium (ISM).     

Magneto-gravitational instability of a fluid through porous medium including finite ion Larmor radius

The magneto-gravitational instability of an infinite, homogenous, and infinitely conducting plasma flowing through a porous medium is studied. The finite ion Larmor radius (FLR) effects and viscosity are also incorporated in the analysis. The prevalent magnetic field is assumed to be uniform and acting in the vertical direction. A general dispersion relation has been obtained from the relevant linearized perturbation equations of the problem. The wave propagation parallel and perpendicular to the direction of the magnetic field have been discussed. It is found that the condition of the instability is determined by the Jeans criterion for a self-gravitating, infinitely conducting, magnetized fluid through a porous medium. Furthermore, for transverse perturbation FLR is found to have stabilizing influence when the medium is considered inviscid.     

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.     

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.     

Wave transformation at the cusp resonance in a finite conductivity isothermal atmosphere permeated by a nearly horizontal magnetic field

The paper considers wave transformation in the vicinity of the cusp resonance in an isothermic finite conductivity medium with a nearly horizontal magnetic field. It is shown that absorption of magnetogravity waves takes place when the inclination angle of the magnetic field is smaller than the critical angle. When the inclination angle is large then the critical magnetogravity waves are transformed into slow magnetoacoustic waves.     

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.     

On thermal-convective instability in a stellar atmosphere with finite Larmor radius and Hall effects

The thermal-convective instability of a stellar atmosphere is considered to include rotation, finite Larmor radius and Hall effects in the presence of a uniform vertical magnetic field. The criterion for monotonic instability is found to be the same even if the above effects are included.     

Suspended particles and the gravitational instability of a rotating plasma

The gravitational instability of an infinite homogeneous self-gravitating and finitely conducting, rotating gas-particle medium, in the presence of a uniform vertical magnetic field, is studied to include finite Larmor radius and suspended particles effects. The particular cases of the effects of rotation, finite conductivity, finite Larmor radius and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. Jeans's criterion determines the gravitational instability.     

The stability of inner cometo-sheath with large Larmor radius effects

An investigation of the linear stability of the cometary inner sheath, the boundary layer surrounding the ionopause which separates the outflowing unmagnetized plasma from an inflowing magnetized plasma, has been carried out by taking into account the large Larmor radius effects. The structure of the boundary layer is determined by the balance between an outward ion-neutral collisional drag force and an inward magnetic stress. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary ionosphere as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. Certain limiting cases of the wave equations are also discussed. In general, the cometary ionosphere is structurally linearly unstable and the effects of recombination, photoionization, plasma pressure, though stabilizing are unable to quench the instability completely. The large Larmor radius also has a destabilizing effect on the system. The instability of the cometosheath is further proved by the _c/_i assuming a value greater than 30 that is sufficient for the convection of perturbations down into the cavity surface and this is in agreement with the observations of ripples in the ionopause.     

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.     

Thermosolutal-convective instability of a composite plasma in a stellar atmosphere including the effects of finite larmor radius and Hall currents

Thermosolutal-convective instability of a composite plasma in a stellar atmosphere is considered to include the effects, separately, due to finite Larmor radius (FLR) and Hall currents in the presence of a uniform horizontal magnetic field. The sufficient conditions for the existence of monotonic instability are derived and are found to hold good both in the presence, separately, of FLR and Hall current effects.     

Local Stability Criterion for a Self-Gravitating Gaseous Disk of Spiral Galaxies

An improved linear stability theory of small-amplitude oscillations of a self-gravitating, infinitesimally thin gaseous disk of spiral galaxies has been developed by Bertin, Lau, Lin, Mark, Morozov, Polyachenko, and others in the approximation of moderately tightly wound gravity perturbations. In this regime, the generalized Lin–Shu type dispersion relation was also found by including higher order terms in the small parameter 1/kr for wavenumber k and radius r. It was shown that in the differentially rotating disks for nonaxisymmetric (spiral)perturbations Toomre's modified critical Q-parameter is larger than the standard one: the fact that the spiral perturbations in the nonuniformly rotating system are more unstable than the axisymmetric ones is taken into account in this modified local stability criterion. We use hydrodynamical simulations to test the validity of the modified local criterion. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Gravitational instability of a thermally-conducting plasma flowing through a porous medium in the presence of suspended particles

Magnetogravitational instability of a thermally-conducting, rotating plasma flowing through a porous medium with finite conductivity and finite Larmor radius in the presence of suspended particles has been investigated. The wave propagation has been considered for both parallel and perpendicular axes of rotation. Magnetic field is being taken in the vertical direction. A general dispersion relation has been derived through relevant linearized perturbation equations. It has been observed that the condition of instability is determined by the Jeans's criterion in its modifed form. Thermal conductivity replaces the adiabatic velocity of sound by the isothermal one. Rotation decreases the Larmor radius. Porosity decreases the Alfvén velocity. In case of a viscous medium the effects of FLR, rotation, and suspended particles are not observed in the Jeans's condition, for transverse propagation for rotational axis parallel to the magnetic field. The effects of rotation and FLR are decreased by the porosity and the suspended particles. Finite conductivity removes the Alfvén velocity from Jeans's condition.     

Time – Distance Modelling in a Simulated Sunspot Atmosphere

In time?–?distance helioseismology, wave travel times are measured from the cross-correlation between Doppler velocities recorded at any two locations on the solar surface. However, one of the main uncertainties associated with such measurements is how to interpret observations made in regions of strong magnetic field. Isolating the effects of the magnetic field from thermal or sound-speed perturbations has proved to be quite complex and has yet to yield reliable results when extracting travel times from the cross-correlation function. One possible way to decouple these effects is by using a 3D sunspot model based on observed surface magnetic-field profiles, with a surrounding stratified, quiet-Sun atmosphere to model the magneto-acoustic ray propagation, and analyse the resulting ray travel-time perturbations that will directly account for wave-speed variations produced by the magnetic field. These artificial travel-time perturbation profiles provide us with several related but distinct observations: i) that strong surface magnetic fields have a dual effect on helioseismic rays?–?increasing their skip distance while at the same time speeding them up considerably compared to their quiet-Sun counterparts, ii) there is a clear and significant frequency dependence of both skip-distance and travel-time perturbations across the simulated sunspot radius, iii) the negative sign and magnitude of these perturbations appears to be directly related to the sunspot magnetic-field strength and inclination, iv) by “switching off” the magnetic field inside the sunspot, we are able to completely isolate the thermal component of the travel-time perturbations observed, which is seen to be both opposite in sign and much smaller in magnitude than those measured when the magnetic field is present. These results tend to suggest that purely thermal perturbations are unlikely to be the main effect seen in travel times through sunspots, and that strong, near-surface magnetic fields may be directly and significantly altering the magnitude and lateral extent of sound-speed inversions of sunspots made by time?–?distance helioseismology.     

Dissipative structures in the F-region of the equatorial ionosphere generated by Rayleigh-Taylor instability

The non-linear regime of electrostatic perturbations of the equatorial ionospheric F-region generated by Rayleigh-Taylor instability has been discussed, taking into account conductivity along magnetic field lines. A closed non-linear equation has been derived in the stationary limit for the polarization electric field potential. It coincides with the Karman equation of an ideal liquid. To solve the equation, the averaged variational Whitham method has been proposed. Some solutions localized along and across the geomagnetic field, B, as well as quasi-periodic solutions in the transverse direction, have been investigated. Non-linear longitudinal localization of perturbations has been shown to be due to electron-ion collisions.     

Effects of finite resistivity on magnetorotational instabilities in a realistic accretion flow

A local perturbation analysis is performed on a realistic background accretion flow in a global magnetic field. The adopted background model is an analytic solution to the resistive MHD equations and describes magnetically-controlled advection-dominated accretion flows (ADAFs) with an accuracy to the first order in the resistive corrections. The results show that there are three independent wave modes, which may be called the Rayleigh, Balbus–Hawley and resistive modes. Within our resistive-MHD corrections to the ideal-MHD limit, a Balbus–Hawley-like criterion for the instability of axisymmetric perturbations appears as a consequence of the competition between damping due to magnetic diffusion and excitation due to shear flow. As for non-axisymmetric perturbations, the former two modes are likely to be unstable in the presence of shears because the magnetic diffusion acts as a stabilizer only to axisymmetric perturbations within our approximation.     

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.     

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

Thermal-convective instability of a hydromagnetic-composite 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 finite Larmor radius.