Thermosolutal instability in porous medium in a partially ionized plasma

The thermosolutal instability in porous medium in a partially ionized plasma in the presence of a uniform vertical magnetic field is considered. The presence of each, magnetic field and stable solute gradient, brings oscillatory modes which were nonexistent in their absence. The collisional effects may also bring in oscillatory modes. The stable solute gradient and magnetic field are found to have stabilizing effect whereas the medium permeability and collisional frequency have destabilizing effect on the thermosolutal instability in porous medium.     

Thermosolutal Instability of a Rotating Plasma

The thermosolutal instability of a plasma is studied to include the effects of coriolis forces and the finiteness of ion Larmor Radius in the presence of transverse magnetic field. It is observed that the effect of rotation is destabilizing only in a typical case. However, the F. L. R. and stable solute gradient have stabilizing effects on stationary convection irrespective of the presence of coriolis forces.     

Effects of finite larmor radius and variable gravitational field on thermal instability of fluid layer under rotation in porous medium

The effect of finite Larmor radius, magnetic field, rotation and variable gravitational field on thermal instability of fluid layer in porous medium is investigated. It is found that the principle of exchange of stability is valid in the absence of magnetic field and rotation. The system is stable/unstable depending upon certain conditions in the presence of rotation, magnetic field and medium permeability. The system is stable in presence of finite Larmor radius. The above work has been carried out under research project financed by University Grants Commission New Delhi (India) and the authors are grateful to University Grants Commission for their financial support.     

Effect of variable gravitational field on thermal instability of a rotating fluid layer with magnetic field in porous medium

The effect of variable gravitational field on thermal instability of a rotating fluid layer in the presence of magnetic field in porous medium is investigated. It is found that the system is stable when gravity is decreasing upwards. The principle of exchange of stability is valid in the absence of rotation and magnetic field when gravity increases upwards. In the stationary convection, rotation has stabilizing or destabilizing effect depending upon whether gravity is increasing or decreasing upwards. The medium permeability and magnetic field have stabilizing or destabilizing effect depending upon condition.     

Hydromagnetic transverse instability of two highly viscous fluid-particle flows with finite ion Larmor radius corrections

A linear analysis of the combined effect of viscosity, finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability of two superposed incompressible fluids in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be transverse to the direction of streaming. A general dispersion relation for such a configuration has been obtained using appropriate boundary conditions. The stability analysis is discussed analytically, and the obtained results are numerically confirmed. Some special cases are recovered and corrected. The limiting cases of absence of suspended particles (or fluid velocities) and finite Larmor radius, absence of suspended particles are discussed in detail. In both cases, all other physical parameters are found to have stabilizing as well as destabilizing effects on the considered system. In the former case, the kinematic viscosity is found to has a stabilizing effect, while in the later case, the finite Larmor radius is found to has a stabilizing influence for a vortex sheet. It is shown also that both finite Larmor radius and kinematic viscosity stabilizations for interchange perturbations are similar to the stabilization effect due to a magnetic field for non-interchange perturbations. Received 13 January 2003 Published online 24 April 2003 RID="a" ID="a"Also at: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt. e-mail: m.elsayed@uaeu.ac.ae     

Finite Larmor radius and Hall effects on thermal instability of a compressible plasma

The effects of compressibility, finite Larmor radius (FLR) and Hall currents are considered on the thermal instability of a plasma in the presence of a uniform horizontal magnetic field. For stationary convection, the compressibility has a stabilizing effect whereas FLR and Hall currents have stabilizing as well as destabilizing effects. For (C _pβ/g)<1, the system is stable. The magnetic field, FLR and Hall currents introduce oscillatory modes in the system for (C _pβ/g)>1.     

Hall effects on thermosolutal instability of a rotating plasma

Summary The thermosolutal instability of a rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of Hall current. When the instability sets in as stationary convection for the case of no rotation, the Hall effects are found to be destabilizing. The stable solute gradient and rotation are found to have stabilizing effects. In the presence of rotation the Hall currents are found to be stabilizing forT ₁>M(1+x)². the case of overstability is also considered and it is shown that such solutions exist. The variation of the frequency with respect to the wave number at the neutral state is graphically shown. The authors of this paper have agreed to not receive the proofs for correction.     

Finite Larmor radius effect on thermal instability of a compressible plasma

The thermal instability of a compressible 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, both the compressibility and the finite Larmor radius are found to have stabilizing effect. The sufficient conditions for the nonexistence of overstability are investigated.     

Thermal convection in Rivlin-Ericksen elastico-viscous fluid in porous medium in hydromagnetics

The thermal instability of a layer of Rivlin-Ericksen elastico-viscous fluid in porous medium acted on by a uniform magnetic field is considered. For stationary convection, Rivlin-Ericksen elastico-viscous fluid behaves like a Newtonian fluid. The magnetic field is found to have stabilizing effect whereas medium permeability has destabilizing effect. The magnetic field introduces oscillatory modes in the system, A sufficient condition for the non-existence of overstability is also obtained.     

Thermosolutal convection in a Maxwellian viscoelastic fluid in porous medium

The thermosolutal convection in a layer of Maxwellian viscoelastic fluid heated and soluted from below in porous medium is considered. The effects of uniform magnetic field and uniform rotation on the thermosolutal convection are also considered. For stationary convection, the Maxwellian viscoelastic fluid behaves like a Newtonian fluid. The sufficient conditions for the nonexistence of overstability are obtained. The critical Rayleigh number is found to increase with the increase in magnetic field, rotation and stable solute gradient.     

Gravitational Instability of a Rotating Viscous Thermally Conducting Plasma

This paper deals with the gravitational instability of an infinite homogeneous viscous rotating plasma of finite electrical conductivity in the combined presence of effects of Hall currents, finite Larmor radius (FLR) and thermal conductivity. The ambient magnetic field is assumed to be uniform and acting along the vertical direction. Both longitudinal and transverse modes of wave propagation have been studied. It is shown that Jean's criterion determines the gravitational instability even in the presence of the effects of thermal conductivity, viscosity, finite electrical conductivity, FLR, rotation and Hall currents. Further it is found that while FLR, viscosity and rotation have a stabilizing influence, both the thermal and the electrical conductivities have a destabilizing influence on the gravitational instability of a plasma.     

The ion Larmor radius effects on the interchange instability in a sheared magnetic field

The localized interchange instability in a low β collisionless plasma is studied as an eigenvalue problem in the presence of magnetic shear. It is found that while shear is always stabilizing, the ion Larmor radius effects become destabilizing if the shear exceeds a certain value.     

Effects of Hall Currents and Gyroviscosity on the Instability of a Self-Gravitating Stratified Plasma

The instability in a horizontal layer of a partially ionized self gravitating plasma has been studied to include simultaneously the effects of Hall currents, viscosity and finiteness of Larmor radius (FLR). The ambient magnetic field is assumed to be uniform and vertical. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of unstable perturbations decreases with the effects of viscosity, neutral gas friction and FLR. The influence of effects of viscosity, neutral gas friction and FLR are consequently stabilizing. It is found that the Hall currents have a destabilizing influence as the growth rate is found to increase with this effect.     

SYNERGETIC MITIGATION OF THE RAYLEIGH—TAYLOR INSTABILITY BY SHEAR AXIAL FLOWS AND FINITE LARMOR RADIUS

1　IntroductionImplodingZ pinchesemployinggaspuffs,cy lindricalfoils,andwirearraysareverycompactandefficientdevicesforcouplingelectromagneticenergyfromapulseforminglineintoadenseplas macolumn.Morerecently,aluminumwirearrayimplosionshaveproducedthehighestX raypowerof40TWonthe20TWSaturnacceleratoratSandiaNationalLaboratory[1].Thesedeviceshavepoten tialapplicationstocontrolledfusionaswellastointensesourcesofkeVX raysfornuclearweaponseffects.Unfortunately,theimplosionsarehighlysusceptibletoR…     

Influence of Finite Larmor Radius with Finite Electrical and Thermal Conductivities on the Gravitational Instability of a Magnetized Rotating Plasma Through a Porous Medium

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.     

Hydromagnetic Stability of a Self-Gravitating Composite Plasma in the Presence of Finite Larmor Radius

The hydromagnetic stability of a self-gravitating composite plasma has been studied to include the effects of ion viscosity and the finiteness of the ion Larmor radius. The whole medium is embedded in a uniform horizontal magnetic field. The F. L. R. effects have been included through the stress tensor. An explicit solution for a semi-infinite plasma of finite depth and with an exponential density variation along the vertical is obtained by means of a variational principle characterizing the problem. Numerical calculations show that the influence of the effects of ion viscosity and F. L. R. is to reduce the growth rate of unstable perturbations. On the other hand the effects of neutral gas collisions have been found to be both stabilizing as well as destabilizing.     

The Effect of Finite Larmor Radius on Gravitational Instability of a Finitely Conducting Magnetised Hall Medium in Presence of Suspended Particles

The problem of stability of a self-gravitating, infinite homogeneous gas in the presence of suspended particles is investigated. The medium is assumed conducting and effect of external magnetic field, Hall current and finite Larmor radius corrections are also considered. The equations of the problem are linearized and from linearized equations a general dispersion relation for a dusty gas-particle medium is obtained. The dispersion relation is reduced for two special cases of wave propagations: Parallel and perpendicular to the direction of uniform magnetic field. The effect of suspended particles on the medium is investigated in both the cases. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans's criterion for a self gravitating finitely conducting magnetised Hall medium.     

Effects of Hall Currents and Gyroviscosity on the Stability of a Finitely Conducting Rotating Viscous Plasma of Variable Density

The Rayleigh-Taylor instability of an incompressible viscous, finitely conducting, rotating plasma of variable density has been investigated in the presence of the effects of Hall currents and finite ion Larmor radius. The proper solution for a semi-infinité plasma layer having exponentially varying density in the vertical direction has been obtained by making use of a variational principle which is shown to characterize the problem. The dispersion relation has been solved numerically. It is found that gyroviscosity, viscosity and coriolis forces have stabilizing influence whereas Hall currents and resistivity have a destabilizing influence.     

Effect of Conductivity on Magneto-Gravitational Instability of a Medium with Finite Larmor Radius and Suspended Particles

The self-gravitational instability of an infinite homogeneous magnetised and finitely conducting gas-particle medium is considered to include the finite Larmor radius effect in the presence of suspended particles. The equations of the problem are linearized and from linearized equations a general dispersion relation for dusty-gas is obtained. The dispersion relations are also obtained for propagation, parallel and perpendicular to the direction of uniform magnetic field. The Jeans, criterion is discussed for these two different directions of wave propagation. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans' criterion for a self gravitating, finitely conducting, magnetized gas-particle medium.     

Wave propagation in a rarefied plasma with finite Larmor radius

Wave propagation in a rarefied two-component plasma immersed in a uniform constant magnetic field has been discussed wherein the plasma pressure is assumed to be anisotropic owing to finite Larmor radius effect. It is shown that, for propagation along the external magnetic field, there exist two modes of wave propagation, namely, the gravitational mode and the hydromagnetic mode. The former is found to be independent of the magnetic field and hence of the Larmor radius, while the latter is appreciably influenced by the finite Larmor radius. On the other hand, for transverse propagation, there are three modes of wave propagation viz. the ion-sound mode, the electron-sound mode and the electromagnetic mode. It is shown that only the lowfrequency ion-sound mode is affected by the finite Larmor radius.