Finite Larmor radius effect on thermosolutal instability of a plasma in porous medium

The thermosolutal instability of a plasma in porous medium is considered in the presence of finite Larmor radius effect. The finite Larmor radius, stable solute gradient and magnetic field introduce oscillatory modes in the systems which were nonexistent in their absence. For stationary convection, the finite Larmor radius and stable solute gradient have stabilizing effects on the thermosolutal instability in porous medium. In presence of finite Larmor radius effect, the medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain condition whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively, on thermosolutal instability of a plasma in porous medium. The sufficient conditions for nonexistence of overstability are obtained.The financial assistance to Mr. Sunil in the form of Senior Research Fellowship of the Council of Scientific and Industrial Research (CSIR), New Delhi is gratefully acknowledged.     

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…     

Suppression of Rayleigh-Taylor instability by gyroviscosity and sheared axial flow in imploding plasma pinches

The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations.The gyroviscosity(or finite Larmor radius) effects are introduced in the momentum equation through an anisotropic ion stress tensor.Dispersion relation with the effect of a density discontinuity is derived.The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the gyroviscosity effects.The long wavelength modes are stabilized by the sufficient sheared axial flow.However,the synergistic effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability.This synergistic effect can compress the Rayleigh-Taylor instability to a narrow wave number region.Even with a sufficient gyroviscosity and large enough flow velocity,the synergistic effect can completely suppressed the Rayleigh-Taylor instability in whole wave number region.     

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.     

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     

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.     

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.     

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 Compressibility on the Rayleigh-Taylor Instability in Z-pinch Implosions

In this paper we shall consider the effect of compressibility on the RT instability in Z-pinch implosions, importance is the comparing growth rates of the RT instability for two systems of the compressible and incompressible MHD plasma. For which reason, we shall use as simple model as possible. Obviously, slab geometry is the most simple. For example, in the case of annular plasma implosion, during the linear growth phase of the RT instability there are vacuums at both sides of the annular plasma shell and its thickness is sufficiently smaller than the pinch radius, allowing us to use slab geometry instead of the annular one. For simplicity, we do not consider the effects of the finite Larmor radius and the sheared axial flow which are the important physical mechanisms to compress the RT instabilities.     

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.     

Density oscillations in laser produced plasma decelerated by external magnetic field

This paper presents the dynamics as well as the stability of laser produced plasma expanding across the magnetic field. Observation of some high frequency fluctuations superimposed on ion saturation current along with structuring in the pin hole images of x-ray emitting plasma plume indicate the presence of instability in the plasma. Two type of slope in the variation of x-ray emission with laser intensity in the absence and presence of magnetic field shows appearance of different threshold intensity of laser corresponding to each magnetic field at which this instability or density fluctuation sets on. This instability has been identified as a large Larmor radius instability instead of classical Rayleigh-Taylor (R-T) instability.     

Measurement of instability growth in a magnetized Z pinch in the finite-Larmor-radius regime

The development of the m = 0 instability in a Z pinch was followed and the measured growth rates compared with 2D MHD simulations. Where MHD is valid, the measured growth rates agree well with simulation. Where the ions are magnetized, i.e., where the ion-cyclotron frequency is smaller than the ion-collision frequency and the ratio of the ion Larmor radius to pinch radius is of the order of 0.1, the growth rate was smaller than expected by a factor of 2.5. This is as predicted by finite-Larmor-radius theory. The product of the wave number and the pinch radius was ka approximately 2pi and was the same for all conditions. Perturbations as large as 30% of the pinch radius were observed; no nonlinear saturation was evident.     

Gravitational Instability of a Rotating Viscous Finitely Conducting Plasma

The gravitational instability of infinite homogeneous plasma has been studied to include simultaneously the effects of rotations, Hall currents, viscosity, finite electrical conductivity and the finite Larmor radius (FLR). Both the longitudinal, and transverse modes of wave propagation have been studied. It is found that the gravitational instability is determined by Jeans' criterion even in the presence of effects of rotation, Hall currents, FLR, viscosity and finite conductivity whether included separately or jointly.     

Resistive Electrostatic Ion Cyclotron Instability in Plasmas

The stability of electrostatic ion cyclotron waves propagating obliquely with respect to the background magnetic field is studied for collisional, fully-ionized plasmas in which there is a relative field-aligned streaming between electrons and ions. It is found that electron-ion collisions, in conjunction with electron streaming, provides a mechanism for instability. The role of electron streaming is to supply a source of free energy and the role of electron-ion collisions is to restrict the field-aligned mobility of the electrons, thus preventing them from establishing a Boltzmann equilibrium. Ion-ion collisions and finite ion Larmor radius are found to exert a stabilizing influence. The instability is analyzed for both current-carrying plasmas and counterstreaming-beam-plasma systems.     

磁层顶中的低混杂漂移不稳定性

本文讨论了具有简单结构磁层顶中的低混杂漂移不稳定性,假定在磁层顶中磁场方向是相互平行的,电子与离子的密度处处相等,总压力为一常数,采用1971年Alpers建立的分布函数做为零级分布,计算了下混杂漂移不稳定性的增长率和饱和时相应的反常电阻,计算表明,当磁层顶厚度接近两个质子迴旋半径时,低混杂漂移不稳定性的增长率约为0.26ω_LH(ω_LH为低混杂频率),反常电阻率为10^-5sec,随着磁层顶厚度成倍增加,反常电阻率以指数形式下降。 关键词：     

Magnetogravitational Instability of Anisotropic Plasma with Finite Ion Larmor and Generalized Polytrope Law

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.     

Nature of the isotope effect on transport in tokamaks

The reduction of energy and particle losses with the increasing mass of the hydrogen isotope is more pronounced under conditions of improved confinement when the dominant ion temperature gradient instability is suppressed and other channels of anomalous transport are of importance. In this Letter, we reconsider the dissipative trapped electron (DTE) instability by taking into account finite Larmor radius effects in the analysis of the ion response to perturbations. By applying the improved mixing length approximation in order to estimate the transport coefficients, it is demonstrated that DTE contribution is intrinsically dependent on the isotope mass and provides a plausible explanation for the isotope effect. Contrary to the common belief, it is shown that the DTE turbulence may be of importance for reactor plasmas of low collisionality.     

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.     

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.