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…     

轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制

利用理想磁流体力学模型对有轴向剪切流的Z箍缩等离子体不稳定性进行了分析。给出了可压缩模型的色散关系,分别对可压缩及不可压缩模型中轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制作用进行了比较,讨论了可压缩性对含有轴向剪切流系统不稳定性的影响。结果表明,可压缩性能够减缓瑞利-泰勒P凯尔文-亥姆霍兹(RTPKH)模扰动的增长,因而使得轴向剪切流对系统不稳定性的抑制作用表现得更为突出。计算结果还说明,在RT不稳定性线性增长阶段,等离子体温度较低,使用可压缩模型能够更真实地描述系统的状态。     

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.     

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.     

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.     

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.     

Gravitational Instability of a Two-Component Viscous Plasma with Finite Conductivity Flowing Through a Porous Medium with Fir Corrections

The gravitational instability of a two component plasma is studied to include the simultaneous effects of collisions, gyroviscosity, finite conductivity, viscosity and porosity of the medium within the framework of two-fluid theory. From linearized equations of the system, using normal mode analysis, the dispersion relations for parallel and perpendicular directions to the magnetic field are derived and discussed. For longitudinal wave propagation it is found that the value of critical JEANS' wave number increases with increasing density and decreasing temperature of the neutral component. For transverse wave propagation the value of critical JEANS' wave number depends on gyroviscosity, ALFVÉN number, ratio of sonic speeds and densities of the two component and porosity of the medium. It is observed that the effect of magnetic field and porosity is suppressed by finite condutivity of the plasma and similarly the effect of gyroviscosity is removed by viscosity from JEANS' expression of instability. For both the directions instability is produced when the velocity perturbations are considered parallel to wave vector. The damping effect is produced due to collisional frequency, permeability of the porous medium and viscosity. The density of the neutral component and porosity of the medium tends to destabilize the system while an increased value of FLR corrections leads the system towards stabilization.     

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.     

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.     

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.     

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.     

Absence of complete finite-Larmor-radius stabilization in extended MHD

The dominant finite-Larmour-radius (FLR) stabilization effects on interchange instability can be retained by taking into account the ion gyroviscosity or the generalized Ohm's law in an extended MHD model. However, recent simulations and theoretical calculations indicate that complete FLR stabilization of the interchange mode may not be attainable by ion gyroviscosity or the two-fluid effect alone in the framework of extended MHD. For a class of plasma equilibria in certain finite-beta or nonisentropic regimes, the critical wave number for complete FLR stabilization tends toward infinity.     

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 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.     

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     

中等半径比反向旋转圆Couette系统流动稳定性的实验和数值研究

圆Couette系统已成为研究从层流转捩为湍流以及有限几何尺寸对图案选择影响的范例.本文以实验和计算机模拟方法研究中等半径比圆Couette系统的稳定性.考察同轴独立旋转圆筒之间的粘性不可压缩流体运动，推广了经典的Rayleigh离心不稳定性理论，导出稳定性判据，用来定量地确定稳定界限.实验采用了流动显示和激光散射技术.仪器有半径比η=0.699，形状比Γ=18.流动状态相图中的显著特征是新的首次失稳态：当外筒静止或反向旋转时，首次失稳出现具有非零方位角波数的螺旋涡流，在轴向和方位角方向为行进波，而并非与时间无关的Taylor涡.初步实验所得的转捩Reynolds数与数值计算结果一致.实验室和数值实验显示出半径比对图案形成和转捩序列的影响. 关键词：     

Instability and equilibration of centrifugally stable stratified Taylor-Couette flow

The flow between two concentric cylinders, V(r), is studied analytically and computationally for a fluid with stable axial density stratification. A sufficient condition for linear, inviscid instability is d(V/r)(2)/dr<0 (i.e., all anticyclonically sheared flows) rather than the Rayleigh condition for centrifugal instability, d(Vr)(2)/dr<0. This implies a far wider range of instability than previously identified. The instability persists with finite viscosity and nonlinearity, leading to chaos and fully developed turbulence through a sequence of bifurcations. Laboratory tests are feasible and desirable.     

Ion larmour radius effect on rf ponderomotive forces and induced poloidal flow in tokamak plasmas

Analytical approximations are used to clarify the effect of Larmour radius on rf ponderomotive forces and on poloidal flows induced by them in tokamak plasmas. The electromagnetic force is expressed as a sum of a gradient part and of a wave momentum transfer force, which is proportional to wave dissipation. The first part, called the gradient electromagnetic stress force, is combined with fluid dynamic (Reynolds) stress force, and gyroviscosity is included into viscosity force to model finite ion Larmour radius effects in the momentum response to the rf fields in plasmas. The expressions for the relative magnitude of different forces for kinetic Alfven waves and fast waves are derived.     

Temperature Gradient,Toroidal and Ion FLR Effects on Drift-Tearing Modes

The influences of the temperature gradient and toroidal effects on drift-tearing modes have been studied using the Gyrokinetic Toroidal code. After the thermal force term is introduced into the parallel electron force balance equation, the equilibrium temperature gradient can cause a significant increase in the growth rate of the drifttearing mode and a broadening of the mode structure. The simulation results show that the toroidal effects increase the growth rate of the drift-tearing mode, and the contours of the perturbation field "squeeze" toward the stronger field side in the poloidal section. Finally, the hybrid model for fluid electrons and kinetic ions has been studied briefly, and the dispersion relation of the drift-tearing mode under the influence of ion finite Larmor radius effects is obtained. Compared with the dispersion relation under the fluid model, a stabilizing effect of the ion finite Larmor radius is observed.     

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.