EFFECT OF FINITE ION LARMOR RADIUS ON THE STABILITY OF SUPERPOSED FLUIDS

1967 ◽  
Vol 45 (4) ◽  
pp. 1579-1585 ◽  
Author(s):  
G. L. Kalra
Keyword(s):  
Magnetic Field ◽  
Vortex Sheet ◽  
Larmor Radius ◽  
General Direction ◽  
Ambient Magnetic Field ◽  
The Stability ◽  
Superposed Fluids

The effect of finite ion Larmor radius on the problem of stability of incompressible and infinitely conducting superposed fluids is investigated for a general direction of perturbation. It is found that whereas the interchange perturbations are stabilized in the presence of Larmor radius, the noninterchange perturbations (which affect the ambient magnetic field) lead to overstability due to Larmor radius effects in a configuration (unstable in the absence of magnetic field) stabilized by a strong enough magnetic field. The configuration which is monotonically unstable in the absence of Larmor radius now, in addition, exhibits overstable modes. Similar conclusions are obtained in the presence of vortex sheet as well.

Effect of finite ion Larmor radius on the stability of rotating superposed fluids

1969 ◽  
Vol 47 (8) ◽  
pp. 831-834 ◽  
Author(s):  
G. L. Kalra
Keyword(s):  
Gravitational Instability ◽  
Equations Of Motion ◽  
Vortex Sheet ◽  
Larmor Radius ◽  
Simultaneous Presence ◽  
Uniform Rotation ◽  
Finite Larmor Radius ◽  
The Stability ◽  
Superposed Fluids ◽  
Macroscopic Equations

The effect of finite ion Larmor radius on the gravitational instability of two superposed fluids in uniform rotation is investigated for interchange perturbations, using the macroscopic equations of motion, where the finite ion Larmor radius effect is incorporated through off-diagonal terms in the pressure tensor. It is found that the region of stable wavelengths is enhanced due to the simultaneous presence of finite Larmor radius and a uniform rotation. A similar conclusion is also arrived at for the situation when a vortex sheet is present between the two superposed fluids.

Hydromagnetic Stability of Two Rivlin-Ericksen Elastico-Viscous Superposed Conducting Fluids

1997 ◽  
Vol 52 (6-7) ◽  
pp. 528-532
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Unstable Configuration ◽  
The Stability ◽  
Superposed Fluids ◽  
The Magnetic Field ◽  
Conducting Fluids

Abstract The stability of the plane interface separating two Rivlin-Ericksen elastico-viscous superposed fluids of uniform densities when the whole system is immersed in a uniform horizontal magnetic field has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities and equal kinematic viscoelasticities. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave-number range of the unstable configuration. The behaviour of growth rates with respect to kinematic viscosity and kinematic viscoelasticity parameters are examined numerically.

Hydromagnetic stability of a compressible jet

1975 ◽  
Vol 14 (3) ◽  
pp. 443-448 ◽  
Author(s):  
B. B. Chakraborty ◽  
H. K. S. Iyengar
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Magnetic Fields ◽  
Axial Direction ◽  
Vortex Sheet ◽  
Fluid Velocities ◽  
The Stability ◽  
Axisymmetric Disturbances ◽  
Jet Velocities ◽  
The Magnetic Field

This paper studies the hydromagnetic stability of a cylindrical jet of a perfectly-conducting, inviscid and compressible fluid. The fluid velocities and magnetic fields, inside and outside the jet, are uniform and in the axial direction, with possible discontinuities in their values across the jet surface. For large wavelength disturbances, the jet behaves as though it were incompressible. Numerical evaluation of the roots of the dispersion relation for a number of different magnetic-field strengths and jet velocities, but for disturbances of finite ranges of wavenumbers, indicates that the jet is stable against axisymmetric disturbances, but instability is present for asymmetric disturbances when the magnetic fields are sufficiently small. The magnetic field is found to have a stabilizinginfluence when compressibility is not very large; for high compressibility, it may have even a destabilizing effect. The paper explains physically the roles of compressibility and the magnetic field in bringing about the stability of the jet. When the wavelengths of disturbances are small, the dispersion relation reduces to that for a two-dimensional jet and a vortex sheet; and the results for these cases are known from earlier studies.

Stability of anisotropic plasmas to almost-perpendicular magnetosonic waves

1971 ◽  
Vol 6 (3) ◽  
pp. 495-512 ◽  
Author(s):  
R. W. Landau† ◽  
S. Cuperman
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Simple Form ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Ion Plasma ◽  
The Stability ◽  
The Magnetic Field

The stability of anisotropic plasmas to the magnetosonic (or right-hand compressional Alfvén) wave, near the ion cyclotron frequency, propagating almost perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and for large ion plasma frequency (w2p+ ≫ Ωp+) the dispersion relation is obtained in a simple form. It is shown that for T # T' (even T ≫ T) no instabifity occurs. The resonant ters are also included, and it is shown that there is no resonant instabifity, only damping.

Effect of Finite Larmor Radius on the Rayleigh-Taylor Instability of Two Component Magnetized Rotating Plasma

1998 ◽  
Vol 53 (12) ◽  
pp. 937-944 ◽  
Author(s):  
P. K. Sharma ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Horizontal Magnetic Field ◽  
Finite Larmor Radius ◽  
Neutral Particles ◽  
Rayleigh Taylor Instability ◽  
Superposed Fluids

Abstract The Rayleigh-Taylor (R-T) instability of two superposed plasmas, consisting of interacting ions and neutrals, in a horizontal magnetic field is investigated. The usual magnetohydrodynamic equations, including the permeability of the medium, are modified for finite Larmor radius (FLR) corrections. From the relevant linearized perturbation equations, using normal mode analysis, the dispersion relation for the two superposed fluids of different densities is derived. This relation shows that the growth rate unstability is reduced due to FLR corrections, rotation and the presence of neutrals. The horizontal magnetic field plays no role in the R-T instability. The R-T instability is discussed for various simplified configurations. It remains unaffected by the permeability of the porous medium, presence of neutral particles and rotation. The effect of different factors on the growth rate of R-T instability is investigated using numerical analysis. Corresponding graphs are plotted for showing the effect of these factors on the growth of the R-T instability.

scholarly journals Larmor Radius and Collisional Effects on the Dynamic Stability of a Composite Medium

1972 ◽  
Vol 25 (3) ◽  
pp. 259 ◽  
Author(s):  
PK Bhatia ◽  
JM Steiner
Keyword(s):  
Magnetic Field ◽  
Dynamic Stability ◽  
Variable Density ◽  
Composite Medium ◽  
Larmor Radius ◽  
Combined Effects ◽  
Composite Media ◽  
Horizontal Magnetic Field ◽  
The Stability ◽  
Streaming Motion

The combined effects of a finite ion Larmor radius and collisions with neutral atoms on the dynamic stability of a composite medium are investigated. The stability analysis has been carried out for a semi-infinite composite medium of variable density in the presence and absence of a uniform streaming motion. Wave propagations transverse to the direction of the uniform horizontal magnetic field have been considered. It is found that the effects of the collisions as well as the finite ion Larmor radius are stabilizing on both streaming and non-streaming composite media.

Resistive instability in a uniformly rotating magnetoplasma

1971 ◽  
Vol 6 (1) ◽  
pp. 73-85
Author(s):  
A. D. Lunn
Keyword(s):  
Magnetic Field ◽  
Growth Rates ◽  
Larmor Radius ◽  
Closed Set ◽  
Finite Larmor Radius ◽  
Integral Methods ◽  
Stabilizing Effect ◽  
Instability Growth ◽  
Linear Differential ◽  
The Stability

A closed set of guiding centre equations, derived for a rotating plasma in a static magnetic field, is applied to the problem of the stability of a plasma in a sheared field. The rotation is found to have a stabilizing effect in the absence of resistivity.A pair of coupled, linear differential equations is derived for the rotating plasma in a weakly sheared field. Dispersion relations are obtained by phase integral methods and, in the absence of finite Larmor radius effects and rotation, instability growth rates proportional to η½13 are found which become proportional to when either is included. The inclusion of both finite Larmor radius and rotation gives growing instabilities proportional to η which are stabilized by the rotation when the finite Larmor radius terms predominate.

scholarly journals On the Kelvin-Helmholtz Discontinuity in Two Superposed Plasmas

1974 ◽  
Vol 27 (1) ◽  
pp. 53 ◽  
Author(s):  
Prem Kumar Bhatia ◽  
Joseph Mendel Steiner
Keyword(s):  
Magnetic Field ◽  
Collision Frequency ◽  
Plane Interface ◽  
Ambient Magnetic Field ◽  
Neutral Particles ◽  
Stabilizing Effect ◽  
The Stability

An investigation has been made of the effects of collisions with neutral particles on the stability of the plane interface separating two streaming superposed plasmas of uniform densities. It has been found that, whereas the ambient magnetic field has a stabilizing influence, a collision frequency has a stabilizing effect when it is small and a destabilizing effect when it exceeds a certain value.

On the stability of the screw pinch in the CGL model

1976 ◽  
Vol 16 (3) ◽  
pp. 261-283 ◽  
Author(s):  
Krishna M. Srivastava ◽  
F. Waelbroeck
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Finite Larmor Radius ◽  
Main Column ◽  
First Order Correction ◽  
The Stability ◽  
The Magnetic Field ◽  
Ideal Plasma

We have investigated the stability of the screw pinch with the help of the double adiabatic (CGL) equations including the finite Larmor radius effects through the anisotropic pressure tensor. The calculations are approximate, with FLR treated as a first-order correction to the ideal plasma equations. The dispersion relation has been solved for various values of R2 = p∥/p⊥ and α for the rale and imaginary part of the frequency (ω = ωR ± iωI) in three particular cases: (a) μ = 0, the θ-pinch, (b) μ = ∞, the Z-pinch, (c) μ = -α/m, field distubances parallel to the equilibrium field. Here μ is the pitch of the magnetic field in the pressureless plasma surrounding the main column, α is the wave number, m is the azimuthal number, p∥ and p⊥ are plasma pressures along and perpendicular to the magnetic field.

scholarly journals Effect of Horizontal and Vertical Magnetic Fields on Kelvin?Helmholtz Instability

1968 ◽  
Vol 21 (6) ◽  
pp. 917 ◽  
Author(s):  
RC Sharma ◽  
KM Srivastava
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Combined Effect ◽  
Horizontal Motion ◽  
Helmholtz Instability ◽  
The Stability ◽  
Superposed Fluids ◽  
Oblique Magnetic Field

This paper discusses the effect of a general oblique magnetic field on the stability of two superposed fluids in relative horizontal motion. The stable and unstable cases at the interface (z = 0) between two uniform fluids with constant denRities and velocities of streaming are separately discussed. The combined effect of horizontal and vertical magnetic fields is to increase the wavelength at which the Kelvin-Helmholtz instability sets in.

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