HYDROMAGNETIC KELVIN INSTABILITY IN THE PRESENCE OF NEUTRAL PARTICLES

1967 ◽  
Vol 45 (8) ◽  
pp. 2779-2785 ◽  
Author(s):  
S. S. Rao ◽  
G. L. Kalra
Keyword(s):  
Magnetic Field ◽  
Speed Of Sound ◽  
Uniform Magnetic Field ◽  
Collision Frequency ◽  
Wave Number ◽  
Tangential Discontinuity ◽  
Neutral Particles ◽  
The Stability

The stability of a tangential discontinuity in velocity in a plasma mixed with cold neutral particles is investigated in the presence of a uniform magnetic field. It is found that the effect of collisions between the plasma and the neutral particles is stabilizing or destabilizing according as ν, the collision frequency, is less than or greater than the parameter kc, where k is the wave number of the perturbation and c is the speed of sound for the plasma.

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.

The stability of viscous flow in a curved channel in the presence of a magnetic field

1961 ◽  
Vol 264 (1317) ◽  
pp. 155-164 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Uniform Magnetic Field ◽  
Axial Direction ◽  
Electrical Conductor ◽  
Curved Channel ◽  
Coaxial Cylinders ◽  
Transverse Pressure ◽  
The Stability ◽  
The Magnetic Field

The stability of viscous flow between two coaxial cylinders maintained by a constant transverse pressure gradient is considered when the fluid is an electrical conductor and a uniform magnetic field is impressed in the axial direction. The problem is solved and the dependence of the critical number for the onset of instability on the strength of the magnetic field and the coefficient of electrical conductivity of the fluid is determined.

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.

The effect of a radial magnetic field on the stability of Couette flow

1994 ◽  
Vol 72 (5-6) ◽  
pp. 258-265 ◽  
Author(s):  
M. A. Ali
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problem ◽  
Incompressible Fluid ◽  
Couette Flow ◽  
Wave Number ◽  
Rotating Cylinders ◽  
Radial Magnetic Field ◽  
Electrically Conducting ◽  
Angular Velocities ◽  
The Stability

The effect of a radial magnetic field on the stability of an electrically conducting incompressible fluid between two concentric rotating cylinders is considered. The eigenvalue problem for determining the critical Taylor number TC and the corresponding wave number aC is solved numerically for different values of ±μ(= Ω2/Ω1), (where Ω1, and Ω2 are me angular velocities of the inner and outer cylinders, respectively) and for different gap sizes. It is observed that the radial magnetic field stabilizes the flow. This effect is more pronounced for cylinders that are corotating as compared with counter-rotating cylinders or the situation where only the inner one is rotating.

On the Hydromagnetic Kelvin-Helmholtz Instability between Compressible Fluids

1974 ◽  
Vol 29 (6) ◽  
pp. 888-892 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Compressible Fluids ◽  
Plane Interface ◽  
Helmholtz Instability ◽  
Solar Plasma ◽  
The Stability ◽  
Conducting Fluids ◽  
Equal Density

We have discussed the effect of gravity on the hydromagnetic Kelvin-Helmholtz instability of a plane interface between compressible, inviscid, infinitely conducting fluids. The stability of the interface is investigated including gravity. The solar plasma and the magnetospheric medium are supposed to be of equal density and to carry a uniform magnetic field (H ) in the direction of streaming. The cases (i) H1 ≠ H2 and x1 (x = cp/cv) not necessarily equal to x2 , (ii) H1= H2 x1 ≠ x2 and (iii) H1 = H2, x1=x2 are discussed for perturbations, transverse as well as parallel to the direction of streaming. It is concluded that the interface is unstable in all the cases except for transverse perturbations, the two media carrying the same magnetic field and being characterized by the same x, when it is found to be verlocity.

Stability of a cold plasma traversed by two electron beams in the presence of an external magnetic field

1969 ◽  
Vol 47 (3) ◽  
pp. 249-256
Author(s):  
R. Jayakaran Isaac
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Short Wavelength ◽  
Cold Plasma ◽  
Electron Beams ◽  
Dispersion Relations ◽  
Wave Number ◽  
Longitudinal Modes ◽  
Transverse Modes ◽  
The Stability

In this paper, the stability of a cold plasma traversed by two electron beams in the presence of an external magnetic field is investigated. Dispersion relations for both longitudinal and transverse modes have been obtained. These dispersion relations have been discussed with respect to the two limiting cases of long- and short-wavelength disturbances. Apart from this, the dispersion relation for transverse modes has been solved numerically for a number of cases. It is found that the system becomes unstable against long-wavelength disturbances while it is stable against short-wavelength disturbances. In particular, for longitudinal modes, those perturbations whose wavelengths are such that their frequencies are near the corresponding frequencies of either of the two beams are found to be unstable. It is also found, numerically, in the case of transverse modes, that under certain conditions there exists a critical value of the wave number α, say α*, such that the system is unstable for the perturbations whose wave numbers satisfy the condition α < α*.

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.

Article

1998 ◽  
Vol 76 (12) ◽  
pp. 937-947
Author(s):  
M Takashima
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Wave Speed ◽  
Critical Reynolds Number ◽  
Maximum Velocity ◽  
Transverse Magnetic ◽  
Wave Number ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of combined plane Poiseuille and Couette flow of an electricallyconducting fluid under a transverse magnetic field is investigated using linear stability theory.In deriving the equations governing the stability, the so-called magnetic Stokes approximationis made using the fact that the magnetic Prandtl number Prm for most electrically conductingfluids is extremely small. The Chebyshev collocation method is adopted to obtain theeigenvalue equation, which is then solved numerically. The critical Reynolds number Rec,the critical wave number αc, and the critical wave speed cc are obtained for wide ranges ofthe Hartmann number Ha and the parameter k = U0 / (U0 + nu0), where U0 is the maximumvelocity of pure Couette flow and nu0 is the maximum velocity of pure Poiseuille flow. It isfound that a transverse magnetic field has both stabilizing and destabilizing effects on theflow depending on the value of k.PACS Nos. 47.20

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