Hydromagnetic Kelvin-Heimholtz Instability in the Presence of Suspended Particles and Finite Larmor Radius Effect

1994 ◽  
Vol 49 (12) ◽  
pp. 1102-1110 ◽  
Author(s):  
R. K. Sanghvi ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Suspended Particles ◽  
Linear Analysis ◽  
Wave Number ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Finite Larmor Radius ◽  
Simplifying Assumptions ◽  
The Magnetic Field

Abstract A linear analysis of the combined influence of a finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be uniform and transverse to the direction of streaming. The medium is assumed to be incompressible. Certain simplifying assumptions are made for the motion of the suspended particles. A dispersion relation for such a medium has been obtained using appropriate boundary conditions. The stabilizing effect of a finite Larmor radius has been reasserted in the absence of the suspended particles. A stability criterion for the medium is derived, which is found to be independent of the presence of the suspended particles. Similarly a condition of instability of the system is also derived. Numerical analysis is presented in a few limiting cases of interest. Furthermore, growth rates of unstable modes of the configuration with increasing relaxation fre­quency of the particles and finite Larmor radius have been evaluated analytically. It is shown that the finite Larmor radius in the presence of the suspended particles destabilizes a certain wave number band which is stable otherwise. Implications of the suspended particles on the growth rate of unstable modes are discussed in the limit of vanishing ion Larmor radius.

scholarly journals Diffusion at the Earth magnetopause: enhancement by Kelvin-Helmholtz instability

2007 ◽  
Vol 25 (1) ◽  
pp. 271-282 ◽  
Author(s):  
R. Smets ◽  
G. Belmont ◽  
D. Delcourt ◽  
L. Rezeau
Keyword(s):  
Magnetic Field ◽  
Distribution Functions ◽  
Larmor Radius ◽  
Simple Analytical Model ◽  
Helmholtz Instability ◽  
Field Reversal ◽  
Finite Larmor Radius ◽  
The Earth ◽  
Specific Distribution ◽  
The Magnetic Field

Abstract. Using hybrid simulations, we examine how particles can diffuse across the Earth's magnetopause because of finite Larmor radius effects. We focus on tangential discontinuities and consider a reversal of the magnetic field that closely models the magnetopause under southward interplanetary magnetic field. When the Larmor radius is on the order of the field reversal thickness, we show that particles can cross the discontinuity. We also show that with a realistic initial shear flow, a Kelvin-Helmholtz instability develops that increases the efficiency of the crossing process. We investigate the distribution functions of the transmitted ions and demonstrate that they are structured according to a D-shape. It accordingly appears that magnetic reconnection at the magnetopause is not the only process that leads to such specific distribution functions. A simple analytical model that describes the built-up of these functions is proposed.

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.

Effect of finite ion Larmor radius on the Kelvin–Helmholtz instability

1978 ◽  
Vol 20 (2) ◽  
pp. 149-160 ◽  
Author(s):  
Hirosh Nagano
Keyword(s):  
Magnetic Field ◽  
Flow Velocity ◽  
Wave Vector ◽  
Uniform Magnetic Field ◽  
Critical Value ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Finite Larmor Radius ◽  
Compressible Plasma ◽  
The Difference

The effect of finite ion Larmor radius on the Kelvin–Helmholtz instability is investigated in the cases of an incompressible and a compressible plasma. When a wave vector is perpendicular to a uniform magnetic field, the effect of finite Larmor radius (FLR) stabilizes perturbations with a wavenumber exceeding a critical value, while there exists another case that the FLR effect destabilizes still more than the usual MHD approximation. The difference between these cases is decided from the configuration of flow velocity and magnetic field. When a wave vector is parallel to a magnetic field, the FLR effect tends to stabilize perturbations with a larger wavenumber.

Rayleigh-Taylor Instability of a Stratified Plasma

1974 ◽  
Vol 29 (3) ◽  
pp. 518-523 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Boussinesq Approximation ◽  
Short Wave ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Disturbances ◽  
Magnetic Field Gradients ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

We have investigated the effect of finite Larmor radius on the Rayleigh-Taylor instability of a semi-infinite, compressible, stratified and infinitely conducting plasma. The plasma is assumed to have a one dimensional density and magnetic field gradients. The eigenvalue problem has been solved under Boussinesq approximation for disturbances parallel to the magnetic field. It has been established that for perturbation parallel to the magnetic field, the system is stable for both stable and unstable stratification. For perturbation perpendicular to the magnetic field, the problem has been solved without Boussinesq approximation. The dispersion relation has been discussed in the two limiting cases, the short and long wave disturbances. It has been observed that the gyroviscosity has a destabilizing influence from k = 0 to k = 4.5 for ß* = 0.1 and for ß* = 0.1 up to k* = 2.85 and then onwards it acts as a stabilizing agent. It has a damping effect on the short wave disturbances. For some parameters, the largets imaginary part has been shown in Figs. 1 and 2

Effect of finite Larmor radius on Rayleigh–Taylor instability of a plasma

1969 ◽  
Vol 47 (22) ◽  
pp. 2435-2437 ◽  
Author(s):  
P. D. Ariel ◽  
P. K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Density Gradient ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Unstable Configuration ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

The effects of a finite Larmor radius of the ions are investigated on the Rayleigh–Taylor instability of a plasma in which there is a density gradient in a direction perpendicular to that of the magnetic field. It is found that the unstable configuration is completely stabilized by the finite Larmor radius effect.

scholarly journals Stability Of Superposed Fluids Through Magnetic Field With Suspended Particles Of Different Permeability Saturated Through Porous Layer

2015 ◽  
Vol 20 (4) ◽  
pp. 889-898
Author(s):  
M. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Viscous Fluid ◽  
Suspended Particles ◽  
Wave Number ◽  
Mode Analysis ◽  
Dust Particles ◽  
Linearized Stability ◽  
Stable Arrangement ◽  
The Magnetic Field

Abstract The instability of plane interface between two superposed Rivlin-Ericksen elastico-viscous fluids saturated through a porous medium has been studied to include the suspended (dust) particles effect. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like Newtonian fluids. It found that for a potentially stable arrangement the Rivlin-Ericksen elastico-viscous fluid of different permeabilities in the presence of suspended particles in a porous medium is stable, whereas in a potentially unstable case instability of the system occurs. In the presence of a magnetic field for a potentially stable arrangement the system is always stable and for the potentially unstable arrangement, the magnetic field succeeds in stabilizing certain wave-number band which was unstable in the absence of the magnetic field.

Evolution of nonlinear Alfvén waves propagating along the magnetic field in a collisionless plasma

1982 ◽  
Vol 28 (3) ◽  
pp. 459-468 ◽  
Author(s):  
M. Khanna ◽  
R. Rajaram
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Momentum Equation ◽  
Finite Amplitude ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Flr Effects ◽  
The Magnetic Field

It is shown that the asymptotic evolution of a finite-amplitude Alfvén wave propagating parallel to the uniform magnetic field in a warm homogeneous collisionless plasma is governed by the modified nonlinear Schrödinger equation. The dispersion is provided by the ion finite Larmor radius (FLR) effects in the momentum equation and the Hall current and electron pressure corrections to the generalized Ohm's law. In the cold plasma limit the equations reduce to those available in the literature. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in the solar wind.

Effects of Finite Larmor Radius and Hall Currents on Thermosolutal Instability of a Partially Ionized Plasma in Porous Medium

1994 ◽  
Vol 49 (3) ◽  
pp. 469-474 ◽  
Author(s):  
Kirti Prakash ◽  
Seema Manchanda
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Wave Number ◽  
Larmor Radius ◽  
Stationary Convection ◽  
Number Range ◽  
Finite Larmor Radius ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
Partially Ionized

Abstract The effects of finite ion Larmor radius (FLR), collisions and Hall currents on thermosolutal instability of a partially ionized plasma in porous medium in the presence of uniform vertical magnetic field are investigated. It is found that the presence of each magnetic field, FLR, Hall currents and collisions, introduces oscillatory modes which were, otherwise, non-existent. In the case of stationary convection, finite Larmor radius, Hall currents, medium permeability and magnetic field may have stabilizing or destabilizing effects, but for a certain wave number range, FLR, magnetic field and Hall currents have a complete stabilizing effect. The stable solute gradient always has stabilizing effect on the system whereas the collisional effects disappear for the case of stationary convection.

scholarly journals Beat wave cyclotron heating of rippled density plasma

2018 ◽  
Vol 36 (4) ◽  
pp. 465-469 ◽  
Author(s):  
Pushplata ◽  
A. Vijay
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Ponderomotive Force ◽  
Beat Frequency ◽  
Magnetized Plasma ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Heating ◽  
The Magnetic Field ◽  
Density Plasma

AbstractLaser beat wave heating of magnetized plasma via electron cyclotron damping is proposed and analyzed. A plasma density ripple is presumed to exist across the magnetic field. Two collinear lasers propagating along the magnetic field exert a beat frequency ponderomotive force on electrons, driving a large amplitude Bernstein quasi-mode which suffers cyclotron damping on electrons. Finite Larmor radius effects play an important role in the heating. Electron temperature initially rises linearly with time. As the temperature rises cyclotron damping becomes stronger and temperature rises rapidly. The process, however, requires ripple wavelength shorter than the wavelength of the beat wave.

Analysis of electromagnetic instabilities parallel to the magnetic field

1971 ◽  
Vol 6 (1) ◽  
pp. 1-17 ◽  
Author(s):  
W. Pilipp ◽  
H. J. Völk
Keyword(s):  
Magnetic Field ◽  
Cyclotron Frequency ◽  
Larmor Radius ◽  
Collisionless Shocks ◽  
Transverse Waves ◽  
Homogeneous Plasma ◽  
Finite Larmor Radius ◽  
Long Wavelength ◽  
The Earth ◽  
The Magnetic Field

Transverse waves and instabilities propagating along the magnetic field in a homogeneous plasma are discussed analytically and numerically for frequencies of the order of the ion cyclotron frequency and below. The free energy driving the instabilities is assumed to be provided by thermal anisotropies, with the parallel temperature exceeding the perpendicular temperature, a situation appropriate to the solar wind near the earth and to the downstream conditions in collisionless shocks propagating approximately parallel to the magnetic field. It is shown that in the case where the ion β is of order one the long wavelength Firehose instability is not stabilized by finite Larmor radius effects, but that for smaller wavelengths it goes over smoothly into the resonant proton mode, discussed by Kennel & Scarf (1968).

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