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.

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.

Self-gravitational instability of dense degenerate viscous anisotropic plasma with rotation

2017 ◽  
Vol 83 (6) ◽  
Author(s):  
Prerana Sharma ◽  
Archana Patidar
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Instability Criterion ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Degenerate Plasma ◽  
Finite Larmor Radius ◽  
Quantum Parameter ◽  
Longitudinal Modes ◽  
The Magnetic Field

The influence of finite Larmor radius correction, tensor viscosity and uniform rotation on self-gravitational and firehose instabilities is discussed in the framework of the quantum magnetohydrodynamic and Chew–Goldberger–Low (CGL) fluid models. The general dispersion relation is obtained for transverse and longitudinal modes of propagation. In both the modes of propagation the dispersion relation is further analysed with respect to the direction of the rotational axis. In the analytical discussion the axis of rotation is considered in parallel and in the perpendicular direction to the magnetic field. (i) In the transverse mode of propagation, when rotation is parallel to the direction of the magnetic field, the Jeans instability criterion is affected by the rotation, finite Larmor radius (FLR) and quantum parameter but remains unaffected due to the presence of tensor viscosity. The calculated critical Jeans masses for rotating and non-rotating dense degenerate plasma systems are$3.5M_{\odot }$and$2.1M_{\odot }$respectively. It is clear that the presence of rotation enhances the threshold mass of the considered system. (ii) In the case of longitudinal mode of propagation when rotation is parallel to the direction of the magnetic field, Alfvén and viscous self-gravitating modes are obtained. The Alfvén mode is modified by FLR corrections and rotation. The analytical as well as graphical results show that the presence of FLR and rotation play significant roles in stabilizing the growth rate of the firehose instability by suppressing the parallel anisotropic pressure. The viscous self-gravitating mode is significantly affected by tensor viscosity, anisotropic pressure and the quantum parameter while it remains free from rotation and FLR corrections. When the direction of rotation is perpendicular to the magnetic field, the rotation of the considered system coupled the Alfvén and viscous self-gravitating modes to each other. The finding of the present work is applicable to strongly magnetized dense degenerate plasma.

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.

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

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.

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.

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 Finite-Larmor-radius equilibrium and currents of the Earth’s flank magnetopause

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
S. S. Cerri
Keyword(s):  
Fluid Model ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Current Layer ◽  
Ion Dynamics ◽  
Finite Larmor Radius ◽  
Analytic Expressions ◽  
The One ◽  
Flr Effects ◽  
The Magnetic Field

We consider the one-dimensional equilibrium problem of a shear-flow boundary layer within an ‘extended-fluid model’ of a plasma that includes the Hall and the electron pressure terms in Ohm’s law, as well as dynamic equations for anisotropic pressure for each species and first-order finite-Larmor-radius (FLR) corrections to the ion dynamics. We provide a generalized version of the analytic expressions for the equilibrium configuration given in Cerri et al., (Phys. Plasmas, vol. 20 (11), 2013, 112112), highlighting their intrinsic asymmetry due to the relative orientation of the magnetic field $\boldsymbol{B}$, $\boldsymbol{b}=\boldsymbol{B}/|\boldsymbol{B}|$, and the fluid vorticity $\unicode[STIX]{x1D74E}=\unicode[STIX]{x1D735}\times \boldsymbol{u}$ (‘$\unicode[STIX]{x1D74E}\boldsymbol{b}$ asymmetry’). Finally, we show that FLR effects can modify the Chapman–Ferraro current layer at the flank magnetopause in a way that is consistent with the observed structure reported by Haaland et al., (J. Geophys. Res. (Space Phys.), vol. 119, 2014, pp. 9019–9037). In particular, we are able to qualitatively reproduce the following key features: (i) the dusk–dawn asymmetry of the current layer, (ii) a double-peak feature in the current profiles and (iii) adjacent current sheets having thicknesses of several ion Larmor radii and with different current directions.

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.

Stability Of Rotating Gravitating Streams

2005 ◽  
Vol 60 (7) ◽  
pp. 484-488 ◽  
Author(s):  
P. K. Bhatia ◽  
R. P. Mathur
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Critical Wave Number ◽  
Horizontal Magnetic Field ◽  
Axis Of Rotation ◽  
Streaming Velocity ◽  
The Stability ◽  
The Magnetic Field

This paper treats the stability of two superposed gravitating streams rotating about the axis transverse to the horizontal magnetic field. The critical wave number for instability is found to be affected by rotation for propagation perpendicular to the axis about which the system rotates. The critical wave number for instability is not affected by rotation when waves propagate along the axis of rotation. The critical wave number is affected by both the magnetic field and the streaming velocity in both cases. Both the magnetic field and the rotation are stabilizing, while the streaming velocity is destabilizing.

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