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 Thermal Instability in Plasma with Finite Larmor Radius

1975 ◽  
Vol 30 (4) ◽  
pp. 461-465
Author(s):  
R. C. Sharma ◽  
Kirti Prakash
Keyword(s):  
Magnetic Field ◽  
Thermal Instability ◽  
Larmor Radius ◽  
Stationary Convection ◽  
Horizontal Magnetic Field ◽  
Finite Larmor Radius ◽  
Stabilizing Effect

Abstract The effects of the finite Larmor radius of the ions on the thermal instability of a plasma are investigated. When the instability sets in as stationary convection, the finite Larmor radius is found to have a stabilizing effect. The conditions for the nonexistence of overstability are investigated. The case with horizontal magnetic field is discussed.

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.

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.

Finite-Larmor-radius effects on anisotropy-driven electromagnetic modes in high-beta plasmas

1979 ◽  
Vol 22 (2) ◽  
pp. 257-275 ◽  
Author(s):  
J. Goedert ◽  
J. P. Mondt
Keyword(s):  
Larmor Radius ◽  
Homogeneous Case ◽  
Ion Energy ◽  
Local Dispersion ◽  
Finite Larmor Radius ◽  
Conducting Wall ◽  
Linear Differential ◽  
The Stability ◽  
High Beta ◽  
Correction Terms

From hybrid-kinetic theory an eigenvalue equation for electromagnetic perturbations with ω ≈ ωci in collisionless theta-pinches with anisotropic ion energy was recently derived. This equation is presently reduced to two ordinary second-order linear differential equations by an expansion in the thermal ion Larmor radius. The leading-order correction terms contain Cherenkov resonances absent in the homogeneous case, which are reached for speeds ≈ υ| β|-½ and wave-numbers typical for unstable modes in the homogeneous case, indicating the importance of Cherenkov resonance on the stability of modes driven by ion energy anisotropy. These equations are supplemented by appropriate boundary conditions for the case when the plasma is surrounded by a cylindrical, perfectly conducting wall. For weak inhomogeneities a local dispersion equation is obtained. The physical mechanism underlying the influence of Cherenkov resonance parallel to the confining magnetic field as a FLR effect on stability behaviour is illustrated.

scholarly journals On Thermal Convection of a Plasma in Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 110-119
Author(s):  
Pardeep Kumar ◽  
Sumit Gupta
Keyword(s):  
Magnetic Field ◽  
Thermal Convection ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
The Magnetic Field

The effect of finite Larmor radius of the ions on thermal convection of a plasma is investigated. The case with vertical magnetic field is discussed. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius is found to have a stabilizing effect. Medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain conditions in the presence of finite Larmor radius effect whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively. The sufficient conditions for the non-existence of overstability are also obtained.

Excitation of Alfvén waves by fast particles in a finite pressure plasma of adiabatic traps

1978 ◽  
Vol 20 (1) ◽  
pp. 137-148 ◽  
Author(s):  
B. I. Meerson ◽  
A. B. Mikhallovskii ◽  
O. A. Pokhotelov
Keyword(s):  
Uniform Magnetic Field ◽  
Alfven Waves ◽  
Larmor Radius ◽  
Alfvén Waves ◽  
Trapped Particles ◽  
Resonance Effects ◽  
Finite Larmor Radius ◽  
Pressure Plasma ◽  
Pressure Stabilization ◽  
Instability Growth

Resonant excitation of Alfvén waves by fast particles in a finite pressure plasma in a non-uniform magnetic field is studied. Plasma compressibility in the wave field is determined both by the curvature of the magnetic lines of force and finite Larmor radius of fast particles. A general expression for the instability growth rate is obtained and analyzed; the applicability of the results obtained in the previous paper has also been studied. The finite pressure stabilization of the trapped particles instability has been found. The bounce-resonance effects are analyzed.

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

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.

Sign in / Sign up

Export Citation Format

Share Document