Dispersion relation for pressure-driven toroidal modes including finite Larmor radius effects

1985 ◽  
Vol 25 (12) ◽  
pp. 1761-1766 ◽  
Author(s):  
P. Andersson ◽  
J. Weiland
Keyword(s):  
Dispersion Relation ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Pressure Driven

Nonlinear theory of large-mode-number ballooning modes in fully toroidal geometry

1985 ◽  
Vol 34 (1) ◽  
pp. 143-161 ◽  
Author(s):  
J. P. Mondt ◽  
J. Weiland
Keyword(s):  
Dispersion Relation ◽  
Aspect Ratio ◽  
Model Equation ◽  
Larmor Radius ◽  
Low Density ◽  
Magnetic Shear ◽  
Explosive Instability ◽  
Finite Larmor Radius ◽  
Special Case ◽  
Toroidal Geometry

A nonlinear model equation describing ballooning modes for β of the order of the inverse aspect ratio and including magnetic shear is derived. For the special case of circular concentric flux surfaces, we obtain an approximate dispersion relation, including finite Larmor radius effects, and show the possibility of explosive instability in the nonlinear regime. The results are shown to remain valid in the presence of a low-density hot-ion constituent.

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.

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.

Finite-Larmor-radius stabilization of the m = 2 instability in the Isar T1-B high-beta stellarator

1977 ◽  
Vol 17 (1) ◽  
pp. 3-11 ◽  
Author(s):  
J. Neuhauser ◽  
M. Kaufmann ◽  
H. Röhr ◽  
G. Schramm
Keyword(s):  
Larmor Radius ◽  
Finite Larmor Radius ◽  
High Beta

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

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