scholarly journals Ion Confinement in a Toroidal Heliac

1998 ◽  
Vol 51 (1) ◽  
pp. 67
Author(s):  
J. L. V. Lewandowski
Keyword(s):  
Numerical Simulations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Larmor Radius ◽  
Collision Term ◽  
Magnetic Topology ◽  
Finite Larmor Radius ◽  
Confinement Mode

A model to describe an unmagnetised plasma in three-dimensional magnetic topology is presented. Ion trajectories are integrated numerically and all finite-Larmor radius effects are retained exactly. A velocity-dependent collision term is included in the equations of motion. Numerical simulations relevant to the low-confinement mode of H1-NF are presented and discussed.

scholarly journals Magnetic holes in plasmas close to the mirror instability

2007 ◽  
Vol 14 (4) ◽  
pp. 373-383 ◽  
Author(s):  
D. Borgogno ◽  
T. Passot ◽  
P. L. Sulem
Keyword(s):  
Numerical Simulations ◽  
Fluid Model ◽  
Instability Threshold ◽  
Landau Damping ◽  
Larmor Radius ◽  
Maxwell System ◽  
Unstable Regime ◽  
Finite Larmor Radius ◽  
Spatio Temporal ◽  
Hall Mhd

Abstract. Non-propagating magnetic hole solutions in anisotropic plasmas near the mirror instability threshold are investigated in numerical simulations of a fluid model that incorporates linear Landau damping and finite Larmor radius corrections calculated in the gyrokinetic approximation. This FLR-Landau fluid model reproduces the subcritical mirror bifurcation recently identified on the Vlasov-Maxwell system, both by theory and numerics. Stable magnetic hole solutions that display a polarization different from that of Hall-MHD solitons are indeed obtained slighlty below threshold, while magnetic patterns and spatio-temporal chaos emerge when the system is maintained in a mirror unstable regime.

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.

Finite Larmor Radius and Three-Dimensional Effects on the Blobs in the Scrape-Off Layer

2008 ◽  
Author(s):  
D. Jovanović ◽  
P. K. Shukla ◽  
F. Pegoraro ◽  
Padma K. Shukla ◽  
Bengt Eliasson ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Dimensional Effects

scholarly journals Latitudinal libration driven flows in triaxial ellipsoids

2015 ◽  
Vol 771 ◽  
pp. 193-228 ◽  
Author(s):  
S. Vantieghem ◽  
D. Cébron ◽  
J. Noir
Keyword(s):  
Numerical Simulations ◽  
Equations Of Motion ◽  
Liquid Core ◽  
Three Dimensional ◽  
Base Flow ◽  
Upper And Lower Bounds ◽  
Earth Planet ◽  
Ekman Layers ◽  
Core Dynamics ◽  
Inertial Instability

Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a resonance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir & Cébron, J. Fluid Mech., vol. 737, 2013, pp. 412–439). This theoretical approach is consistent with the results of Chan et al. (Phys. Earth Planet. Inter., vol. 187, 2011, pp. 404–415) and Zhang et al. (J. Fluid Mech., vol. 692, 2012, pp. 420–445) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear stability analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz & Hameiri, Phys. Fluids A, vol. 3, 1991, p. 2644; Gledzer & Ponomarev, Acad. Sci., USSR, Izv., Atmos. Ocean. Phys., vol. 13, 1977, pp. 565–569) that allow us to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.

Proposed Solution Methodology for the Dynamically Coupled Nonlinear Geared Rotor Mechanics Equations

1985 ◽  
Vol 107 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. D. Mitchell ◽  
J. W. David
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Three Dimensional ◽  
Dynamic Coupling ◽  
State Response ◽  
Shaft System ◽  
Coupling Terms ◽  
Solution Methodology

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Quasi-particles in magnetized plasmas: second-order approximation

1995 ◽  
Vol 53 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Petro P. Sosenko†
Keyword(s):  
Magnetic Fields ◽  
Order Approximation ◽  
Equations Of Motion ◽  
Second Order ◽  
Larmor Radius ◽  
Magnetized Plasmas ◽  
Quasi Particle ◽  
Second Order Approximation ◽  
Finite Larmor Radius ◽  
Particle Properties

A second-order approximation is formulated and studied within the context of the quasi-particle description of magnetized plasmas. The general case of relativistic particles in non-uniform but stationary magnetic fields, and in additional force fields that are strongly non-uniform but slowly evolving in time compared with particle gyrations with the cyclotron frequency, is considered. In order to reveal the physical significance of the second-order approximation, the mean (reduced) particle velocity is calculated up to second order, when polarization particle drift as well as the renormalization of the lower-order result become equally significant. A general expression for the velocity of particle polarization drift is obtained in terms of quasi-particle properties, and with account taken of finite-Larmor-radius effects and non-uniformity of magnetic fields. A guiding-centre transformation is found that makes it possible to achieve equal mean velocities of particle, guiding centre and quasi-particle up to second order. Then polarization drifts enter the particle, guiding-centre and quasi-particle equations of motion.

Gyrokinetic Simulation of Magnetic Compressional Modes in General Geometry

2011 ◽  
Vol 10 (4) ◽  
pp. 899-911 ◽  
Author(s):  
Peter Porazik ◽  
Zhihong Lin
Keyword(s):  
Balance Equation ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Force Balance ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Phase Space Integration ◽  
General Geometry ◽  
Compressional Component ◽  
Force Balance Equation

AbstractA method for gyrokinetic simulation of low frequency (lower than the cyclotron frequency) magnetic compressional modes in general geometry is presented. The gyrokinetic-Maxwell system of equations is expressed fully in terms of the compressional component of the magnetic perturbation, δB∥, with finite Larmor radius effects. This introduces a “gyro-surface” averaging of δB∥ in the gyrocenter equations of motion, and similarly in the perpendicular Ampere’s law, which takes the form of the perpendicular force balance equation. The resulting system can be numerically implemented by representing the gyro-surface averaging by a discrete sum in the configuration space. For the typical wavelength of interest (on the order of the gyroradius), the gyro-surface averaging can be reduced to averaging along an effective gyro-orbit. The phase space integration in the force balance equation can be approximated by summing over carefully chosen samples in the magnetic moment coordinate, allowing for an efficient numerical implementation.

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