On Hydromagnetic Stability of Stationary Equilibria

Frieman, E. A.; Rotenberg, Manuel

doi:10.1103/revmodphys.32.898

Cited by 435 publications

(415 citation statements)

References 2 publications

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“…The advantages of using the Frieman and Rotenburg [16] for mode analysis are tremendous, especially for an investigation of electrostatic modes, where from the start specific forms of the displacement ξ can be chosen so that δJ = 0 and δB = 0. In particular, it will be shown below that GAMs and zonal flow continua in rotating plasmas can be derived intuitively, rigourously and briefly.…”

Section: B Gams and Zonal Flows In Isothermal Ideal Mhd Rotating Plamentioning

confidence: 99%

“…For a description of linear perturbed ideal MHD in a rotating plasma we follow the approach by Frieman and Rotenburg [16]. In this work, a Lagrangian displacement ξ is employed, which can be defined in terms of the Lagrangian perturbed fluid velocity as ∆U ≡ dξ dt = ∂ξ ∂t + U · ∇ξ where the perturbed Lagrangian flow ∆U is related to the Eulerian perturbed vectors X (including the fluid velocity) as ∆X = δX + ξ · ∇X so that Ohm's law…”

Section: B Gams and Zonal Flows In Isothermal Ideal Mhd Rotating Plamentioning

confidence: 99%

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Generalised zonal modes in stationary axisymmetric plasmas

Graves

Wahlberg

2017

Plasma Phys. Control. Fusion

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The MHD model enables derivation and analysis of the rich structure of geodesic acoustic modes (GAMs) and zonal modes in axisymmetric magnetic confined plasmas. The modes are identifiable from a single dispersion relation as two branches of slow magnetosonic continua. The lower frequency branch can be identified as a zonal flow, which in the simplified limit of static plasmas, has vanishing magnetic component. It is shown in this contribution that axisymmetric, and lesser known nonaxisymmetric, zonal modes can be derived from MHD and kinetic models. The work provides a comprehensive derivation of the GAMs and zonal flow continua in static and stationary toroidally rotating plasmas, and investigates the exact solution and structure of a generalised family of zonal modes.

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Section: B Gams and Zonal Flows In Isothermal Ideal Mhd Rotating Plamentioning

confidence: 99%

Section: B Gams and Zonal Flows In Isothermal Ideal Mhd Rotating Plamentioning

confidence: 99%

Generalised zonal modes in stationary axisymmetric plasmas

Graves

Wahlberg

2017

Plasma Phys. Control. Fusion

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“…One of the earliest results on the effect of equilibrium flow on the spectrum is by Frieman and Rotenberg (1960). They showed that the eigenvalue problem becomes quadratic, which implies that the spectrum is no longer restricted to the axes in the complex plane.…”

Section: Introductionmentioning

confidence: 99%

Spectrum and stability of a rigidly rotating compressible plasma

1997

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We consider the spectrum and stability of a compressible, rigidly rotating plasma column with constant magnetic pitch. It is found that when the pressure on axis is zero, a continuous spectrum arises, which may become unstable. When the pressure on axis is finite or a conducting core is included, the spectrum is discrete, but may still be unstable. The instability is due to the poloidal magnetic field and/or the rotation of the cylinder in combination with the density profile. It is found numerically that the pressure stabilizes both types of instabilities.

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“…By differentiating L with respect to , using the -flow analogue of (3.4) (after changing variables to x 0 , y 0 , z 0 , where, as in Frieman & Rotenberg (1960), superscript 0 refers to = 0) and integration by parts (Gauss' theorem) we find the convenient identity…”

Section: Holonomically Constrained and Free Variationsmentioning

confidence: 99%

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

et al. 2015

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Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for the global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, relaxed magnetohydrodynamics (RxMHD), such that all static solutions are Taylor states but also allows state with flow. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, multi-region relaxed magnetohydrodynamics (MRxMHD) is developed.

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On Hydromagnetic Stability of Stationary Equilibria

Cited by 435 publications

References 2 publications

Generalised zonal modes in stationary axisymmetric plasmas

Generalised zonal modes in stationary axisymmetric plasmas

Spectrum and stability of a rigidly rotating compressible plasma

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

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