The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle

Andries, Jesse

doi:10.1063/1.3505095

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…(A3) actually represents the self-adjoint Galilean invariant generalized force operator deployed for example in Refs. [38,39]. The total force operator of Frieman and Rotenberg [12] is given by…”

Section: Generalmentioning

confidence: 99%

Flow shear stabilization of rotating plasmas due to the Coriolis effect

Haverkort

Blank

2012

Phys. Rev. E

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A radially decreasing toroidal rotation frequency can have a stabilizing effect on nonaxisymmetric magnetohydrodynamic (MHD) instabilities. We show that this is a consequence of the Coriolis effect that induces a restoring pressure gradient force when plasma is perturbed radially. In a rotating cylindrical plasma, this Coriolis-pressure effect is canceled by the centrifugal effect responsible for the magnetorotational instability. In a magnetically confined toroidal plasma, a large aspect ratio expansion shows that only half of the effect is canceled. This analytical result is confirmed by numerical computations. When the plasma rotates faster toroidally in the core than near the edge, the effect can contribute to the formation of transport barriers by stabilizing MHD instabilities.

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Section: Generalmentioning

confidence: 99%

Flow shear stabilization of rotating plasmas due to the Coriolis effect

Haverkort

Blank

2012

Phys. Rev. E

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“…The method has been applied to the exemplary 1D problems of Rayleigh-Taylor and Kelvin-Helmholtz instabilities of a plane gravitating plasma with arbitrary velocity field. A variational counterpart has been formulated recently [29]. The method is presently being applied to the magneto-rotational instabilities of accretion disks (with Keppens) and to the resistive wall mode instabilities of tokamaks (with J P Freidberg).…”

Section: Perspectivesmentioning

confidence: 99%

New approach to magnetohydrodynamics spectral theory of stationary plasma flows

Goedbloed

2011

Plasma Phys. Control. Fusion

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While the basic equations of MHD spectral theory date back to 1958 for static plasmas (Bernstein et al 1958 Proc. R. Soc. A 244 17) and to 1960 for stationary plasma flows (Frieman and Rotenberg 1960 Rev. Mod. Phys. 32 898), progress on the latter subject has been slow since it suffers from lack of analytical insight concerning the structure of the spectrum. One of the reasons is the usual misnomer of 'non-self adjointness' of the stationary flow problem. Actually, self-adjointness of the occurring operators, namely the generalized force operator and the Doppler-Coriolis gradient operator −iρv•∇, was proved right away by Frieman and Rotenberg. Based on the reality of the two quadratic forms corresponding to these operators, we here construct (a) an effective method to compute the solution paths in the complex ω plane on which the eigenvalues are situated, (b) the counterpart of the oscillation theorem for eigenvalues of static equilibria (Goedbloed and Sakanaka 1974 Phys. Fluids 17 908) for the eigenvalues of stationary flows, based on the monotonicity of the alternating ratio, or alternator, of the boundary values of the displacement ξ and the total pressure perturbation . This enables one to map out the complete spectrum of eigenvalues in the complex ω-plane. The intricate topology of the solution paths is discussed for the fundamental examples of Rayleigh-Taylor, Kelvin-Helmholtz and combined instabilities.

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“…Different approaches have been taken to study such processes. For example Goedbloed (2009a) and Andries (2010) have developed methods to construct the eigenfunction spectrum of stationary magnetohydrodynamic flows. Goedbloed (2009b) has applied his method in a plane geometry to study the Kelvin-Helmholtz and Rayleigh-Taylor instabilities in the presence of a gravitational field.…”

Section: Introductionmentioning

confidence: 99%

Energy exchange and wave action conservation for magnetohydrodynamic (MHD) waves in a general, slowly varying medium

Walker

2014

Ann. Geophys.

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Abstract. Magnetohydrodynamic (MHD) waves in the solar wind and magnetosphere are propagated in a medium whose velocity is comparable to or greater than the wave velocity and which varies in both space and time. In the approximation where the scales of the time and space variation are long compared with the period and wavelength, the ray-tracing equations can be generalized and then include an additional first-order differential equation that determines the variation of frequency. In such circumstances the wave can exchange energy with the background: wave energy is not conserved. In such processes the wave action theorem shows that the wave action, defined as the ratio of the wave energy to the frequency in the local rest frame, is conserved. In this paper we discuss ray-tracing techniques and the energy exchange relation for MHD waves. We then provide a unified account of how to deal with energy transport by MHD waves in nonuniform media. The wave action theorem is derived directly from the basic MHD equations for sound waves, transverse Alfvén waves, and the fast and slow magnetosonic waves. The techniques described are applied to a number of illustrative cases. These include a sound wave in a medium undergoing a uniform compression, an isotropic Alfvén wave in a steady-state shear layer, and a transverse Alfvén wave in a simple model of the magnetotail undergoing compression. In each case the nature and magnitude of the energy exchange between wave and background is found.

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The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle

Cited by 4 publications

References 9 publications

Flow shear stabilization of rotating plasmas due to the Coriolis effect

Flow shear stabilization of rotating plasmas due to the Coriolis effect

New approach to magnetohydrodynamics spectral theory of stationary plasma flows

Energy exchange and wave action conservation for magnetohydrodynamic (MHD) waves in a general, slowly varying medium

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