New construction of the magnetohydrodynamic spectrum of stationary plasma flows. I. Solution path and alternator

Goedbloed, J. P.

doi:10.1063/1.3271164

Cited by 15 publications

(26 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will consider the stability of modes that are radially highly localized, without taking into account the coupling between poloidal harmonics leading to poloidal localization. For such localized modes, the Coriolis shift [44] is much smaller than the Doppler shift so that we can assume that marginal stability holds for ω D ≈ 0. When γ > 1, the ω − -continuum will not vanish at the rational surface.…”

Section: Derivation Of a Stability Criterionmentioning

confidence: 99%

Stability of localized modes in rotating tokamak plasmas

Haverkort

Blank

2011

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

The ideal magnetohydrodynamic stability is investigated of localized interchange modes in a large-aspect ratio tokamak plasma. The resulting stability criterion includes the effects of toroidal rotation and rotation shear and contains various well-known limiting cases. The analysis allows for a general adiabatic index, resulting in a stabilizing contribution from the convective effect. A further stabilizing effect from rotation exists when the angular frequency squared decreases radially more rapidly than the density. Flow shear, however, also decreases the stabilizing effect of magnetic shear through the KelvinHelmholtz mechanism. Numerical simulations reveal the merits and limitations of the performed local analysis.

show abstract

Section: Derivation Of a Stability Criterionmentioning

confidence: 99%

Stability of localized modes in rotating tokamak plasmas

Haverkort

Blank

2011

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

show abstract

“…The following quadratic form ͑called the average Doppler-Coriolis shift by Goedbloed et al 2,7,10 ͒ needs no adjustment:…”

Section: Reformulation Of Quadratic Forms and Stability Criteriamentioning

confidence: 99%

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

Andries

2010

Physics of Plasmas

View full text Add to dashboard Cite

The frequencies of the normal modes of oscillation of linear magnetohydrodynamic perturbations of a stationary equilibrium are related to the stationary points of a quadratic functional over the Hilbert space of Lagrangian displacement vectors, which is subject to a constraint. In the absence of a background flow (or of a uniform flow), the relation reduces to the well-known Rayleigh–Ritz variational principle. In contrast to the existing variational principles for perturbations of stationary equilibria, the present treatment does neither impose additional symmetry restrictions on the equilibrium, nor does it involve the generalization to bilinear functionals instead of quadratic forms. This allows a more natural interpretation of the quadratic forms as energy functionals.

show abstract

“…Taking the inner product of Eqs. (56) or (58) with n ⁄ and integrating over the entire plasma volume gives, solving for x [58,60] …”

Section: Stabilitymentioning

confidence: 99%

The Brunt–Väisälä frequency of rotating tokamak plasmas

Haverkort

Blank

Koren

2012

Journal of Computational Physics

View full text Add to dashboard Cite

a b s t r a c tThe continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt-Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.

show abstract

New construction of the magnetohydrodynamic spectrum of stationary plasma flows. I. Solution path and alternator

Cited by 15 publications

References 59 publications

Stability of localized modes in rotating tokamak plasmas

Stability of localized modes in rotating tokamak plasmas

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

The Brunt–Väisälä frequency of rotating tokamak plasmas

Contact Info

Product

Resources

About