Geodesic Acoustic Mode Induced by Toroidal Rotation in Tokamaks

Wahlberg, Christer

doi:10.1103/physrevlett.101.115003

Cited by 62 publications

(110 citation statements)

References 25 publications

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“…[8] it was shown that continuum modes oscillating at the Brunt-Väisälä [9] frequency directly impacts the stabilily threshold of the internal kink mode, and that inconsistent treatment of the effect of toroidal rotation on the continuum mode would lead to erroneous results. The mode oscillating at the Brunt-Väisälä frequency is in fact a finite n zonal mode, which arises as one of two roots [10] from a dispersion relation that also defines the geodesic acoustic mode. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Generalised zonal modes in stationary axisymmetric plasmas

Graves

Wahlberg

2017

Plasma Phys. Control. Fusion

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“…According to Ref. [65], at the rational surface these frequencies are equal. 1 Repeating the procedure of Refs.…”

Section: A Torusmentioning

confidence: 97%

“…1) for isothermal magnetic surfaces, this result agrees with that of Refs. [44,65,47] for the low-frequency Alfvén continuum. In the limit f ?…”

Section: A Torusmentioning

confidence: 99%

The Brunt–Väisälä frequency of rotating tokamak plasmas

Haverkort

Blank

Koren

2012

Journal of Computational Physics

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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.

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“…͑13b͒ ͑for 1 Ͼ 0͒ of the GAM induced by the plasma rotation. 15 This frequency appears in the stability problem as a finite continuum frequency in the q Ϸ 1 layer, and it is this continuum frequency that, in a mathematical sense, is responsible for the stabilization seen in the examples discussed above. It is this stabilization that is interpreted as gyroscopic in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…In a recent paper, 15 the effect of the parametrization in Eq. ͑2a͒ for the continuous MHD spectrum of rotating plasmas was discussed, in particular the vanishing of the stabilizing continuum frequency in Eq.…”

Section: Introductionmentioning

confidence: 99%

Importance of centrifugal effects for the internal kink mode stability in toroidally rotating tokamak plasmas

Wahlberg

Chapman

Graves³

2009

Physics of Plasmas

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Analytical theory and two different magnetohydrodynamical stability codes are used in a study of the effects of toroidal plasma rotation on the stability of the ideal, internal kink mode in tokamaks. The focus of the paper is on the role that the centrifugal effects on the plasma equilibrium play for the stability of this mode, and results from one code where centrifugal effects are self-consistently included ͑CASTOR-FLOW͒ ͓E. Strumberger et al., Nucl. Fusion 45, 1156 ͑2005͔͒ are compared with the results from another code where such effects are not taken into account ͑MISHKA-F͒ ͓I. T. Chapman et al., Phys. Plasmas 13, 062511 ͑2006͔͒. It is found that, even at rather modest flow speeds, the centrifugal effects are very important for the stability of the internal kink mode. While the results from the two codes can be quite similar for certain profiles in the plasma, completely opposite results are obtained for other profiles. A very good agreement between analytical theory and the numerical results are, both for inconsistent and consistent equilibria, found for plasmas with large aspect ratio. From the analytical theory, the distinctly different stability properties of equilibria with and without centrifugal effects included can be traced to the stabilizing effect of the geodesic acoustic mode ͑GAM͒ induced by the plasma rotation. This GAM exists solely as a consequence of the nonuniform plasma density and pressure created by the centrifugal force on the flux surfaces, and a stabilizing coupling of the internal kink instability to this mode cannot therefore take place if the centrifugal effects are not included in the equilibrium. In addition to the GAM stabilization, the effects of the radial profiles of the plasma density and rotation velocity are also found to be significant, and the importance of these effects increases with decreasing aspect ratio.

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Geodesic Acoustic Mode Induced by Toroidal Rotation in Tokamaks

Cited by 62 publications

References 25 publications

Generalised zonal modes in stationary axisymmetric plasmas

Generalised zonal modes in stationary axisymmetric plasmas

The Brunt–Väisälä frequency of rotating tokamak plasmas

Importance of centrifugal effects for the internal kink mode stability in toroidally rotating tokamak plasmas

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