Singular global components and frequency shift of the geodesic acoustic continuum modes in shaped tokamaks

Wahlberg, Christer; Graves, J. P.

doi:10.1088/1361-6587/ab1d22

Cited by 7 publications

(40 citation statements)

References 56 publications

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“…In addition, we stress that the assumption of (κ 2 − 1)/(κ 2 + 1) ∼ O(ϵ) is not adopted in this paper, and consequently, equations ( 13) and ( 14) are suitable for an arbitrary value of κ. Except for the inherent discrepancies caused by gyro-kinetic model and MHD model, equation ( 13) coincides with equation (3) in the shaping effects, the result of Sorokina et al [32], and is also qualitatively similar to the result of Wahlberg et al, equation (1.4) of [33].…”

Section: Dispersion Relationsupporting

confidence: 74%

“…Recently, TCV reported a nearly linear increasing GAM frequency with δ from − 0.2 to 0.3 measured by Z. Huang and S. Coda, and the dependence tended to be weakened for negative δ, as the figure 5(b) shown in [33]. Compared to TCV results, equation (3) indicates a fairly weak dependence on δ.…”

Section: Introductionmentioning

confidence: 84%

“…Compared to TCV results, equation (3) indicates a fairly weak dependence on δ. By utilizing MHD equations and a global shaping model, another result containing the Shafranov shift gradient ∆ ′ was obtained by Wahlberg and Graves [33]. However, discrepancies still exist between the existing analytical results and TCV observations.…”

Section: Introductionmentioning

confidence: 99%

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Shaping effects on the geodesic acoustic mode in tokamaks

Chen

Ren

2023

Nucl. Fusion

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The geodesic acoustic mode (GAM) is investigated with gyro-kinetic equations in Miller local equilibrium model for shaped tokamak plasmas with an arbitrary elongation κ and a finite triangularity δ. In particular, the effects of triangularity on GAM frequency and damping rate are analyzed both analytically and numerically. The asymptotic analytical and exact numerical results both show that the frequency almost linearly increases with the triangularity but increases relatively more slowly for a negative δ, which agree well with the TCV observation on the trend. The analytical results clearly claim that the triangularity effect strength is dependent on the inverse aspect ratio ε and Shafranov shift gradient Δ′, while the numerical results indicate that the safety factor q also has a significant impact on the triangularity effects. In addition, the damping rate increases rapidly with triangularity when q is not too large and then saturates when δ is above about 0.3.

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Section: Dispersion Relationsupporting

confidence: 74%

Section: Introductionmentioning

confidence: 84%

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Shaping effects on the geodesic acoustic mode in tokamaks

Chen

Ren

2023

Nucl. Fusion

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“…The dependence is almost linear, and of particular interest, continues to decrease with negative triangularity. While some analytic formulations, such as that of Sorokina, equation (259) which includes δ terms, indicate a weak positive frequency dependence, a comparison with the MHD formulation of Wahlberg which also retained κ, Δ and their radial gradients showed a more reasonable agreement [157]. The sign and magnitude of δ was recently found to have a significant impact on the core turbulence in TCV [457], specifically a reduction of turbulent electron temperature fluctuations and correlation lengths with negative δ was observed.…”

Section: Plasma Shapementioning

confidence: 97%

“…Using an MHD model, Wahlberg [157,167] obtained for a non-circular cross section with finite κ and average δ,…”

Section: Plasma Shapementioning

confidence: 99%

Geodesic acoustic modes in magnetic confinement devices

Smolyakov

Ido

2021

Nucl. Fusion

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Geodesic acoustic modes (GAMs) are ubiquitous oscillatory flow phenomena observed in toroidal magnetic confinement fusion plasmas, such as tokamaks and stellarators. They are recognized as the non-stationary branch of the turbulence driven zonal flows which play a critical regulatory role in cross-field turbulent transport. GAMs are supported by the plasma compressibility due to magnetic geodesic curvature—an intrinsic feature of any toroidal confinement device. GAMs impact the plasma confinement via velocity shearing of turbulent eddies, modulation of transport, and by providing additional routes for energy dissipation. GAMs can also be driven by energetic particles (so-called EGAMs) or even pumped by a variety of other mechanisms, both internal and external to the plasma, opening-up possibilities for plasma diagnosis and turbulence control. In recent years there have been major advances in all areas of GAM research: measurements, theory, and numerical simulations. This review assesses the status of these developments and the progress made towards a unified understanding of the GAM behaviour and its role in plasma confinement. The review begins with tutorial-like reviews of the basic concepts and theory, followed by a series of topic orientated sections covering different aspects of the GAM. The approach adopted here is to present and contrast experimental observations alongside the predictions from theory and numerical simulations. The review concludes with a comprehensive summary of the field, highlighting outstanding issues and prospects for future developments.

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Characteristics of an axisymmetric magnetic oscillation closely related to L-H transition on experimental advanced superconducting tokamak (EAST)

Zhang

Xiang

et al. 2019

Physics of Plasmas

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An axisymmetric magnetic oscillation (AMO) of 5–10 kHz in the L-mode plasma edge has been studied on an experimental advanced superconducting tokamak. The analysis shows that this oscillation only occurs at the plasma very close to the L-H transition. The structure of magnetic oscillation is axisymmetric (n = 0) toroidally and demonstrates an m = 2 standing wave in the poloidal direction. The density fluctuation of AMO measured by reflectometry at the midplane is nearly in phase, indicating that the AMO is not a radial traveling wave. The AMO shows an obvious modulation effect on the background magnetic/density fluctuation, and as a result, the edge density/density gradient and particle flux onto the divertor are also modulated by the AMO. The frequency scaling of the AMO is fm∝(∇ne/Ip2)−1. The bicoherence analyses show a strong nonlinear interaction between the AMO and the background turbulence, and other nonlinear interactions between the AMO and three other coherent fluctuations with frequencies (∼4, ∼11, and ∼15 kHz) are also found.

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Singular global components and frequency shift of the geodesic acoustic continuum modes in shaped tokamaks

Cited by 7 publications

References 56 publications

Shaping effects on the geodesic acoustic mode in tokamaks

Shaping effects on the geodesic acoustic mode in tokamaks

Geodesic acoustic modes in magnetic confinement devices

Characteristics of an axisymmetric magnetic oscillation closely related to L-H transition on experimental advanced superconducting tokamak (EAST)

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