MHD-model for low-frequency waves in a tokamak with toroidal plasma rotation and problem of existence of global geodesic acoustic modes

Lakhin, V. P.; Sorokina, E. A.; Ilgisonis, V. I.; Konovaltseva, Ludmila V.

doi:10.1134/s1063780x15120077

Cited by 9 publications

(5 citation statements)

References 28 publications

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“…Experimentally, GAMs are known to appear also in form of eigenmodes, which oscillate with constant frequency across a finite radial extent [64,65] also in non-uniform equilibria. This feature is known from theory [5,66,67] and has been reproduced also numerically [68,69]. Here, we suppose the GAM behaves as a continuum [32], i.e.…”

Section: Physical Interpretation Of Dissipative Broadeningsupporting

confidence: 52%

Complex-Hamiltonian paraxial description of damped geodesic acoustic modes

et al. 2020

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Geodesic acoustic modes (GAMs) are a fundamental part of turbulence and zonal-flow dynamics in tokamaks. They exhibit simple yet non-trivial dispersive and dissipative properties. In linear numerical simulations, they are often initialized in the form of (e.g. Gaussian) packets which evolve in time. Depending on the parameters, dispersion and damping can act on comparable time scales during the GAM evolution. Wigner-function methods developed in the frame of non-Hermitian quantum mechanics are shown to be applicable to damped geodesic oscillations. In this approach, the standard approximation of "weak damping", often introduced for the treatment of plasma waves, is not needed. The method requires that the properties of the plasma do not vary significantly across the width of the packet (i.e. in the radial direction), so that a paraxial expansion of the underlying equations around the centre of the packet can be applied. For a quadratic Hamiltonian, the equations for the Wigner function governing the packet in the paraxial limit are shown to be equivalent to the equations of paraxial WKB theory (usually applied to the description of high-frequency wave beams in plasmas), with the real Hamiltonian replaced by the corresponding complex one. Analytic solutions are derived in particular cases and shown to agree with the results of global gyrokinetic simulations.

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Section: Physical Interpretation Of Dissipative Broadeningsupporting

confidence: 52%

Complex-Hamiltonian paraxial description of damped geodesic acoustic modes

et al. 2020

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“…The m = 2 component is critical for the existence of the GGAM eigenmodes [12,13,[161][162][163]. When the m = 2 is artificially omitted from full MHD equations, no eigenmode occurs, even for profiles with a local maximum in the GAM frequency as shown numerically [164] and analytically [165]. [14] or…”

Section: Electromagnetic Effects and Relation To Alfvén Eigenmodesmentioning

confidence: 99%

“…The effect of toroidal and/or poloidal rotation on the continuum GAM has been extensively investigated theoretically using an MHD (electrostatic) framework in the large aspect ratio, circular plasma geometry. As an example of many, Lakhin [165,268] modelled the toroidal rotation effect with an ideal single fluid MHD framework in the low β ∼ 2 , isodense magnetic surfaces, and large aspect ratio limit to obtain:…”

Section: Frequencymentioning

confidence: 99%

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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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“…To describe the perturbations, which are assumed to be proportional to exp(−iωt), we use the following set of reduced equations for low-frequency modes in rotating tokamak plasmas obtained in reference [25]:…”

Section: Equations Of Global Zf In Toroidally Rotating Tokamak Plasmasmentioning

confidence: 99%

Low-frequency zonal flow eigen-structures in tokamak plasmas

Ilgisonis¹,

Lakhin²,

Marusov³

et al. 2022

Nucl. Fusion

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The nonlocal eigenmode analysis of low-frequency zonal flows in toroidally rotating tokamak plasmas is performed in the framework of the reduced one-fluid ideal MHD-model. It is shown that for typical profiles of plasma parameters toroidal plasma rotation results in the global zonal flow formation on the periphery of plasma column. For some types of equilibria these zonal flows are aperiodically unstable that leads to the excitation of the differential plasma rotation at the tokamak plasma edge.

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MHD-model for low-frequency waves in a tokamak with toroidal plasma rotation and problem of existence of global geodesic acoustic modes

Cited by 9 publications

References 28 publications

Complex-Hamiltonian paraxial description of damped geodesic acoustic modes

Complex-Hamiltonian paraxial description of damped geodesic acoustic modes

Geodesic acoustic modes in magnetic confinement devices

Low-frequency zonal flow eigen-structures in tokamak plasmas

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