An extended hybrid magnetohydrodynamics gyrokinetic model for numerical simulation of shear Alfvén waves in burning plasmas

Wang, X.; Briguglio, S.; Chen, L.; Troia, C. Di; Fogaccia, G.; Vlad, G.; Zonca, F.

doi:10.1063/1.3587080

Cited by 54 publications

(86 citation statements)

References 60 publications

(152 reference statements)

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“…(1), contribute to both finite Larmor radius correction to the plasma inertia [the second term of the first line in Eq. (15), responsible for KAW] 75 as well as to the linear diamagnetic response (the first term of the second line), 76,77 for these terms depend explicitly on perpendicular pressure. Other linear terms in Eq.…”

Section: Equations For Drift Alfv En Waves Excited By Energetic Pmentioning

confidence: 99%

Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

2014

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A unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, “Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation,” Phys. Plasmas 21, 072121 (2014)].

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Section: Equations For Drift Alfv En Waves Excited By Energetic Pmentioning

confidence: 99%

Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

2014

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“…In the present paper, the extended version [36] of the nonlinear MHD-Gyrokinetic code HMGC [15,35] (XHMGC) has been used to simulate self-consistenly the BAE mode driven by anisotropic Maxwellian fast ions. In XHMGC, a shifted circular magnetic flux surfaces, low-β tokamak equilibrium is adopted.…”

Section: Xhmgc Modelmentioning

confidence: 99%

“…Finally, resonance detuning and radial decoupling saturation mechanisms are examined, for a nonuniform tokamak plasma, within the 'fishbone' paradigm. In section 3, self-consistent simulations using an extended version of the hybrid magnetohydrodynamics (MHD) Gyrokinetic code (XHMGC) [35,36] are performed for a beta-induced Alfvén eigenmode (BAE) in a tokamak equilibrium with monotonic safety factor profile; here, the expression 'beta' (β) refers to the ratio between the kinetic pressure of the bulk plasma and the magnetic pressure. The effects of varying toroidal number is analysed.…”

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confidence: 99%

Saturation of single toroidal number Alfvén modes

Wang

Briguglio

2016

New J. Phys.

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The results of numerical simulations are presented to illustrate the saturation mechanism of a single toroidal number Alfvén mode, driven unstable, in a tokamak plasma, by the resonant interaction with energetic ions. The effects of equilibrium geometry non-uniformities and finite mode radial width on the wave-particle nonlinear dynamics are discussed. Saturation occurs as the fast-ion density flattening produced by the radial flux associated to the resonant particles captured in the potential well of the Alfvén wave extends over the whole region where mode-particle power exchange can take place. The occurrence of two different saturation regimes is shown. In the first regime, dubbed resonance detuning, that region is limited by the resonance radial width (that is, the width of the region where the fast-ion resonance frequency matches the mode frequency). In the second regime, called radial decoupling, the power exchange region is limited by the mode radial width. In the former regime, the mode saturation amplitude scales quadratically with the growth rate; in the latter, it scales linearly. The occurrence of one or the other regime can be predicted on the basis of linear dynamics: in particular, the radial profile of the fast-ion resonance frequency and the mode structure. Here, we discuss how such properties can depend on the considered toroidal number and compare simulation results with the predictions obtained from a simplified nonlinear pendulum model.Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. © EUROfusionunstable. As the EP pressure gradient exceeds a certain threshold, even strongly damped continuum oscillations, besides these normal modes of the background plasma, can be driven unstable; they are called energetic particle modes (EPM) [3]. Alvénic fluctuations of various types, excited by EPs, have been identified in several tokamak experiments [4][5][6][7][8][9].Linear properties of Alfvénic fluctuations driven by EPs can be investigated within the theoretical framework of the generalised fishbone-like dispersion relation [3,10,11]. On this basis, several successful comparison between theoretical predictions and experimental observations, as well as numerical simulation results, have been reported [12][13][14][15][16][17][18][19][20].Concerning the nonlinear dynamics of Alfvén modes (and its consequences on the overall performances of tokamak plasmas), it is determined by two main factors: the nonlinear wave-wave coupling and nonlinear waveparticle interactions. With reference to the former factor, various wave-wave interactions leading to the breaking of the Alfvénic state have been analyzed in [21,22]. Although these effects play a crucial role in multi-scale dynamics in burning plasmas, we will focus, in our current work, on the nonlinear wave-particle interactions. This issue has been first addressed withi...

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“…In this way, note that energetic ions 7 , even though they do not contribute to plasma inertia due to Eq. (2.32), contribute to both finite Larmor radius correction to the plasma inertia (KAW) as well as to the diamagnetic response Wang et al, 2011) (see Sec. III.C), for these terms depend explicitly on perpendicular pressure.…”

Section: Reduced Equations For Low-β Drift Alfvén Wavesmentioning

confidence: 99%

Physics of Alfvén waves and energetic particles in burning plasmas

2016

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Dynamics of shear Alfvén waves and energetic particles are crucial to the performance of burning fusion plasmas. This article reviews linear as well as nonlinear physics of shear Alfvén waves and their self-consistent interaction with energetic particles in tokamak fusion devices. More specifically, the review on the linear physics deals with wave spectral properties and collective excitations by energetic particles via wave-particle resonances. The nonlinear physics deals with nonlinear wave-wave interactions as well as nonlinear wave-energetic particle interactions. Both linear as well as nonlinear physics demonstrate the qualitatively important roles played by realistic equilibrium nonuniformities, magnetic field geometries, and the specific radial mode structures in determining the instability evolution, saturation, and, ultimately, energetic-particle transport. These topics are presented within a single unified theoretical framework, where experimental observations and numerical simulation results are referred to elucidate concepts and physics processes.

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An extended hybrid magnetohydrodynamics gyrokinetic model for numerical simulation of shear Alfvén waves in burning plasmas

Cited by 54 publications

References 60 publications

Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

Saturation of single toroidal number Alfvén modes

Physics of Alfvén waves and energetic particles in burning plasmas

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