Comparison of methods for numerical calculation of continuum damping

Bowden, George; Könies, A.; Hole, Matthew; Gorelenkov, N. N.; Dennis, Graham

doi:10.1063/1.4879802

Cited by 13 publications

(12 citation statements)

References 18 publications

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“…In this regard we should note that the agreement was demonstrated for two damping rate mechanisms added together. A very recent study [567] shows that the continuum damping computed perturbatively within the NOVA ideal MHD approach cannot be used for accurate stability calculations due to intrinsic singularities the solutions have at the continuum.…”

Section: Verification and Validation Of Ae Growth And Damping Ratesmentioning

confidence: 99%

Energetic particle physics in fusion research in preparation for burning plasma experiments

2014

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The area of energetic particle (EP) physics in fusion research has been actively and extensively researched in recent decades. The progress achieved in advancing and understanding EP physics has been substantial since the last comprehensive review on this topic by Heidbrink and Sadler (1994 Nucl. Fusion 34 535). That review coincided with the start of deuterium-tritium (DT) experiments on the Tokamak Fusion Test Reactor (TFTR) and full scale fusion alphas physics studies. Fusion research in recent years has been influenced by EP physics in many ways including the limitations imposed by the 'sea' of Alfvén eigenmodes (AEs), in particular by the toroidicity-induced AE (TAE) modes and reversed shear AEs (RSAEs). In the present paper we attempt a broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices. Introductory discussions on the basic ingredients of EP physics, i.e., particle orbits in STs, fundamental diagnostic techniques of EPs and instabilities, wave particle resonances and others, are given to help understanding of the advanced topics of EP physics. At the end we cover important and interesting physics issues related to the burning plasma experiments such as ITER (International Thermonuclear Experimental Reactor).

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Section: Verification and Validation Of Ae Growth And Damping Ratesmentioning

confidence: 99%

Energetic particle physics in fusion research in preparation for burning plasma experiments

2014

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“…which is ∼ 8% assuming 10% uncertainties in the plasma profiles. Continuum damping can also be a significant contributor, which is clear from the eigenmodes' intersecting the continuum around √ ψ N ≈ 0.8 in figure 5, although absolute uncertainties can be of order Δ(γ/ω 0 ) ∼ 0.1% [35].…”

Section: Kinetic-mhd Simulations With Nova-kmentioning

confidence: 97%

Simultaneous measurements of unstable and stable Alfvén eigenmodes in JET

Tinguely¹,

Gonzalez-Martin²,

Puglia³

et al. 2022

Nucl. Fusion

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In this paper, we report the novel experimental observation of both unstable and stable Toroidicity-induced Alfvén Eigenmodes (TAEs) measured simultaneously in a JET tokamak plasma. The three-ion-heating scheme (D-DNBI-3He) is employed to accelerate deuterons to MeV energies, thereby destabilizing TAEs with toroidal mode numbers n = 3 - 5, each decreasing in mode amplitude. At the same time, the Alfvén Eigenmode Active Diagnostic resonantly excites a stable n = 6 TAE with total normalized damping rate -γ/ω0 ≈ 1% - 4%. Hybrid kinetic-MHD modeling with codes NOVA-K and MEGA both find eigenmodes with similar frequencies, mode structures, and radial locations as in experiment. NOVA-K demonstrates good agreement with the n = 3, 4, and 6 TAEs, matching the damping rate of the n = 6 mode within uncertainties and identifying radiative damping as the dominant contribution. Improved agreement is found with MEGA for all modes: the unstable n = 3 - 5 and stable n = 2, 6 modes, with the latter two stabilized by higher intrinsic damping and lower fast ion drive, respectively. While some discrepancies remain to be resolved, this unique validation effort gives us confidence in TAE stability predictions for future fusion devices.

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“…The application of the complex contour technique based on this formula has been described previously by Könies and Kleiber 11 and Bowden et al 16 . Using the shooting method de- scribed in the latter and considering only the (2, −2) and (3, −2) harmonics, a TAE is found with normalised frequency Ω = 0.370887 − 0.00174204i corresponding to a damping ratio of γ ωr = −0.00469695.…”

Section: Tokamak Resultsmentioning

confidence: 99%

“…This approach assumes that the other continuum resonance interaction does not significantly alter the mode structure. This is not always the case, even for low values of damping 16 . However, in this example we will assume that damping due to the resonance near the edge is much larger than that near the core.…”

Section: A Torsatron Eigenmodesmentioning

confidence: 92%

Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria

2015

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In ideal MHD, shear Alfvén eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfvén continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient.The complex contour method has been applied to the three-dimensional finite element ideal MHD code CKA. In this paper we discuss the application of the complex contour technique to calculate the continuum damping of global modes in tokamak as well as torsatron, W7-X and H-1NF stellarator cases. To the authors' knowledge these stellarator calculations represent the first calculation of continuum damping for eigenmodes in fully three-dimensional equilibria. The continuum damping of global modes in W7-X and H-1NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics.

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Comparison of methods for numerical calculation of continuum damping

Cited by 13 publications

References 18 publications

Energetic particle physics in fusion research in preparation for burning plasma experiments

Energetic particle physics in fusion research in preparation for burning plasma experiments

Simultaneous measurements of unstable and stable Alfvén eigenmodes in JET

Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria

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