Helically localized ballooning instabilities in three-dimensional tokamak pedestals

Cote, T. B.; Hegna, C. C.; Willensdorfer, M.; Strumberger, E.; Suttrop, W.; Zohm, H.

doi:10.1088/1741-4326/aaf01d

Cited by 11 publications

(11 citation statements)

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“…The inclusion of more toroidal modes resulted in further destabilisation and stronger poloidal localisation of the peeling-ballooning mode. The strong poloidal and field-line localisation in 3D geometry is a feature that is observed experimentally in AUG in cases of ELM mitigation [18], and was successfully reproduced by theory based on a local ballooning analysis [17]. In those cases the 3D ballooning mode was localised around specific field lines, that coincided with locations where the plasma response crosses zero, i.e.…”

Section: Discussionmentioning

confidence: 60%

“…In particular, the imposed 3D fields lead to local changes of plasma equilibrium parameters, that play a crucial role in determining the stability of the plasma. This leads to the destabilisation of high n 4 ideal ballooning modes, where n is the toroidal mode number of the perturbation, which is localised about the most unstable magnetic field lines [15][16][17]. Such a feature is computationally and experimentally observed in ASDEX Upgrade (AUG) discharges, when ELM mitigation occurs [18].…”

Section: Introductionmentioning

confidence: 99%

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Peeling-ballooning stability of tokamak plasmas with applied 3D magnetic fields

Tzanis¹,

Ham²,

Snyder³

et al. 2020

Nucl. Fusion

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The poloidal harmonics of the toroidal normal modes of an unstable axisymmetric tokamak plasma are employed as basis functions for the minimisation of the 3D energy functional. This approach presents a natural extension of the perturbative method considered in [M.S. Anastopoulos Tzanis et al, Nuclear Fusion 59:126028, 2019]. This variational formulation is applied to the stability of tokamak plasmas subject to external non-axisymmetric magnetic fields. A comparison of the variational and perturbative methods shows that for D-shaped, high β N plasmas, the coupling of normal modes becomes strong at experimentally relevant applied 3D fields, leading to violation of the assumptions that justify a perturbative analysis. The variational analysis employed here addresses strong coupling, minimising energy with respect to both toroidal and poloidal Fourier coefficients. In general, it is observed that ballooning unstable modes are further destabilised by the applied 3D fields and fieldaligned localisation of the perturbation takes place, as local ballooning theory suggests. For D-shaped high β N plasmas, relevant to experimental cases, it is observed that the existence of intermediate n unstable peeling-ballooning modes, where a maximum in the growth rate spectrum typically occurs, leads to a destabilising synergistic coupling that strongly degrades the stability of the 3D system.

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Section: Discussionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Peeling-ballooning stability of tokamak plasmas with applied 3D magnetic fields

Tzanis¹,

Ham²,

Snyder³

et al. 2020

Nucl. Fusion

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“…The measured corrugation compares well to the displacement of the 3D VMEC equilibrium normal to the axisymmetric equilibrium ξ n (VMEC). Linear ideal ballooning theory shows a mode on the field line region that is least stable against field line bending due to the 3D corrugation [66,67]. Measurements of T e and n e perturbations with a new fast He beam diagnostic [68] show neither a phase delay between T e and n e oscillation nor an inversion radius as expected for an island (see figure 9).…”

Section: No Elm Regimes and 3d Perturbationsmentioning

confidence: 93%

Overview of physics studies on ASDEX Upgrade

et al. 2019

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The ASDEX Upgrade (AUG) programme, jointly run with the EUROfusion MST1 task force, continues to significantly enhance the physics base of ITER and DEMO. Here, the full tungsten wall is a key asset for extrapolating to future devices. The high overall heating power, flexible heating mix and comprehensive diagnostic set allows studies ranging from mimicking the scrape-off-layer and divertor conditions of ITER and DEMO at high density to fully non-inductive operation (q 95 = 5.5, ) at low density. Higher installed electron cyclotron resonance heating power 6 MW, new diagnostics and improved analysis techniques have further enhanced the capabilities of AUG. Stable high-density H-modes with MW m−1 with fully detached strike-points have been demonstrated. The ballooning instability close to the separatrix has been identified as a potential cause leading to the H-mode density limit and is also found to play an important role for the access to small edge-localized modes (ELMs). Density limit disruptions have been successfully avoided using a path-oriented approach to disruption handling and progress has been made in understanding the dissipation and avoidance of runaway electron beams. ELM suppression with resonant magnetic perturbations is now routinely achieved reaching transiently . This gives new insight into the field penetration physics, in particular with respect to plasma flows. Modelling agrees well with plasma response measurements and a helically localised ballooning structure observed prior to the ELM is evidence for the changed edge stability due to the magnetic perturbations. The impact of 3D perturbations on heat load patterns and fast-ion losses have been further elaborated. Progress has also been made in understanding the ELM cycle itself. Here, new fast measurements of and E r allow for inter ELM transport analysis confirming that E r is dominated by the diamagnetic term even for fast timescales. New analysis techniques allow detailed comparison of the ELM crash and are in good agreement with nonlinear MHD modelling. The observation of accelerated ions during the ELM crash can be seen as evidence for the reconnection during the ELM. As type-I ELMs (even mitigated) are likely not a viable operational regime in DEMO studies of ‘natural’ no ELM regimes have been extended. Stable I-modes up to have been characterised using -feedback. Core physics has been advanced by more detailed characterisation of the turbulence with new measurements such as the eddy tilt angle—measured for the first time—or the cross-phase angle of and fluctuations. These new data put strong constraints on gyro-kinetic turbulence modelling. In addition, carefully executed studies in different main species (H, D and He) and with different heating mixes highlight the importance of the collisional energy exchange for interpreting energy confinement. A new regime with a hollow profile now gives access to regimes mimicking aspects of burning plasma conditions and lead to nonlinear interactions of energetic particle modes despite the sub-Alfvénic beam energy. This will help to validate the fast-ion codes for predicting ITER and DEMO.

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“…Experimental observations showed that the application of a MP field causes inter-ELM modes and the ELM onset to appear in certain helical positions (at certain toroidal phase angles) instead of being randomly located along the toroidal direction [10]. The toroidal mode localization for infinite-n ballooning modes, which are located at a single flux surface, was studied analytically by [11]. The helical localization of intermediate to high toroidal mode number peeling-ballooning modes in non-axisymmetric tokamak plasmas in the limit of weak MP fields (perturbative stability analysis) was investigated by [12].…”

Section: Introductionmentioning

confidence: 99%

Helical mode localization and mode locking of ideal MHD instabilities in magnetically perturbed tokamak plasmas

et al. 2023

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In H-mode tokamak plasmas, the achievable pressure-gradient is limited by type-IEdge Localized Modes (ELMs), which are projected to cause severe damage to futurefusion devices. There are several approaches aiming to mitigate/suppress the occur-rence of ELMs, such as the application of an external non-axisymmetric magneticperturbation (MP) field, which breaks the axisymmetry of the tokamak plasma. Inthis work we use the CASTOR3D code to investigate helical localization and modelocking of edge-localized ideal MHD instabilities in rotating and flow-free magneticallyperturbed tokamak plasmas with N P = 2 periodicity. Helically localized instabilitiesare separated into two classes: quasi-locked and strictly locked. In a non-rotatingplasma, the localization of quasi-locked modes is determined by an envelope whiletheir precise location under the envelope is arbitrary, whereas strictly locked modescan only occur at a single helical position. Strictly locked modes only rotate if thetoroidal plasma rotation exceeds a critical threshold; above the threshold the forcedrotation of the strictly locked modes is non-uniform. For quasi-locked modes, nosuch critical threshold exists; they rotate uniformly beneath their envelope in the caseof finite plasma rotation. The helical localization of both quasi-locked and strictlylocked instabilities is determined by the energetic decomposition of the instabilitiesclose to the most unstable flux-surface; for example, strongly current-density driveninstabilities are aligned with regions of augmented parallel equilibrium current-density.Finally, we compare the computationally determined localization of MHD instabili-ties to experimental observations. The determined MHD instability is located at thesame position as the experimentally measured modes with respect to the equilibriumcorrugation, verifying that ideal MHD can describe the experimentally observed instabilities.

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Helically localized ballooning instabilities in three-dimensional tokamak pedestals

Cited by 11 publications

References 50 publications

Peeling-ballooning stability of tokamak plasmas with applied 3D magnetic fields

Peeling-ballooning stability of tokamak plasmas with applied 3D magnetic fields

Overview of physics studies on ASDEX Upgrade

Helical mode localization and mode locking of ideal MHD instabilities in magnetically perturbed tokamak plasmas

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