Onset Of Tearing Modes Research Articles

The root cause of disruptive NTMs and paths to stable operation in DIII-D ITER baseline scenario plasmas

Abstract Analyses of the DIII-D ITER Baseline Scenario database support that the disruptive m,n=2,1 magnetic islands are pressure gradient driven, non-linear instabilities seeded in a sequence of stochastic transient magnetic perturbations, and that the current profile relaxation does not affect the m,n=2,1 island onset rate. At low torque, these Neoclassical Tearing Modes are most commonly seeded by non-linear 3-wave coupling when the differential rotation between the q=1 & q=2 rational surfaces approaches zero. Lack of statistically significant difference between the current profiles of stable and unstable states, as well as lack of correlation between the tearing mode onset rate and the current profile relaxation both reject causality between the current profile evolution and the 2,1 magnetic island onsets in these plasmas. These support that preserving the differential rotation between the q=1 and q=2 rational surfaces is key to long pulse stable operation in the plasma scenario planned for ITER, while optimization of the current profile within the explored parameter space may lead to much weaker improvements than sustaining the differential rotation.

Use of differential plasma rotation to prevent disruptive tearing mode onset from 3-wave coupling

Abstract Plasma differential rotation is found to be capable of preventing disruptive neoclassical tearing modes (NTMs) seeded by nonlinear three-wave coupling. As tearing modes degrade confinement and can lead to disruptions, stabilization strategies are crucial to the successful operation of future devices. In ITER-relevant scenarios on DIII-D, rotationally coupled m / n = 1/1 and 3/2 modes have been observed to drive 2/1 islands through three-wave coupling. The frequency of the driven 2/1 mode is set by matching conditions and the frequencies of the driving modes. When the driven mode frequency matches the local plasma rotation frequency, e.g. at low differential rotation, the driven 2/1 island can grow into a disruptive NTM. Using neutral beam torque as an actuator to scan the differential rotation, these experiments demonstrate that a sufficiently large frequency mismatch prevents destabilization of disruptive 2/1 NTMs by three-wave coupling. This work indicates that differential rotation can be used as an actuator to prevent NTMs seeded by three-wave coupling.

Empirical probability and machine learning analysis of m, n = 2, 1 tearing mode onset parameter dependence in DIII-D H-mode scenarios

m, n = 2, 1 tearing mode onset empirical probability and machine learning analyses of a multiscenario DIII-D database of over 14 000 H-mode discharges show that the normalized plasma beta, the rotation profile, and the magnetic equilibrium shape have the strongest impact on the 2,1 tearing mode stability, in qualitative agreement with neoclassical tearing modes (m and n are the poloidal and toroidal mode numbers, respectively). In addition, 2,1 tearing modes are most likely to destabilize when n > 1 tearing modes are already present in the core plasma. The covariance matrix of tearing sensitive plasma parameters takes a nearly block-diagonal form, with the blocks incorporating thermodynamic, current and safety factor profile, separatrix shape, and plasma flow parameters, respectively. This suggests a number of paths to improved stability at fixed pressure and edge safety factor primarily by preserving a minimum of 1 kHz differential rotation, increasing the minimum safety factor above unity, using upper single null magnetic configuration, and reducing the core impurity radiation. In addition, lower triangularity, lower elongation, and lower pedestal pressure may also help to improve stability. The electron and ion temperature, collisionality, resistivity, internal inductance, and the parallel current gradient appear to only weakly correlate with the 2,1 tearing mode onsets in this database.

Drift kinetic theory of the NTM magnetic islands in a finite beta general geometry tokamak plasma

In (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) a new 4D drift kinetic nonlinear theory, valid in the limit of a low beta, small inverse aspect ratio, circular cross section, toroidal geometry, to describe the plasma response to the neoclassical tearing mode (NTM) magnetic perturbation is derived. In (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) this theory is reduced in a low collisionality limit, which allows a dimensionality reduction to a 3D problem to efficiently resolve the collisional dissipation layer in the vicinity of the trapped-passing boundary. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) adopts an improved model for the magnetic drift frequency, which reduces the threshold magnetic island half-width from , where is the trapped ion banana orbit width, to , making it in closer agreement with experimental observations for the large aspect ratio tokamak equilibrium. In the present paper, the theory is extended to a high beta, arbitrary tokamak geometry to capture the plasma shaping effects on the NTM threshold physics with the focus on the non-zero triangularity discharges that are known to have a strong impact on the plasma MHD stability. First, it is found that the higher triangularity plasma is more prone to NTMs which is in agreement with the tearing mode onset relative frequency measurements in DIII-D. Second, the NTM threshold dependence on the tokamak inverse aspect ratio obtained in (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) is refined and extended to a finite aspect ratio limit. Third, the NTM threshold dependence on poloidal beta is obtained and benchmarked against the EAST threshold island width measurements.

Onset of tearing modes in plasma termination on JET: the role of temperature hollowing and edge cooling

In this work the onset of tearing modes in the termination phase of plasma pulses on JET is investigated. It is shown that the broadening or the shrinking of the current density profile, as a consequence of a core hollowing or an edge cooling of the electron temperature profile, strongly increases the probability of destabilizing a 2/1 tearing mode also in absence of an external trigger (e.g. a sawtooth crash). Two parameters are defined to highlight changes in the shape of the temperature profile that can lead to MHD instabilities and an empirical stability diagram is introduced into the space of the two new parameters. A large data-set of pulses carried out in the high-current scenario at JET with ITER-like wall is analyzed and criteria for the development of disruption alerts based on the two risk indicators for MHD instabilities are discussed, taking into account the different dynamics of the observed phenomena leading to the onset of 2/1 tearing modes.

Overview of the FTU results

Since the 2016 IAEA Fusion Energy Conference, FTU operations have been mainly devoted to experiments on runaway electrons and investigations into a tin liquid limiter; other experiments have involved studies of elongated plasmas and dust. The tearing mode onset in the high density regime has been studied by means of the linear resistive code MARS, and the highly collisional regimes have been investigated. New diagnostics, such as a runaway electron imaging spectroscopy system for in-flight runaway studies and a triple Cherenkov probe for the measurement of escaping electrons, have been successfully installed and tested, and new capabilities of the collective Thomson scattering and the laser induced breakdown spectroscopy diagnostics have been explored.

High performance double-null plasmas under radiating divertor and mantle scenarios on DIII-D

Experiments to combine a radiating divertor or mantle with high power, high βN plasma operation have successfully reduced the divertor heat flux by 40% but have also encountered several challenging problems. For example, injecting either neon or argon seed impurities have led both to significant fuel dilution of the core plasma and to the emergence of harmful tearing mode activity which compromised plasma beta and energy confinement time. Increased divertor closure resulted in more effective control over the injected seed impurity inventory, although it was also observed that small radial variations in the placement of the outer separatrix strike point within the DIII-D ‘closed’ divertor could lead to clear differences in the impurity build-up inside the core plasma. Active particle pumping of argon seed impurities through the divertor leg on the high-field side of a double-null divertor configuration showed little effect on seed impurity inventory and only modest control over the deuterium fuel inventory. Typically, 80% or greater of injected argon was removed by the corresponding cryo-pump on the low-field (outboard) side of that divertor, with the remaining argon being removed by the outboard cryo-pump from the opposite divertor. For single-null divertor cases, the contribution of the inner (high-field) cryo-pump to impurity and main-ion control appears to be complicated by the levels of divertor recycling and degree of divertor detachment. In general, divertor design that impedes the escape of seed impurities, plasma shaping that allows a higher stability limit, and electron cyclotron deposition profiles that prevent tearing mode onset and impede impurity accumulation in the core are under consideration for addressing the issues presented in this paper.

Event hazard function learning and survival analysis for tearing mode onset characterization

It is shown that concepts from survival analysis (branch of statistics dealing with various types of time-to-event data) are helpful when trying to quantify and understand the onset of tearing modes in tokamaks. It is argued that a probabilistic event prediction problem should be decomposed into (i) dynamical system evolution and (ii) event hazard function integration. Successful machine learning of a hazard (events per time) function from experimental data is demonstrated. The hazard function exhibits statistical properties that are consistent with expectation. A specific tearing delta-prime proxy is found to not contribute to the likelihood of the hazard function for the present case. Although in this paper the event is the onset of a tearing mode in a particular plasma scenario, these ideas should be equally applicable to disruption events.

Influence of rotation on the (m, n) = (3, 2) neoclassical tearing mode threshold in the ASDEX Upgrade

The influence of rotation on the (m, n) = (3, 2) neoclassical tearing mode onset and the marginal point at the ASDEX Upgrade is investigated. In this context, the different trigger mechanisms are identified and the influence of not only the rotation but also the rotation gradient and the differential rotation between the resonant and the triggering surface on the neoclassical tearing mode (NTM) stability is analysed. The existence of an upper NTM onset threshold can be observed in correlation with the rotation normalized to the Alfvén velocity. It can also clearly be verified that at the ASDEX Upgrade the NTM onset threshold increases with co- and counter-current directed rotation and also with positive and negative rotation gradient.

The influence of rotation on the βN threshold for the 2∕1 neoclassical tearing mode in DIII-D

Utilizing a capability to vary neutral beam torque injection in the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak, m∕n=2∕1 neoclassical tearing mode onset thresholds are found to fall by about one unit in βN, from ∼3 to ∼2, in ITER-like sawtoothing high-energy confinement modes of plasma operation [R. Aymar, Plasma Phys. Control. Fusion 42, B385 (2000)] as “co-injected” torque and rotation are reduced. However, increasing levels of torque and rotation in the counter-direction do not lead to corresponding rises in βN thresholds. More encouragingly, error field sensitivity is not found to increase in low rotation plasmas, as might be expected theoretically. These results pose an interesting physics problem, as well as raising concern for future devices such as ITER. Further analyses have explored possible physics origins of the behavior. They suggest many of the usual effects expected to lead to a rotation dependence (mode coupling, wall drag, ion polarization currents) are not significant, with instead models that depend on the size and sign of rotation shear playing a role. Onset behavior suggests the mode is close to being intrinsically (classically) unstable when it appears, and a conceptual explanation is offered for a mechanism by which rotation shear feeds into the onset process through changes to the classical tearing stability index, Δ′. Further parameter extensions and studies are desirable to fully resolve the underlying physics of this interesting process.

Beta limit due to m/n = 2/1 tearing mode onset in the DIII-D hybrid scenario

The performance (βN ≈ 3, q95 ≈ 4.4, fBS ≈ 0.5, H89 > 2) of hybrid scenario plasmas in DIII-D (Luxon 2002 Nucl. Fusion 42 614) is limited by m/n = 2/1 tearing modes. Unlike conventional plasmas (Hender et al 2004 Nucl. Fusion 44 798), the linear dependence scaling of the global beta for onset of the instability with normalized local ion gyroradius is modified as the n = 1 ideal kink beta limit is approached, suggesting that small island neoclassical tearing mode (NTM) threshold physics does not impose the dominant criterion for NTM stability. The hybrid scenario tends to go unstable just at or below the no wall n = 1 ideal kink beta limit of about 4ℓi. Experimentally 4ℓi decreases with beta as . Thus the ‘ceiling’ in beta due to coupling of tearing to the ideal kink comes down as beta is increased. Scaling of the tearing unstable beta that combines both NTM threshold physics and a pole in Δ′r due to coupling to the ideal kink is presented.

Influence of the dynamic ergodic divertor on transport properties in TEXTOR

Experiments to investigate transport properties under the influence of the dynamic ergodic divertor (DED) on TEXTOR are discussed. Relativistic runaway electrons are applied for studying transport properties of ergodization such as enhanced runaway loss. The ergodization causes an enhanced loss rate; this loss is higher for low relativistic electrons than for highly relativistic ones, in good agreement with particle orbit mapping. Edge transport can be controlled by the DED perturbation: in limiter H-mode plasmas ELM-like particle and heat bursts associated with the formation of enhanced edge pressure gradients are mitigated in the 6/2 configuration on the expense of a reduced pedestal height. Finally, the plasma is driven back to L-mode under the influence of the magnetic perturbation. In the 3/1 configuration the onset of tearing modes limits the possibility to affect edge transport. A mode of spontaneous density built-up has been found for the TEXTOR-DED as well. This mode is in particular strong for an inward shifted plasma; the built-up has a resonant character with respect to q(a). Langmuir probe measurements with two probe arrays show a strong influence of the magnetic ergodization on both the edge plasma equilibrium and fluctuation parameters. In particular, in the ergodic zone the turbulence properties and turbulence-driven flux are profoundly modified.

A categorization of tearing mode onset in tokamaks via nonlinear simulation

A theoretical categorization of the onset of tearing modes in tokamaks is presented using DIII-D equilibrium reconstructions as initial conditions in the NIMROD nonlinear three-dimensional resistive magnetohydrodynamic code (Sovinec C.R. et al 2004 J. Comput. Phys. 195 355). The onset mechanism of tearing modes are categorized into three types: spontaneous, mixed and forced depending on the importance of linear instability versus forced reconnection. The physics of the early evolution of growing tearing modes in simulations with time varying linear instability drive, nonlinear coupling between modes and neoclassical bootstrap drive are compared to experimental data to explain this qualitative categorization. Important effects, such as rotational shear and thermal anisotropy, are included and confirm that this categorization is consistent with the experimental observations in DIII-D.

Nonlinear simulation of tearing mode based on 4-field RMHD model

Simulations of dynamics of tearing modes based on a 4-field reduced magneto hydro dynamics model are performed, laying an emphasis on interaction with microscopic and transport processes. The simulation results show the importance of turbulent fluctuations for the onset of tearing mode. The helical current perturbation associated with a magnetic island is studied. The perturbed bootstrap current has a structure in the magnetic island (including a phase difference), indicating the need to improve assumptions in the theory of neoclassical tearing mode.

A mechanism for tearing onset near ideal stability boundaries

The prevention of neoclassical tearing modes (NTMs) in tokamak plasmas is a major challenge for fusion. Ideal modes can seed NTMs through forced reconnection, yet in sawtoothing discharges it is not well understood why a particular sawtooth crash seeds a NTM after several preceding sawteeth did not. Also, tearing modes sometimes appear and grow without an obvious ideal mode causing a seed island. Based on theoretical and experimental results a new mechanism for tearing mode onset is proposed and tested which explains these puzzling observations. Tearing stability calculations based on experimental equilibria from the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] indicate that tearing modes can be driven unstable by a rapid increase in the linear tearing stability index Δ′ just before onset. Near the ideal kink limit in βN≡β/(I/aBT), Δ′ becomes large and positive as it approaches a pole discontinuity. The relative time scales of the change in Δ′ vs the effects of finite island width will determine the evolution of the island, and the eventual nonlinear state. Theoretical predictions of the onset point, the βN at a specified small island width, and the early evolution characteristics are compared with results from new DIII-D experiments designed specifically to test this hypothesis. Time integration of the island evolution equation shows that these predictions are consistent with the experimental observations. The nonlinear 3D resistive magnetohydrodynamic code NIMROD [A. H. Glasser et al., Plasma Phys. Control. Fusion 41, A747 (1999)] is used to evolve equilibria reconstructed from these experiments in time to provide a more comprehensive prediction of the island evolution during the early nonlinear phase. The simulations are also consistent with the proposed mechanism.

Generic structure of externally driven tearing modes instabilities

A major limit to steady state and advanced high βp operation of tokamaks of reactor class is due to the onset of tearing modes that develop magnetic and may cause loss of energy confinement or a major disruption. Here the structure of a classical problem about the effects of external control helical fields is analysed and it is shown to offer a general paradigm of response of low order classical and neoclassical tearing modes to a wide class of external perturbations. New results of principle on the structural stability of the response model are obtained, leading to a clear interpretation of the role of “seed islands” in the onset of neo-classical tearing modes and the role of finite ion larmor radius corrections to Ohm’s law.