Neoclassical Tearing Modes Research Articles

Magnetohydrodynamics-induced internal crash near density limit in ohmic discharge on experimental advanced superconducting tokamak

The magnetohydrodynamics (MHD)-induced internal crash (IC) is one of the most fundamental dynamics of a tokamak discharge. Study of IC and the consequent formation of seed island (for neo-classical tearing modes) are still attractive in both experimental and numerical studies. In this work, a set of MHD-induced sawtooth like crashes (SLCs) have been observed in experimental advanced superconducting tokamak (EAST) ohmic discharge near density limit. With the tomography of high-resolution upgraded soft x-ray imaging system, it is observed that m/n = 2/1 tearing mode converts to a m/n = 1/1 instability, and it then triggers crash in the plasma core, here, m is the poloidal mode number and n is the toroidal mode number. Similar to sawtooth crash (SC), the crash of SLC here is due to m/n = 1/1 mode nonlinear dynamic. An extended MHD simulation code M3D is used to understand of the dynamics of m/n = 1/1 internal kink mode in SC in torus. A complex SC is reproduced from M3D nonlinear simulation under EAST realistic magnetic flux equilibrium and experimental resistivity. The rapid growth of unstable m/n = 1/1 kink and interaction with its higher harmonics, are responsible for SC. The simulation results show an existence of annular chaos belt outside q = 1 surface during SC. Furthermore, magnetic islands with higher poloidal mode number are found after SC. The formation of island after SC make plasma current profile flat in the core.

A reduced MHD model for ITG-NTM interplay

A six-field reduced-MHD model is derived for plasma dynamics. The new model describes coherently both ion temperature gradient (ITG) mode and tearing mode and includes neoclassical effects. The model allows the construction of an energylike quantity with a linear pressure contribution that is conserved except for dissipative, finite Larmor radius, and neoclassical terms. This model may be used to study the nonlinear interaction between ITG microturbulence and neoclassical tearing mode, which is responsible for large-scale magnetic islands in tokamaks, and opens the way to a coherent description of turbulent impurity transport in magnetic islands.

Control of neoclassical tearing mode by synergetic effects of resonant magnetic perturbation and electron cyclotron current drive in reversed magnetic shear tokamak plasmas

Synergetic effects of resonant magnetic perturbation (RMP) and electron cyclotron current drive (ECCD) on stabilizing neoclassical tearing mode (NTM) in reversed magnetic shear (RMS) tokamak plasmas are numerically investigated based on a set of reduced MHD equations. For the moderate separation, it is found that the explosive burst induced by the fast reconnection of double tearing mode (DTM) in the RMS configuration can be completely suppressed by externally applied RMPs. Zonal flows with strong shear induced by a rotating RMP play an important role in this suppression process. Moreover, turning on ECCD in advance is essential to mitigate the NTM. For the large separation without the explosive burst, two strategies, i.e. a continuous ECCD with static RMP and a modulated ECCD with rotating RMP, are separately investigated. It is shown that when the NTM is decelerated by a relatively slow rotating RMP, the modulated ECCD can have a better stabilizing effect. In addition, the ECCD deposition widths in both radial and helical angle directions, as well as the ECCD on-duty time, are analyzed in detail. The best effectiveness of ECCD is obtained and the relevant physical mechanisms are discussed.

Suppressive effects of diamagnetic drift on neoclassical double tearing modes based on four-field reduced MHD model

The explosive behavior of neo-classical double tearing mode (NDTM) is numerically investigated by a reduced four-field-drift-magnetohydrodynamic code [Ye et al., Nuclear Fusion 59, 096044 (2019)] with the bootstrap current effect. It is numerically observed that the explosive burst of NDTM can be absolutely suppressed by diamagnetic drift flow. The dependence of the critical value of diamagnetic drift flow V0*c for avoiding the explosion on typical plasma parameters is numerically studied in detail. It is found that V0*c decreases with increasing Δrs, while it increases with an increasing bootstrap current fraction. The plasma viscosity and resistivity can raise the threshold through their effects on the rotation of magnetic islands and the instability of system, respectively. Furthermore, the perpendicular transport and parallel transport, which are significant to the driven effects of the bootstrap current, have the opposite effects on V0*c. The underlying mechanisms are discussed.

On the triggerless onset of 2/1 neoclassical tearing modes in TCV

Triggerless 2/1 neoclassical tearing modes (NTMs), i.e. 2/1 NTMs that originate from unstable safety factor profiles (with positive classical stability index at zero island width, i.e. ) and saturate neoclassically under the effect of perturbed bootstrap current, have been observed reproducibly in TCV discharges with a strong near-axis electron cyclotron current drive (ECCD). An unexpected density dependence of the onset of these NTMs is newly observed based on the statistics of many TCV discharges, suggesting a certain range of density within which the NTMs can occur. The range is found to broaden with increasing near-axis ECCD power. Based on a different set of experiments and corresponding interpretative simulations with the modified Rutherford equation (MRE), a simple analytical model for has been developed. This model proves to explain well the observed density dependence of mode onset, resulting from the density dependence of the stability of ohmic plasmas and of the ECCD efficiency. The simulations have also quantified various effects and reproduced self-consistently the entire island width evolution of the triggerless NTM, from the onset as a tearing mode at zero island width to the neoclassical saturation as an NTM. The standard terms of the MRE model used in the paper are relevant for NTMs that are seeded by other mechanisms.

Interaction of magnetic islands with turbulent electron temperature fluctuations in DIII-D and in GENE nonlinear gyrokinetic simulations

We present localized measurements of interactions between neoclassical tearing modes (NTMs) and turbulent electron temperature fluctuations () in the expected kθρs = 0–0.5 wave-number range of the ion temperature gradient (ITG) instability measured via correlation electron cyclotron emission (kθ and ρs are the poloidal wave-number and ion-sound Larmor radius, respectively). Comparison to GENE gyrokinetic simulations, shows qualitative agreement with being reduced (increased) inside (outside) of the islands due to modified local gradients, and being higher (lower) in the region outside the island where lower (higher) flow shear is expected due to radially asymmetric island shape. These results are consistent with previously reported modifications of long and intermediate wavelength turbulent density fluctuations and cross-field electron thermal diffusivity reduction at the O-point of magnetic islands. Interestingly, a 30% increase of is detected at the NTM rational surface when the island width is a few times ρs, which is replicated by GENE through zonal flow damping due to the destroyed magnetic field topology of the NTM rational surface.

Design of ECH launcher for KSTAR advanced Tokamak operation

For the advanced tokamak operation in Korea Superconducting Tokamak Advanced Research (KSTAR), up to 6 MW of electron cyclotron heating (ECH) is planned. The ECH launcher should be able to operate in steady state and serve as a central/off-axis heating and current drive, q-profile control, and control of the neoclassical tearing mode (NTM) and sawtooth. The water cooled launchers have been upgraded to include continuous operation with precise, high-speed real-time control of the beams by integration with the plasma control system (PCS) for supporting the experiments, in particular for suppressing NTM. In this study, the launcher was successfully operated for 78 s with about 650 kW EC power, where the temperature of the coolant, with a flow rate of 9.6 lpm, is saturated and approximately 2 °C. The launcher control system had a maximum control cycle of 5 kHz and a motor latency of about 10 ms, and the poloidal scanning speed of the beam was 20°/s. Additionally, for the higher localization of power deposition, the curvature and size of the mirrors in the launcher were optimized. This paper presents the ECH launcher design and its control system with the operation results.

NTM threshold island width measurements on Globus-M based on the Fitzpatrick heat transport model

We estimate the neoclassical tearing mode (NTM) threshold island width, Wc, associated with the bootstrap current contribution to the time evolution of the magnetic island. Following the original work by Fitzpatrick, we solve the heat transport equation for the electron temperature distribution with Wc being the input parameter. The obtained model temperature profile is then fitted to the Globus-M Thomson scattering (TS) data to deduce the actual Wc value. Due to the relatively low resolution of the Globus-M TS in the island region, we have also adopted ASTRA to provide the benchmarking.

Controlled neoclassical tearing mode (NTM) healing by fueling pellets and its impact on electron cyclotron current drive requirements for complete NTM stabilization

Controlled partial stabilization of core m/n = 2/1 neoclassical tearing modes (NTMs) by fueling deuterium pellets is reported in DIII-D and KSTAR H-mode plasmas (m/n are the poloidal/toroidal mode numbers). Analyses of DIII-D data exploring possible physics origins show that an explanation is offered by NTM-turbulence multi-scale interaction, triggered by a sudden increase of local gradients near q = 2 caused by the pellet. Pellet injection from the high-field side allows deep fueling which reaches the island region. In turn, low-k turbulent density fluctuations () increase by in the island region. This can drive transport across the island separatrices, reducing the pressure flat spot at the O-point and diminishing the NTM drive. The Mirnov probe array detects the reduction of the 2/1 magnetic amplitude by up to . Causality between elevated gradients outside of the island, turbulence spreading into the island and reduced NTM drive is qualitatively supported by non-linear gyrokinetic turbulence simulations. These show increased penetration of ion-scale from the background plasma to the O-point region when the background gradient is increased. This interaction has potentially far reaching consequences as it can lead to a reduction of the required electron cyclotron current density () for NTM suppression by 70%, as predicted by the modified Rutherford equation. This beneficial effect of fueling pellets can be important as is the anticipated active NTM control technique for ITER, but its efficiency will be lowered by third harmonic absorption in Pre-Fusion Power Operation-1 (PFPO-1) at half magnetic field.

Numerical study on toroidal mode coupling and triggering of neoclassical tearing modes by sawteeth

Numerical simulations have been carried out to understand the seeding of neoclassical tearing modes (NTMs), using a single fluid model and the four-field equations. The paper starts by considering a simplified physics situation: the destabilization of a linearly stable m/n = 3/2 mode by an unstable m/n = 2/2 mode (m/n being the poloidal/toroidal mode number). Within the single fluid model the mode coupling is found to be weakened by relative mode rotation and enhanced by finite plasma β value. For the four-field equations in case of a sufficiently low electron diamagnetic drift frequency, the results are similar to those from the single fluid equations. For a sufficiently large diamagnetic drift frequency, three regimes are found: (a) suppression regime for moderate plasma β values, in which the originally unstable 2/2 mode is stabilized by its coupling to the originally stable 3/2 mode; (b) oscillation regime for a sufficiently large β value, in which the 3/2 mode has the feature of an ideal mode, and the diamagnetic drift frequency reaches the shear Alfven frequency outside the tearing layer; (c) NTM regime for sufficiently large β value and bootstrap current density. Consistent with these findings, in our simulations 3/2 modes are triggered by sufficiently strong sawtooth crashes at high β value and/or a low electron diamagnetic drift frequency. A sufficiently large bootstrap current density is then required for the 3/2 island to grow into the NTM regime.

Non-linear simulations of neoclassical tearing mode control by externally driven RF current and heating, with application to ITER

Neoclassical tearing modes (NTM) must be controlled or suppressed to prevent a degradation of the energy confinement in tokamak plasmas. This can be done applying RF-current via electron cyclotron current drive and -heating at the rational surface where the instability appears. Both the current and heating generated by the RF waves are known to provide a stabilizing effect on the magnetic island. In the present work, we address the issue of neoclassical tearing mode stabilization by heating and current drive in an ITER-like configuration, using a stiff transport model. From a revised generalized Rutherford equation, we revisit the criterion on the RF current and power required to stabilize an NTM, showing that the level of plasma background heating (residual heat sources) in ITER significantly lowers the benefit of the RF heating contribution. Nonlinear magnetohydrodynamic simulations with the XTOR code, where a stiff transport model as well as RF-power and -current drive are implemented, are performed to compute the NTM stabilization efficiency. The stabilization efficiency due to the RF current contribution is found to be less than theoretically predicted in the case of continuous application, but consistent with theory in the modulated control scheme, suggesting an enhanced destabilization at the X-point. The role of RF heating for continuous application is found to be moderate for the range of power envisaged in ITER, essentially because of the detrimental effect of residual heat sources. This numerical work confirms the capability of the ITER RF system to control the NTM.

Tokamak-agnostic actuator management for multi-task integrated control with application to TCV and ITER

The plasma control system (PCS) of a long-pulse tokamak must be able to handle multiple control tasks simultaneously, and must be capable of robust event handling with a limited set of actuators. For ITER, this is particularly challenging given the large number of actuator-conflicting control requirements. To deal with these issues, this work develops a task-based approach, where a plasma supervisory controller and an actuator manager make high-level decisions on how to handle the considered control tasks, using generic actuator resources and controllers. This simplifies the interface for operators and physicists since the generic control tasks (instead of controllers) can be directly defined from the general physics goals. This approach also allows one to decompose the PCS into a tokamak-dependent layer and a tokamak-agnostic layer. The developed scheme is first implemented and tested on TCV for simultaneous β control, neoclassical tearing mode (NTM) control, central co-current drive, and H-mode control tasks. It is then applied to an ITER test scenario to prove its flexibility and applicability to systematically handle a large number of tasks and actuators.

Control of neoclassical tearing modes and integrated multi-actuator plasma control on TCV

The control of 2/1 neoclassical tearing modes (NTMs) with electron cyclotron (EC) waves has been studied both experimentally and numerically on TCV. Dynamic evolutions of NTMs along with time-varying deposition locations of the control beam have been studied in detail. The prevention of NTMs by means of preemptive EC (i.e. the control beam is switched on before the mode onset) has also been explored. A small sinusoidal sweeping with full amplitude of 0.07 (normalized to the minor radius) has been added to the control beam in two of the experiments to facilitate the comparison between NTM stabilization and prevention. It is shown that the prevention of NTMs is more efficient than NTM stabilization in terms of the minimum EC power required. Interpretative simulations with the modified Rutherford equation (MRE) have been performed to better quantify various effects, with coefficients well defined by dedicated experiments. Specifically, in order to obtain more insight on the dominant dependencies, a simple ad-hoc analytical model has been proposed to evaluate the time-varying classical stability index in the test discharges, based on the -triggered nature of these 2/1 NTMs. This allows simulating well the entire island width evolution with the MRE, starting from zero width and including both NTM stabilization and prevention cases for the first time. The exploration of NTM physics and control has facilitated the development of an NTM controller that is independent of the particular features of TCV and has been included in a generic plasma control system (PCS) framework. Integrated control of 2/1 NTMs, plasma (the ratio of plasma pressure to magnetic pressure) and model-estimated safety factor q profiles has been demonstrated on TCV.

Seeding of neoclassical tearing modes by internal crash events in the ASDEX Upgrade and DIII-D tokamaks

Seeding of neoclassical tearing modes (NTMs) by perturbations from other MHD instabilities (sawteeth, fishbones, ELMs, etc) is one of the main MHD problems which has to be avoided or controlled in ITER. NTMs can lead to strong degradation of plasma confinement or even to a disruption. This paper compares the seeding of (3,2) NTMs in DIII-D and ASDEX Upgrade tokamaks. It was found in both devices that a mode can start as an ideal kink mode that converts into a tearing mode on a time-scale much longer () than the duration of the trigger event (). These findings are in good agreement with those for (2,1) mode seeding in ASDEX Upgrade as well as with non-linear MHD simulations. This result revises the simplified picture of fast island formation occurring only during the trigger event.

On the effect of electron cyclotron waves on the evolution of neoclassical tearing modes in tokamak plasmas

In this paper we study the generation of current in a tokamak plasma in the presence of a magnetic island, using electron cyclotron (EC) waves in a process known as electron cyclotron current drive. We study some features related to the efficiency of the method, adopting a simplified model for a tokamak which incorporates the existence of a magnetic island associated with the occurrence of a neoclassical tearing mode instability. The study utilizes a self-consistent treatment of the interaction of EC waves with the plasma in the tokamak and the consequent current generation, taking into account the existence of the tokamak loop voltage and the occurrence of radial transport of particles, and also the existence of induced effects. The formalism also includes an approximate self-consistent description of the evolution of the width of the magnetic islands, which depends on the plasma current through the so-called modified Rutherford equation. The evolution of the islands depends on classical effects, which are driven mainly by the equilibrium current gradient, on neoclassical effects related to the perturbed bootstrap current and on the current generated by the radio waves. The results obtained in our numerical analyses confirm that the width of the islands can be substantially reduced by the use of EC waves, and lead to an estimate of the minimum amount of EC power required to be effective in reducing the width of magnetic islands. The results also show that, although the density of current generated by EC waves in the island region decreases along late time evolution, the total amount of plasma current is increased compared with the case in which the width of the island is assumed to remain constant.

Loss of bootstrap current in vicinity of magnetic islands

Profiles of the ion density and bootstrap current in the vicinity of magnetic islands are investigated based on the first principles gyro-kinetic particle simulation via the gyro-kinetic toroidal code. The physics on the recovery of the ion density gradient inside the islands in various collision regimes is discussed. Simulation results show that for small magnetic islands, the ion density gradient can survive inside the island due to the combination effect of both the banana-orbit width of trapped ions and the drift-orbit displacement of passing ions. It is suggested that the recovery of the pressure gradient inside small islands may play a more important role in the reduction of driving force of the ion bootstrap current in the evolution of the neoclassical tearing mode, rather than the so-called finite banana-orbit effects.

Effects of resonant magnetic perturbation on locked mode of neoclassical tearing modes

The effects of externally applied resonant magnetic perturbation (RMP) on the locked mode of the neoclassical tearing mode (NTM) are numerically investigated by means of a set of reduced magnetohydrodynamic equations. It is found that, for a small bootstrap current fraction, three regimes, namely the slight suppression regime, the small locked island (SLI) regime and the big locked island (BLI) regime, are discovered with the increase of RMP strength. For a much higher bootstrap current fraction, however, a new oscillation regime appears instead of the SLI regime, although the other regimes still remain. The physical process in each regime is analyzed in detail based on the phase difference between the NTM and the RMP. Moreover, the critical values of the RMP in both SLI and BLI regimes are obtained, and their dependence on key plasma parameters is discussed as well.

Quantitative modeling of neoclassical tearing mode driven fast ion transport in integrated TRANSP simulations

The TRANSP-‘Kick’ energetic particle transport model has been extended to study neoclassical tearing mode (NTM) driven fast ion (FI) transport with zero free parameters. FI transport induced by the NTM is obtained by calculating perturbed FI orbits via the guiding center particle following code orbit in the magnetic field of an experimentally characterized island chain. Transport probabilities are then used in TRANSP’s Monte Carlo module NUBEAM to modify the FI distribution in every time step of the full TRANSP analysis. This procedure retains all TRANSP functionality and self-consistently predicts the NTM impact on beam torque, current drive and heating. Comparisons to DIII-D steady state, hybrid and ITER baseline plasmas are encouraging with the model quantitatively recovering the measured neutron rates. FI effects depend on the location and width of FI phase space resonances which are not accounted for by the former ad hoc beam diffusivity model of TRANSP. Resonance overlaps result in a transport threshold, for the cases investigated herein, at . When the FI transport is dominated by energy and momentum redistribution. In particular, m/n = 3/2 NTMs lead to hollow profile at q = m/n and broadened profile in the core. When FI losses increase, the neutral beam torque () and driven current () decrease across the entire plasma. The effects on NB profiles can strongly depend on the NTM frequency and mode numbers with the 3/2 (2/1) broadening (peaking) near the magnetic axis.

Numerical study of tearing mode seeding in tokamak X-point plasma

A detailed understanding of island seeding is crucial to avoid neoclassical tearing modes and their negative consequences like confinement degradation and disruptions. In the present work, we investigate the growth of 2/1 islands in response to magnetic perturbations. Although we use externally applied perturbations produced by resonant magnetic perturbation (RMP) coils for this study, the results are directly transferable to island seeding by other MHD instabilities creating a resonant magnetic field component at the rational surface. Experimental results for 2/1 island penetration from ASDEX Upgrade are presented extending previous studies. Simulations are based on an ASDEX Upgrade L-mode discharge with low collisionality and active RMP coils. Our numerical studies are performed with the 3D, two-fluid, nonlinear MHD code JOREK. All three phases of mode seeding observed in the experiment are also seen in the simulations: first, a weak response phase characterized by large perpendicular electron flow velocities followed by a fast growth of the magnetic island size accompanied by a reduction of the perpendicular electron velocity and finally the saturation to a fully formed island state with perpendicular electron velocity close to zero. Thresholds for mode penetration are observed in the plasma rotation as well as in the RMP coil current. A hysteresis of the island size and electron perpendicular velocity is observed between the ramping up and down of the RMP amplitude consistent with an analytically predicted bifurcation. The transition from dominant kink/bending to tearing parity during the penetration is investigated.

Integrated current profile, normalized beta and NTM control in DIII-D

There is an increasing need for integrating individual plasma-control algorithms with the ultimate goal of simultaneously regulating more than one plasma property. Some of these integrated-control solutions should have the capability of arbitrating the authority of the individual plasma-control algorithms over the available actuators within the tokamak. Such decision-making process must run in real time since its outcome depends on the plasma state. Therefore, control architectures including supervisory and/or exception-handling algorithms will play an essential role in future fusion reactors like ITER. However, most plasma-control experiments in present devices have focused so far on demonstrating control solutions for isolated objectives. In this work, initial experimental results are reported for simultaneous current-profile control, normalized-beta control, and Neoclassical Tearing Mode (NTM) suppression in DIII-D. Neutral beam injection (NBI), electron-cyclotron (EC) heating & current drive (H&CD), and plasma current modulation are the actuation methods. The NBI power and plasma current are always modulated by the Profile Control category within the DIII-D Plasma Control System (PCS) in order to control both the current profile and the normalized beta. EC H&CD is utilized by either the Profile Control or the Gyrotron categories within the DIII-D PCS as dictated by the Off-Normal and Fault Response (ONFR) system, which monitors the occurrence of an NTM and regulates the authority over the gyrotrons. The total EC power and poloidal mirror angles are the gyrotron-related actuation variables. When no NTM suppression is required, the gyrotrons are used by the Profile Control category, but when NTM suppression is required, the ONFR transfers the authority over the gyrotrons to the NTM stabilization algorithm located in the Gyrotron category. Initial experimental results show that simultaneous control of different aspects of the plasma dynamics may improve the overall control and plasma performances. Also, the potential of the ONFR system to successfully integrate competing control algorithms is demonstrated.