Neoclassical Tearing Modes Research Articles

Reduction of neoclassical polarization current contribution to NTM evolution

The neoclassical polarization current, which can be generated by a time-dependent electric field resulting from magnetic island rotation, is believed to play an important role in the initial stage of the neoclassical tearing mode (NTM) evolution in tokamak plasmas. In the previous analytical description of the neoclassical polarization current contribution to the evolution of NTMs in the limit of low collision frequency (νii≪εω, νii is ion collision frequency, ε is the inverse aspect ratio, and ω is the island propagation frequency in the plasma rest frame), the width of magnetic islands has been assumed to be much larger than the finite-banana-width (FBW) of the trapped ions in order to solve the drift-kinetic equation of ions by using the perturbation method. In this paper, we introduce a new analytical approach to investigate the neoclassical polarization current contribution to the NTM evolution without the assumption of the large island width by solving the drift-kinetic equation in a so-called ion-banana-center coordinate system. The results show that, when the island width is comparable to the FBW of the thermal ion, the neoclassical polarization current term in the equation of the NTM evolution is much smaller than the previous analytical expression but matches well with the empirical anticipation commonly adopted in experiments.

The ASDEX Upgrade Program Targeting Gaps to Fusion Energy

Recent experiments in ASDEX Upgrade aimed at improving the physics base for ITER and DEMO to prepare operation and aid the design. In order to increase its exhaust capabilities and operational flexibility, a new bulk W divertor as well as an adjustable cryopump had been installed prior to the 2014 campaign. In experiments with high-field-side pellet injection, central electron densities twice as high as the Greenwald density limit could be achieved without strongly increasing the pedestal density and deleterious effect on confinement. Due to its large installed heating power, a large normalized heat flux $P_{\mathrm{ sep}}/R = 10$ MWm $^{-1}$ has been reached, representing two-thirds of the ITER value, under partially detached conditions with a peak target heat flux well below 10 MWm $^{-2}$ . The divertor load could be further reduced by increasing the core radiation, still keeping the confinement in the range of $H_{98y2}\approx 1$ . Suppression of edge-localized modes (ELMs) at low collisionality has been observed in a narrow spectral window in contrast to earlier results at high densities. The ITER $Q = 10$ baseline scenario has been investigated, matching as close as possible the triangularity, the plasma beta, $q_{95}$ , and the distance to the L-H threshold. It turned out that the ELM frequency is low and consequently the energy ejected by a single ELM is very high and ELM mitigation appears to be difficult. As a possible alternative, a scenario has been developed achieving a similar performance at a lower plasma current (and consequently higher $q_{95})$ . Experiments using electron cyclotron current drive (ECCD) with feedback-controlled deposition have allowed successfully testing several control strategies for ITER, including automated control of (3, 2) and (2, 1) neoclassical tearing modes during a single discharge. Concerning advanced scenarios, experiments with central ctr-ECCD have been performed in order to modify the q-profile. A strong reversal of the q-profile could be stationarily achieved and an internal transport barrier could be triggered. In disruption mitigation studies with massive gas injection (MGI), a runaway electron beam could be provoked and mitigated by a second MGI. Ongoing enhancements aim at strengthening the power supplies in order to allow full use of the installed heating power, the exchange of two ion cyclotron resonance heating (ICRH) antennas to reduce the W influx during ICRH, and the upgrading of the electron cyclotron resonance heating (ECRH) system to 7–8 MW for 10 s.

NTM stabilization by alternating O-point EC current drive using a high-power diplexer

At the tokamak ASDEX Upgrade, experiments to stabilize neoclassical tearing modes (NTMs) by electron cyclotron (EC) heating and current drive in the O-points of the magnetic islands were performed. For the first time, injection into the O-points of the revolving islands was performed via a fast directional switch, which toggled the EC power between two launchers synchronously to the island rotation. The switching was performed by a resonant diplexer employing a sharp resonance in the transfer function, and a small frequency modulation of the feeding gyrotron around the slope of the resonance. Thus, toggling of the power between the two outputs of the diplexer connected to two articulating launchers was possible. Phasing and control of the modulation were performed via a set of Mirnov coils and appropriate signal processing. In the paper, technological issues, the design of the diplexer, the tracking of the diplexer resonance to the gyrotron frequency, the generation and processing of control signals for the gyrotron, and the typical performance concerning switching contrast and efficiency are discussed. The plasma scenario is described, and plasma experiments are presented, where the launchers scanned the region of the resonant surface continuously and also where the launchers were at a fixed position near to the q = 1.5-surface. In the second case, complete stabilization of a 3/2 NTM could be reached. These experiments are also seen as a technical demonstration for the applicability of diplexers in large-scale ECRH systems.

Nonlinear evolution of multi-helicity neo-classical tearing modes in rotating tokamak plasmas

Plasma perturbations from the core and/or boundary regions of tokamaks can provide seed islands for the excitation of neo-classical tearing modes (NTMs) with negative , where is the linear instability parameter of the classical tearing mode. In this work, by means of reduced magnetohydrodynamic simulations, we numerically investigate the nonlinear evolution of multi-helicity NTMs in rotating tokamak plasmas with these two types of plasma perturbations with different boundary conditions. In the first case of initial plasma perturbations from the core region with a zero boundary condition, the meta-stable property of seed-island triggered NTM with negative is verified in the single helicity simulation. Nevertheless in the multiple helicity simulation, this seed-island triggered NTM with negative can be suppressed by a spontaneous NTM with positive through the competitive interaction between NTMs with different helicities. If a fixed poloidal rotation is taken into account in the first case, two different helicity NTMs could coexist in the saturation stage, which is different qualitatively from the process without plasma rotation. In the second case of initial plasma perturbations from the boundary region with a nonzero boundary condition, as the amplitude of plasma perturbations on the boundary increases, the mode with negative gradually changes from the driven-reconnection state to the NTM state, accompanied by an enhancement of magnetic island width in the single helicity simulation. Nevertheless in the multi-helicity simulation, the spontaneous NTM with positive can make the driven-reconnection triggered NTM with negative transfer from the NTM state back to the driven-reconnection state again. The underlying mechanism behind these transitions is analyzed step by step. Effects of fixed and unfixed poloidal rotations on the nonlinear interaction processes are also investigated in detail. In addition, the appearance and disappearance of the magnetic stochasticity resulting from the nonlinear coupling among the multi-helicity NTMs are discussed in the second case.

Neoclassical tearing mode seeding by coupling with infernal modes in low-shear tokamaks

A numerical and an analytical study of the triggering of resistive MHD modes in tokamak plasmas with low magnetic shear core is presented. Flat q profiles give rise to fast growing pressure driven MHD modes, such as infernal modes. It has been shown that infernal modes drive fast growing islands on neighbouring rational surfaces. Numerical simulations of such instabilities in a MAST-like configuration are performed with the initial value stability code XTOR-2F in the resistive frame. The evolution of magnetic islands are computed from XTOR-2F simulations and an analytical model is developed based on Rutherford’s theory in combination with a model of resistive infernal modes. The parameter is extended from the linear phase to the non-linear phase. Additionally, the destabilising contribution due to a helically perturbed bootstrap current is considered. Comparing the numerical XTOR-2F simulations to the model, we find that coupling has a strong destabilising effect on (neoclassical) tearing modes and is able to seed 2/1 magnetic islands in situations when the standard NTM theory predicts stability.

Extended magneto-hydro-dynamic model for neoclassical tearing mode computations

A self-consistent fluid model for describing neoclassical tearing modes in global magneto-hydro-dynamic simulations is presented. It is illustrated by its application to a simple toroidal configuration unstable to the (2, 1) tearing mode. The island saturation is verified to increase with the bootstrap current fraction. New features that are specific to this model are evidenced, like the unsteady saturated state of the island, and its deformation to a droplet shape, when the magnetic Prandtl number is not too high. Synthetic diagnostics demonstrate that diamagnetic and neoclassical effects should have in this case a measurable impact on the signature of magnetic islands.

Design of Control System for Suppression of Neoclassical Tearing Modes with Electron Cyclotron Heating and Current Drive on EAST

This paper discusses a control system for the Experimental Advanced Superconducting Tokamak (EAST) that suppresses neoclassical tearing modes (NTMs) (3/2 and 2/1) by applying electron cyclotron (EC) heating and current drive. It allows the magnetic island to be detected and localized in real time and the EC beam to be deposited exactly on the island position by stepwise tuning of the steerable launch mirror. The mode features are identified with temperature perturbation to develop the algorithm for real-time island location. The necessary parameters for the design of the control system are discussed and determined based on simulation of the nonlinear island growth of NTMs with application of EC current drive. Although similar work has been done on many other devices, this is the first attempt on EAST.

Modulation of Core Turbulent Density Fluctuations by Large-Scale Neoclassical Tearing Mode Islands in the DIII-D Tokamak.

We report the first observation of localized modulation of turbulent density fluctuations n[over ˜] (via beam emission spectroscopy) by neoclassical tearing modes (NTMs) in the core of the DIII-D tokamak. NTMs are important as they often lead to severe degradation of plasma confinement and disruptions in high-confinement fusion experiments. Magnetic islands associated with NTMs significantly modify the profiles and turbulence drives. In this experiment n[over ˜] was found to be modulated by 14% across the island. Gyrokinetic simulations suggest that n[over ˜] could be dominantly driven by the ion temperature gradient instability.

Non-perturbative measurement of cross-field thermal diffusivity reduction at the O-point of 2/1 neoclassical tearing mode islands in the DIII-D tokamak

Neoclassical tearing modes (NTMs) often lead to the decrease of plasma performance and can lead to disruptions, which makes them a major impediment in the development of operating scenarios in present toroidal fusion devices. Recent gyrokinetic simulations predict a decrease of plasma turbulence and cross-field transport at the O-point of the islands, which in turn affects the NTM dynamics. In this paper, a heat transport model of magnetic islands employing spatially non-uniform cross-field thermal diffusivity (χ⊥) is presented. This model is used to derive χ⊥ at the O-point from electron temperature data measured across 2/1 NTM islands in DIII-D. It was found that χ⊥ at the O-point is 1 to 2 orders of magnitude smaller than the background plasma transport, in qualitative agreement with gyrokinetic predictions. As the anomalously large values of χ⊥ are often attributed to turbulence driven transport, the reduction of the O-point χ⊥ is consistent with turbulence reduction found in recent experiments. Finally, the implication of reduced χ⊥ at the O-point on NTM dynamics was investigated using the modified Rutherford equation that predicts a significant effect of reduced χ⊥ at the O-point on NTM saturation.

Kinetic effects on the currents determining the stability of a magnetic island in tokamaks

The role of the bootstrap and polarization currents for the stability of ă neoclassical tearing modes is investigated employing both a drift ă kinetic and a gyrokinetic approach. The adiabatic response of the ions ă around the island separatrix implies, for island widths below or around ă the ion thermal banana width, density flattening for islands rotating at ă the ion diamagnetic frequency, while for islands rotating at the ă electron diamagnetic frequency the density is unperturbed and the only ă contribution to the neoclassical drive arises from electron temperature ă flattening. As for the polarization current, the full inclusion of ă finite orbit width effects in the calculation of the potential ă developing in a rotating island leads to a smoothing of the ă discontinuous derivatives exhibited by the analytic potential on which ă the polarization term used in the modeling is based. This leads to a ă reduction of the polarization-current contribution with respect to the ă analytic estimate, in line with other studies. Other contributions to ă the perpendicular ion current, related to the response of the particles ă around the island separatrix, are found to compete or even dominate the ă polarization-current term for realistic island rotation frequencies.

Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co-Ip direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with PRF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.

An improved neoclassical drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in tokamak plasmas

The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes in tokamak plasmas is calculated using an improved, neoclassical, four-field, drift-magnetohydrodynamical model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing or stabilizing provided that ηi≡dlnTi/dlnne does not exceed some threshold value. In certain ranges of ηi, the polarization current is found to have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.

Modeling of neoclassical tearing mode stabilization by electron cyclotron heating and current drive in tokamak plasmas

An integrated numerical system is established to model time-dependent behavior of the neoclassical tearing mode (NTM) in a tokamak which solves the modified Rutherford equation (MRE) by coupling with plasma transport, equilibrium, heating and current drive. The MRE is formulated in a simple form to be well-suited for time-dependent simulations including a predictive purpose for the feedback controller design by coupling the electron cyclotron effect self-consistently. In particular the electron cyclotron heating (ECH) effect is newly included to the MRE in addition to the electron cyclotron current drive (ECCD) effect to investigate their impact to stabilize the NTM. The integrated numerical system is applied to experiments for benchmarking in which NTMs are stabilized by ECCD and by ECH at ASDEX Upgrade and TCV, respectively. The impact of ECCD and ECH on stabilizing NTMs is identified in the simulations.

Rotation profile flattening and toroidal flow shear reversal due to the coupling of magnetic islands in tokamaks

The electromagnetic coupling of helical modes, even those having different toroidal mode numbers, modifies the distribution of toroidal angular momentum in tokamak discharges. This can have deleterious effects on other transport channels as well as on magnetohydrodynamic (MHD) stability and disruptivity. At low levels of externally injected momentum, the coupling of core-localized modes initiates a chain of events, whereby flattening of the core rotation profile inside successive rational surfaces leads to the onset of a large m/n = 2/1 tearing mode and locked-mode disruption. With increased torque from neutral beam injection, neoclassical tearing modes in the core may phase-lock to each other without locking to external fields or structures that are stationary in the laboratory frame. The dynamic processes observed in these cases are in general agreement with theory, and detailed diagnosis allows for momentum transport analysis to be performed, revealing a significant torque density that peaks near the 2/1 rational surface. However, as the coupled rational surfaces are brought closer together by reducing q95, additional momentum transport in excess of that required to attain a phase-locked state is sometimes observed. Rather than maintaining zero differential rotation (as is predicted to be dynamically stable by single-fluid, resistive MHD theory), these discharges develop hollow toroidal plasma fluid rotation profiles with reversed plasma flow shear in the region between the m/n = 3/2 and 2/1 islands. The additional forces expressed in this state are not readily accounted for, and therefore, analysis of these data highlights the impact of mode coupling on torque balance and the challenges associated with predicting the rotation dynamics of a fusion reactor—a key issue for ITER.

Mechanical analyses of the waveguide flange coupling for the first confinement system of the ITER electron cyclotron upper launcher

The four electron cyclotron (EC) upper port antennas (or “upper launchers” —UL) will be used to drive current locally inside magnetic islands located at the q=2 (or smaller) rational surfaces in order to stabilize neoclassical tearing modes (NTMs), as well as heat inside of ρ of about 0.4. Each antenna consists of eight beam lines that are designed for the transmission of 1.5 MW of mm-wave power at 170GHz. The First Confinement System (FCS) is formed by the ex-vessel mm-wave waveguide components, for which SIC-1 classification requirements apply.The beam lines in the FCS comprise a Z shaped set of straight corrugated waveguides with a nominal diameter of 50mm connected by miter bends. This system is subjected to imposed displacements coming mainly from the thermal expansion of the vacuum vessel, seismic events and/or plasma disruption events. In absence of suitable SIC-1 waveguide bellows, the FCS waveguides must provide the necessary mechanical functional compliance. This has required the development of a dedicated, flange type coupling system with double metallic seals, capable of resisting the generated external loads while maintaining vacuum tightness and alignment. This paper presents the results of the design, analysis and pre-qualification experimental work done on the waveguides and the integrated SIC-1 compliant coupling system.

Numerical analysis of the optimized performance of the electron cyclotron wave system in a HL-2M tokamak**Project supported by the National Natural Science Foundation of China (Grant Nos. 11375085, 11405082, 11505092, 11475083, and 11375053), the National Magnetic Confinement Fusion Science Program of China (Grant Nos. 2013GB104004, 2013GB111000, 2014GB107000, and 2014GB108002), and the Natural Science Foundation of Hunan Province, China (Grant No.

The capabilities of current drive, neoclassical tearing mode (NTM) stabilization, and sawtooth control are analyzed for the electron–cyclotron wave (ECW) system in a HL-2M tokamak. Better performance of the upper launcher is demonstrated in comparison with that of a dropped upper launcher, in terms of JEC/Jbs for NTM stabilization and IECCD/(Δρtor)2 for sawtooth control. 1-MW ECW power is enough for the 3/2 NTM stabilization, and 1.8-MW ECW power is required to suppress 2/1 NTM in a single null divertor equilibrium with 1.2-MA toroidal current with the upper launcher. Optimization simulation of electron–cyclotron current drive (ECCD) is carried out for three mirrors in an equatorial port, indicating that the middle mirror has a good performance compared with the top and bottom mirrors. The results for balanced co- and counter-ECCD in an equatorial port are also presented.

The dynamics of a neoclassical tearing mode (NTM) influenced by energetic ions on EAST

In the 2014 year’s campaign of experimental advanced superconducting tokamak (EAST), a series of Magnetohydrodynamics (MHD) instabilities were observed as the launching of Neutral Beam Injection (NBI), the most interesting one of which is the neoclassical tearing mode (NTM). Evidence clearly shows that a kink mode present after a strong sawtooth-like (ST-like) crash leaves a perturbation near the location of the magnetic island, providing the initial seed. The interaction of energetic ions makes the magnetic island oscillate both in island width and in rotation frequency. Analysis indicates that the bulk plasma still dominates the dynamics of NTM, and the orbit excursion of energetic ions induces a polarization current and modifies the width and rotation frequency of the neoclassical magnetic island.

New insights into the generalized Rutherford equation for nonlinear neoclassical tearing mode growth from 2D reduced MHD simulations

Two dimensional reduced MHD simulations of neoclassical tearing mode growth and suppression by ECCD are performed. The perturbation of the bootstrap current density and the EC drive current density perturbation are assumed to be functions of the perturbed flux surfaces. In the case of ECCD, this implies that the applied power is flux surface averaged to obtain the EC driven current density distribution. The results are consistent with predictions from the generalized Rutherford equation using common expressions for and . These expressions are commonly perceived to describe only the effect on the tearing mode growth of the helical component of the respective current perturbation acting through the modification of Ohm’s law. Our results show that they describe in addition the effect of the poloidally averaged current density perturbation which acts through modification of the tearing mode stability index. Except for modulated ECCD, the largest contribution to the mode growth comes from this poloidally averaged current density perturbation.

Suppressing magnetic island and accelerating its rotation by modulated resonant magnetic perturbation

A new method is investigated for stabilizing large magnetic islands or neoclassical tearing modes (NTMs) and for accelerating mode rotation by using modulated resonant magnetic perturbation (RMP). The RMP is applied via feedback control only when the phase difference between the mode and RMP is in the range of π ⩽ Φ ⩽ 2π. Nonlinear numerical modeling based on reduced magnetohydrodynamics (MHD) equations has been carried out. It is found that the mode/island can be either completely or substantially suppressed, when the RMP is applied in the phase region π ⩽ Φ ⩽ 1.5π or π ⩽ Φ ⩽ 2π. The mode frequency is significantly increased for the second case. This method can also be utilized for avoiding mode locking, which often triggers plasma disruption.

Real-Time Detection for Magnetic Island of Neoclassical Tearing Mode in EAST Plasma Control System**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2014GB103000, 2012GB103000, and 2012GB103002), National Natural Science Foundation of China (No. 11205200)

Accurate detection of a magnetic island in real time is one of the important issues for the tearing mode (TM) and neoclassical tearing mode (NTM) control. This paper presents a real-time detection system for the magnetic island of NTM control in the EAST Plasma Control System (PCS). Diagnosis is based on magnetic periodic perturbation and electron temperature fluctuation caused by the magnetic island. Therefore, a Mirnov measurement has been selected to calculate the island's parameters, such as island width, frequency of island rotation, and toroidal number. The electron cyclotron emission (ECE) system can detect the island position, which is calculated by two fast detection algorithms called correlation analysis and Hilbert transform. For future NTM control, real-time equilibrium reconstruction (rt-EFIT) is needed to locate the rational q-surface where the island is detected. This fast detection system is able to detect an island within 3 ms. It can be integrated into PCS to provide effective parameters of the island for NTM control by using EC resonance heating (ECRH) in the next experiment of EAST.