R.J. La Haye

Chapter 3: MHD stability, operational limits and disruptions

Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 Nucl. Fusion 39 2137-2664), is reviewed. Recent theoretical and experimental research has made important advances in both understanding and control of MHD stability in tokamak plasmas. Sawteeth are anticipated in the ITER baseline ELMy H-mode scenario, but the tools exist to avoid or control them through localized current drive or fast ion generation. Active control of other MHD instabilities will most likely be also required in ITER. Extrapolation from existing experiments indicates that stabilization of neoclassical tearing modes by highly localized feedback-controlled current drive should be possible in ITER. Resistive wall modes are a key issue for advanced scenarios, but again, existing experiments indicate that these modes can be stabilized by a combination of plasma rotation and direct feedback control with non-axisymmetric coils. Reduction of error fields is a requirement for avoiding non-rotating magnetic island formation and for maintaining plasma rotation to help stabilize resistive wall modes. Recent experiments have shown the feasibility of reducing error fields to an acceptable level by means of non-axisymmetric coils, possibly controlled by feedback. The MHD stability limits associated with advanced scenarios are becoming well understood theoretically, and can be extended by tailoring of the pressure and current density profiles as well as by other techniques mentioned here. There have been significant advances also in the control of disruptions, most notably by injection of massive quantities of gas, leading to reduced halo current fractions and a larger fraction of the total thermal and magnetic energy dissipated by radiation. These advances in disruption control are supported by the development of means to predict impending disruption, most notably using neural networks. In addition to these advances in means to control or ameliorate the consequences of MHD instabilities, there has been significant progress in improving physics understanding and modelling. This progress has been in areas including the mechanisms governing NTM growth and seeding, in understanding the damping controlling RWM stability and in modelling RWM feedback schemes. For disruptions there has been continued progress on the instability mechanisms that underlie various classes of disruption, on the detailed modelling of halo currents and forces and in refining predictions of quench rates and disruption power loads. Overall the studies reviewed in this chapter demonstrate that MHD instabilities can be controlled, avoided or ameliorated to the extent that they should not compromise ITER operation, though they will necessarily impose a range of constraints.

Neoclassical tearing modes and their control

A principal pressure limit in tokamaks is set by the onset of neoclassical tearing modes (NTMs), which are destabilized and maintained by helical perturbations to the pressure-gradient driven “bootstrap” current. The resulting magnetic islands break up the magnetic surfaces that confine the plasma. The NTM is linearly stable but nonlinearly unstable, and generally requires a “seed” to destabilize a metastable state. In the past decade, NTM physics has been studied and its effects identified as performance degrading in many tokamaks. The validation of NTM physics, suppressing the NTMs, and/or avoiding them altogether are areas of active study and considerable progress. Recent joint experiments give new insight into the underlying physics, seeding, and threshold scaling of NTMs. The physics scales toward increased NTM susceptibility in ITER, underlying the importance of both further study and development of control strategies. These strategies include regulation of “sawteeth” to reduce seeding, using static...

Effect of resonant magnetic perturbations on COMPASS-C tokamak discharges

Experimental results from the COMPASS-C tokamak reveal a sharp threshold in amplitude above which externally applied static resonant magnetic perturbations (RMPs) induce stationary magnetic islands. Such islands (in particular, m=2, n=1 islands) give rise to a significant degradation in energy and particle confinement, suppression of the sawtooth oscillation and a large change in the impurity ion toroidal velocity. The observed threshold for inducing stationary (2,1) islands is consistent with a phenomenological resistive MHD model which takes into account plasma rotation (including poloidal flow damping) and externally applied resonant fields. Broadly similar results are found for applied fields other than m=2, n=1. Other results from RMP experiments are also discussed, such as the stabilization of rotating MHD activity, stimulated disruptions and extensions to the disruptive density limit. Finally, the likely effect of field errors on large tokamaks is briefly examined in the light of the COMPASS-C results

Role of the radial electric field in the transition from L (low) mode to H (high) mode to VH (very high) mode in the DIII-D tokamak

The hypothesis of stabilization of turbulence by shear in the E×B drift speed successfully predicts the observed turbulence reduction and confinement improvement seen at the L (low)–H (high) transition; in addition, the observed levels of E×B shear significantly exceed the value theoretically required to stabilize turbulence. Furthermore, this same hypothesis is the best explanation to date for the further confinement improvement seen in the plasma core when the plasma goes from the H mode to the VH (very high) mode. Consequently, the most fundamental question for H‐mode studies now is: How is the electric field Er formed? The radial force balance equation relates Er to the main ion pressure gradient ∇Pi, poloidal rotation vθi, and toroidal rotation vφi. In the plasma edge, observations show ∇Pi and vθi are the important terms at the L–H transition, with ∇Pi being the dominant, negative term throughout most of the H mode. In the plasma core, Er is primarily related to vφi. There is a clear temporal and sp...

Suppression of large edge localized modes with edge resonant magnetic fields in high confinement DIII-D plasmas

Large sub-millisecond heat pulses due to Type-I edge localized modes (ELMs) have been eliminated reproducibly in DIII-D for periods approaching nine energy confinement times (τE) with small dc currents driven in a simple magnetic perturbation coil. The current required to eliminate all but a few isolated Type-I ELM impulses during a coil pulse is less than 0.4% of plasma current. Based on magnetic field line modelling, the perturbation fields resonate with plasma flux surfaces across most of the pedestal region (0.9 ≤ ψN ≤ 1.0) when q95 = 3.7 ± 0.2, creating small remnant magnetic islands surrounded by weakly stochastic field lines. The stored energy, βN, H-mode quality factor and global energy confinement time are unaltered by the magnetic perturbation. Although some isolated ELMs occur during the coil pulse, long periods free of large Type-I ELMs (Δt > 4–6 τE) have been reproduced numerous times, on multiple experimental run days in high and intermediate triangularity plasmas, including cases matching the baseline ITER scenario 2 flux surface shape. In low triangularity, lower single null plasmas, with collisionalities near that expected in ITER, Type-I ELMs are replaced by small amplitude, high frequency Type-II-like ELMs and are often accompanied by one or more ELM-free periods approaching 1–2 τE. Large Type-I ELM impulses represent a severe constraint on the survivability of the divertor target plates in future burning plasma devices. Results presented in this paper demonstrate that non-axisymmetric edge magnetic perturbations provide a very attractive development path for active ELM control in future tokamaks such as ITER.

Sustained rotational stabilization of DIII-D plasmas above the no-wall beta limit

Sustained stabilization of the n=1 kink mode by plasma rotation at beta approaching twice the stability limit calculated without a wall has been achieved in DIII-D by a combination of error field reduction and sufficient rotation drive. Previous experiments have transiently exceeded the no-wall beta limit. However, demonstration of sustained rotational stabilization has remained elusive because the rotation has been found to decay whenever the plasma is wall stabilized. Recent theory [Boozer, Phys. Rev. Lett. 86, 5059 (2001)] predicts a resonant response to error fields in a plasma approaching marginal stability to a low-n kink mode. Enhancement of magnetic nonaxisymmetry in the plasma leads to strong damping of the toroidal rotation, precisely in the high-beta regime where it is needed for stabilization. This resonant response, or “error field amplification” is demonstrated in DIII-D experiments: applied n=1 radial fields cause enhanced plasma response and strong rotation damping at beta above the no wal...

Active feedback stabilization of the resistive wall mode on the DIII-D device

A proof of principle magnetic feedback stabilization experiment has been carried out to suppress the resistive wall mode (RWM), a branch of the ideal magnetohydrodynamic (MHD) kink mode under the influence of a stabilizing resistive wall, on the DIII-D tokamak device [Plasma Phys. and Contr. Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. The RWM was successfully suppressed and the high beta duration above the no wall limit was extended to more than 50 times the resistive wall flux diffusion time. It was observed that the mode structure was well preserved during the time of the feedback application. Several lumped parameter formulations were used to study the feedback process. The observed feedback characteristics are in good qualitative agreement with the analysis. These results provide encouragement to future efforts towards optimizing the RWM feedback methodology in parallel to what has been successfully developed for the n = 0 vertical positional control. Newly developed MHD codes have been extremely useful in guiding the experiments and in providing possible paths for the next step.

Critical error fields for locked mode instability in tokamaks

Otherwise stable discharges can become nonlinearly unstable to disruptive locked modes when subjected to a resonant m=2, n=1 error field from irregular poloidal field coils, as in DIII‐D [Nucl. Fusion 31, 875 (1991)], or from resonant magnetic perturbation coils as in COMPASS‐C [Proceedings of the 18th European Conference on Controlled Fusion and Plasma Physics, Berlin (EPS, Petit‐Lancy, Switzerland, 1991), Vol. 15C, Part II, p. 61]. Experiments in Ohmically heated deuterium discharges with q≊3.5, n ≊ 2 × 1019 m−3 and BT ≊ 1.2 T show that a much larger relative error field (Br21/BT ≊ 1 × 10−3) is required to produce a locked mode in the small, rapidly rotating plasma of COMPASS‐C (R0 = 0.56 m, f≊13 kHz) than in the medium‐sized plasmas of DIII‐D (R0 = 1.67 m, f≊1.6 kHz), where the critical relative error field is Br21/BT ≊ 2 × 10−4. This dependence of the threshold for instability is explained by a nonlinear tearing theory of the interaction of resonant magnetic perturbations with rotating plasmas that p...

Edge Localized Mode Control with an Edge Resonant Magnetic Perturbation

This work was funded by the U.S. Department of Energy under Grant Nos. DE-FC02-04ER54698, DE-FG02- 04ER54758, DE-FG03-01ER54615, W-7405-ENG-48, DEFG03-96ER54373, DE-FG02-89ER53297, DE-AC05- 00OR22725, and DE-AC04-94AL85000.

Nonaxisymmetric field effects on Alcator C-Mod

A set of external coils (A-coils) capable of producing nonaxisymmetric, predominantly n=1, fields with different toroidal phase and a range of poloidal mode m spectra has been used to determine the threshold amplitude for mode locking over a range of plasma parameters in Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda, P. Bonoli, S. Fairfax, C. Fiore, J. Goetz, S. Golovato, R. Granetz, M. Greenwald et al., Phys. Plasmas 1, 1511 (1994)]. The threshold perturbations and parametric scalings, expressed in terms of (B21∕BT), are similar to those observed on larger, lower field devices. The threshold is roughly linear in density, with typical magnitudes of order 10−4. This result implies that locked modes should not be significantly more problematic for the International Thermonuclear Experimental Reactor [I. P. B. Editors, Nucl. Fusion 39, 2286 (1999)] than for existing devices. Coordinated nondimensional identity experiments on the Joint European Torus [Fusion Technol. 11, 13 (1987)], DIII-D [Fusion T...