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.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S03/pdf

Chapter 3: MHD stability, operational limits and disruptions

An investigation is made into the electron temperature perturbations associated with tearing modes in tokamak plasmas. It is found that there is a critical magnetic island width below which the conventional picture where the temperature is flattened inside the separatrix is invalid. This effect comes about because of the stagnation of magnetic field lines in the vicinity of the rational surface and the finite parallel thermal conductivity of the plasma. Islands whose widths lie below the critical value are not destabilized by the perturbed bootstrap current, unlike conventional magnetic islands. This effect may provide an explanation for some puzzling experimental results regarding error field‐induced magnetic reconnection. The critical island width is found to be fairly substantial in conventional tokamak plasmas, provided that the long mean‐free path nature of parallel heat transport and the anomalous nature of perpendicular heat transport are taken into account in the calculation.

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Helical temperature perturbations associated with tearing modes in tokamak plasmas

The DIII-D tokamak evolved from the earlier Doublet III device in 1986. Since then, the facility has undergone a number of changes including the installation of divertor baffles and pumping chambers in the vacuum vessel, the addition of a radiation shield, the development of extensive neutral beam and RF heating systems, and the addition of a comprehensive plasma control system. The facility has become the focus of a broad fusion plasma science research programme. An integrated picture of the facility and its capabilities is presented.

https://iopscience.iop.org/article/10.1088/0029-5515/42/5/313/pdf

A design retrospective of the DIII-D tokamak

A basic theoretical framework is developed for the investigation of tearing mode interactions in cylindrical geometry. A set of equations describing the coupled evolution of the amplitude and phase of each mode in the plasma is obtained by combining electromagnetic and fluid flow information. Two interactions are investigated in detail as examples. The first example considered is the slowing down of a rotating magnetic island interacting with a resistive wall. Under certain conditions bifurcated steady state solutions are obtained, allowing the system to make sudden irreversible transitions from high rotation to low rotation states as the interaction strength is gradually increased, and vice versa. The second example considered is the interaction of a rotating tearing mode with a static external magnetic perturbation. In general, a rotating island is stabilized to some extent by the interaction, whereas a locked island is destabilized. In fact, a rotating island of sufficiently small saturated width can be completely stabilized. However, once the island width becomes too large, conventional mode locking occurs prior to complete stabilization. The interaction with a tearing-stable plasma initially gives rise to a modification of the bulk plasma rotation, with little magnetic reconnection induced at the rational surface. However, once a critical perturbation field strength is exceeded, there is a sudden change in the plasma rotation as a locked island is induced at the rational surface, with no rotating magnetic precursor. The implications of these results for typical ohmically heated tokamaks are evaluated. The comparatively slow mode rotation in large tokamaks renders such devices particularly sensitive to error-field induced locked modes, and the collapse of mode rotation due to wall interactions

/pdf/interaction-of-tearing-modes-with-external-structures-in-5ch1ty2ofe.pdf

Interaction of tearing modes with external structures in cylindrical geometry (plasma)

A review of experiments and theory of electron cyclotron resonance heating (ECRH) and current drive (ECCD) is presented. An outline of the basic linear theory of wave propagation and absorption in the electron cyclotron range of frequencies and their harmonics is given and compared with experimental results from many devices. The experimental data base on quasilinear and nonlinear physics as well as on parametric wave decay is reviewed and compared to theory. Experiments and theory on doppler shifted absorption either by bulk or tail electrons (which can be created by other means) are discussed. ECRH provides means for controlled plasma breakdown and current ramp up in tokamaks and plays a key role in net current-free stellarator research. Start-up was investigated in many tokamaks and stellarators and the results are discussed in the light of the present day theoretical understanding. The role of ECRH to improve the understanding of both particle and energy confinement is described and special heating correlated features, such as 'density pump out' during ECRH are discussed. The application of modulated ECRH for perturbative heat wave studies and the comparison with both sawtooth heat pulse propagation and the steady state power balance analysis is presented. Electron cyclotron current drive is a possible method for current profile and MHD control in tokamaks and provides means for bootstrap current compensation in stellarators. The basic theory of electron cyclotron current drive is presented and compared to experiments in both tokamaks and stellarators. Experiments on sawtooth stabilization and MHD control by ECRH or ECCD are discussed and compared to theory. An increasing number of fusion devices is equipped with ECRH for bulk heating and sophisticated plasma physics investigations. A remarkable extension of the accessible plasma parameter range became possible by the recent development of sources with high power (1 MW) and frequency (110-160 GHz). Particular emphasis is given to new experiments and the refinement of theory incorporating plasma phenomena and the mutual impact on the wave physics.

http://iopscience.iop.org/article/10.1088/0741-3335/36/12/001/pdf

Electron cyclotron resonance heating and current drive in toroidal fusion plasmas

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

/pdf/effect-of-resonant-magnetic-perturbations-on-compass-c-nc9naqbxij.pdf

Effect of resonant magnetic perturbations on COMPASS-C tokamak discharges

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...

http://farside.ph.utexas.edu/Papers/1.860017.pdf

Critical error fields for locked mode instability in tokamaks

The question of the influence of nonaxisymmetric field perturbations on tokamaks is investigated. Recent experiments in the COMPASS‐C tokamak [in Proceedings of the 15th Symposium on Fusion Technology, Utrecht (North‐Holland, Amsterdam, 1989), Vol. 1, p. 361] with externally applied helical fields reveal that magnetic islands do not appear until the applied field exceeds a certain value, when plasma rotation and confinement are affected. A new resistive magnetohydrodynamic model including plasma rotation now provides an explanation of this threshold, and is quantitatively consistent with experimental results in Ohmic plasmas. The results indicate the tolerable error fields in future tokamaks. The effects of perturbations with various poloidal and toroidal mode numbers have been studied.

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Driven magnetic reconnection in the COMPASS‐C tokamak

A Mega Amp Spherical Tokamak (known as MAST) is proposed to be constructed at Culham Laboratory. The aim is to continue the highly successful tight aspect ratio work pioneered on the START machine at Culham.

The Mega Amp Spherical Tokamak

Non-inductive current drive using second harmonic ECRH at both 28 GHz and 60 GHz has been studied in the CLEO tokamak. At 60 GHz, RF driven currents of up to 5 kA have been observed at e = 4 × 1018m−3 for 185 kW of injected power, indicating an efficiency of η ≡ eIRFR0/PRF = 0.001 (1020 m−3, A, m, W−1). The RF driven current scaled linearly with total plasma current in the range of 5-15 kA and was maximized when the cyclotron resonance was located near to the centre of the plasma. Sawtooth activity was normally strongly affected and transient sawtooth stabilization was often observed. With detailed theoretical studies it is possible to reproduce both the high absorption efficiencies and the scaling of RF driven current with resonance position seen in the 60 GHz experiments. However, the magnitude of the observed current is a factor of about three below that theoretically predicted. At 28 GHz, no evidence of RF driven current could be detected. Possible reasons for this are discussed.

https://iopscience.iop.org/article/10.1088/0029-5515/28/6/005/pdf

T.N. Todd

Papers

Effect of resonant magnetic perturbations on COMPASS-C tokamak discharges

Critical error fields for locked mode instability in tokamaks

Driven magnetic reconnection in the COMPASS‐C tokamak

The Mega Amp Spherical Tokamak

ECRH current drive studies in the CLEO tokamak