Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document 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 S128 Chapter 3: MHD stability, operational limits and disruptions 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.

The maximum normalized beta achieved in long-pulse tokamak discharges at low collisionality falls significantly below both that observed in short pulse discharges and that predicted by the ideal MHD theory. Recent long-pulse experiments, in particular those simulating the International Thermonuclear Experimental Reactor ͑ITER͒ ͓M. Rosenbluth et al., Plasma Physics and Controlled Nuclear Fusion ͑International Atomic Energy Agency, Vienna, 1995͒, Vol. 2, p. 517͔ scenarios with low collisionality e * , are often limited by low-m/n nonideal magnetohydrodynamic ͑MHD͒ modes. The effect of saturated MHD modes is a reduction of the confinement time by 10%-20%, depending on the island size and location, and can lead to a disruption. Recent theories on neoclassical destabilization of tearing modes, including the effects of a perturbed helical bootstrap current, are successful in explaining the qualitative behavior of the resistive modes and recent results are consistent with the size of the saturated islands. Also, a strong correlation is observed between the onset of these low-m/n modes with sawteeth, edge localized modes ͑ELM͒, or fishbone events, consistent with the seed island required by the theory. We will focus on a quantitative comparison between both the conventional resistive and neoclassical theories, and the experimental results of several machines, which have all observed these low-m/n nonideal modes. This enables us to single out the key issues in projecting the long-pulse beta limits of ITER-size tokamaks and also to discuss possible plasma control methods that can increase the soft ␤ limit, decrease the seed perturbations, and/or diminish the effects on confinement.

A kinetic theory for magnetic islands in a low collision frequency tokamak plasma is presented. Self-consistent equations for the islands’ width, w, and propagation frequency, ω, are derived. These include contributions from the perturbed bootstrap current and the toroidally enhanced ion polarization drift. The bootstrap current is independent of the island propagation frequency and provides a drive for the island in tokamak plasmas when the pressure decreases with an increasing safety factor. The polarization drift is frequency dependent, and therefore its effect on the island stability cannot be deduced unless ω is known. This frequency is determined by the dominant dissipation mechanism, which for low effective collision frequency, νeff=ν/ε<ω, is governed by the electrons close to the trapped/passing boundary. The islands are found to propagate in the electron diamagnetic direction in which case the polarization drift is stabilizing and results in a threshold width for island growth, which is of the order of the ion banana width. At larger island widths the polarization current term becomes small and the island evolution is determined by the bootstrap current drive and Δ′ alone, where Δ′ is a measure of the magnetic free energy.

A detailed comparison is made between the tearing-type modes observed in TFTR supershot plasmas and the nonlinear, neoclassical pressure-gradient -driven tearing mode theory. Good agreement is found on the nonlinear evolution of single helicity magnetic islands (m/n = 3/2, 4/3, or 5/4, where m and n are the poloidal and toroidal mode numbers, respectively). The saturation of these neoclassical tearingtype modes requires 6' ( 0 (where 5' is the well-known parameter for classical current-driven tearing instability), which is also consistent with the numerical calculation using the experimental data.PACS numbers: 52.55. Fa, 52.30.Jb, 52.35.Py, Understanding the tearing-type MHD (magnetohydrodynamic) instabilities observed in TFTR neutral-beam (NB) heated supershot [1] plasmas has long been a challenge for plasma theory. These modes typically have low frequency ( f (50kHz) and low mode numbers (m/n = 3/2, 4/3, and 5/4). The m/n = 2/1 modes are not usually seen in the high-performance supershot plasmas. The important effects of these MHD modes on plasma performance have been discussed in Ref. [2]. It is found that when these modes are large they can cause a strong deterioration in plasma performance [2] as measured by the DD or DT neutron rate, plasma-stored energy, energy confinement time, etc. Considerable effort has been expended on the theoretical interpretation and numerical simulation of these modes. These works have been mostly based upon the classical current-driven tearing mode theory [3,4]. However, the results have been unsatisfactory [5,6]. In this Letter, we compare the experimental results with a relatively new theory, the neoclassical pressure-gradient-(7'p) driven tearing mode theory [7,8]. The results are found to be very encouraging.The evolution of two typical tearing-type modes in the high power NB heated, high P (plasma pressure/magnetic field pressure) supershot plasmas is shown in Fig. 1.Discharge A developed an m/n = 3/2 mode. Discharge B developed an m/n = 4/3 mode. Detailed analyses of the MHD modes and their deterioration effect on plasma transport [see Fig.