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.
Energetic ions can drive Alfven gap modes unstable, causing large losses of fast ions. Toroidicityinduced Alfven eigenmodes (TAE) were expected to disappear into the shear Alfven continuum and become stable as the plasma beta increased. Although TAE modes may disappear, another dangerous instability with similar properties but approximately half the TAE frequency appears in a spectral gap that is created by finite beta effects. The measured frequency of the new mode agrees with the theoretical frequency of beta-induced Alfven eigenmodes.PACS numbers: 52.55.Fa, 52.35.Bj, 52.55.Pi An ignited magnetic fusion reactor must confine charged fusion products while they thermalize. Collective modes driven by alpha particles may degrade the alpha confinement and prevent ignition in a deuteriumtritium tokamak reactor. One way to study the physics of alpha-driven instabilities is to inject deuterium neutral beams into low toroidal field deuterium plasmas. In previous experiments, beam ions destabilized toroidicityinduced Alfven eigenmodes (TAE) in TFTR [1] and in DIII-D [2,3]. These modes are dangerous because they cause large, concentrated losses of the resonant fast ions that clamp the beam beta near the point of marginal stability [1,4]. ("Beta" is the ratio of kinetic to magnetic energy.) TAE modes appear in a gap in the Alfven continuum that is caused by the toroidal curvature of the plasma. The center of this "TAE gap" occurs at a frequencywhere VA ^B/^jAnntmi is the Alfven speed, q is the safety factor, R is the tokamak major radius, B is the magnetic field, and /!,-and m, are the ion density and mass [5], (An example of the gap structure appears in Fig. 4.) Analysis of the TAE mode suggested that its frequency would decrease into the Alfven continuum (where it would be heavily damped) as the plasma beta approached the stability limit for ideal ballooning modes [6]. But recent calculations found a new gap underneath the Alfven continuum caused by the compressional response of the plasma to shear Alfven waves in the presence of finite pressure and curvature [7]. The energy associated with this compression produces a frequency shift that raises the Alfven continuum, thus opening a low-frequency gap. Global modes in this gap with the dominant polarization of shear Alfven waves were discovered numerically [8]; we call these modes beta-induced Alfven eigenmodes (BAE). In this Letter, experimental evidence of destabilization of BAE modes by energetic beam ions is reported for the first time.The experiments are performed in the DIII-D tokamak (/?-1.8 m, a =0.65 m) in relatively pure (Z e fr^2) deuterium plasmas. Near tangential (tangency radius /? t an -1.10 m), -75 keV deuterium neutrals are injected in the direction of the plasma current; in some plasmas, near-perpendicular beams G?tan -0.74 m) are also injected. The normalized beta, p^=p t aB t /I p , is usually near the nominal limit of Z^ -3.5, although larger values can be obtained with current ramping. (Here p t is the toroidal beta in percent, a is the minor radius...
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