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 onset of a neoclassical tearing mode (NTM) depends on the existence of a large enough seed island. It is shown in the Joint European Torus that NTMs can be readily destabilized by long-period sawteeth, such as obtained by sawtooth stabilization from ion-cyclotron heating or current drive. This has important implications for burning plasma scenarios, as alpha particles strongly stabilize the sawteeth. It is also shown that, by adding heating and current drive just outside the inversion radius, sawteeth are destabilized, resulting in shorter sawtooth periods and larger beta values being obtained without NTMs.

Abstract. Optimal design and use of electron cyclotron heating (ECH) requires that accurate and relatively quick computer codes be available for prediction of wave coupling, propagation, damping, and current drive at realistic levels of EC power. To this end, a number of codes have been developed in laboratories worldwide. A detailed comparison of these codes is desirable since they use a variety of methods for modeling 2 the behavior and effects of the waves. The approach used in this benchmarking study is to apply these codes to a small number of representative cases. Following minor remedial work on some codes, the agreement between codes for off-axis application is excellent.The largest systematic differences are found between codes with weakly relativistic and fully relativistic evaluation of the resonance condition, but even there the differences amount to less than 0.02 in normalized minor radius. For some other cases, for example for central current drive, the code results may differ significantly due to differences in the physics models used.

Neoclassical tearing modes (NTMs) are magnetohydrodynamic modes that can limit the performance of high β discharges in a tokamak, leading eventually to a plasma disruption. A NTM is sustained by the perturbation of the ‘bootstrap’ current, which is a consequence of the pressure flattening across a magnetic island. Control and suppression of this mode can be achieved by means of electron cyclotron waves (ECWs) which allow the deposition of highly localized power at the island location. The ECW power replenishes the missing bootstrap current by generating a current perturbation either inductively, through a temperature perturbation (electron cyclotron resonance heating), or non-inductively by direct current drive (electron cyclotron current drive). Although both methods have been applied successfully to experiments showing a predominance of ECRH for medium-sized limiter tokamaks (TEXTOR, T-10) and of ECCD for mid-to-large-sized divertor tokamaks (AUG, DIII-D, JT-60), conditions determining their relative importance are still unclear. We address this problem with a numerical study focused on the contributions of heating and current drive to the temporal evolution of NTMs as described by the modified Rutherford equation. For the effects of both heating as well as current drive, simple analytical expressions have been found in terms of an efficiency fore-factor times a ‘geometrical’ term depending on the power deposition width w dep, location and modulation. When the magnetic island width w equals the width of the deposition profile, w ≈ w dep, both geometric terms are practically identical. Whereas for current drive the geometric term approaches a constant for small island widths and is inversely proportional to (w/w dep)2 for large island widths, the heating term approaches a constant for large island widths and is proportional to (w/w dep) for small island widths. For medium-sized tokamaks (TEXTOR, AUG) the heating and current drive efficiencies are of the same order of magnitude, whereas in a future, large reactor like ITER the current drive efficiency is expected to be significantly larger.

In tokamak plasmas with a tearing mode, strong scattering of high power millimeter waves, as used for heating and noninductive current drive, is shown to occur. This new wave scattering phenomenon is shown to be related to the passage of the O point of a magnetic island through the high power heating beam. The density determines the detailed phasing of the scattered radiation relative to the O-point passage. The scattering power depends strongly nonlinearly on the heating beam power.