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.

A model for sawtooth oscillations in tokamak experiments is outlined. A threshold criterion for the onset of internal kink modes and a prescription for the relaxed profiles immediately after the sawtooth crash have been implemented in a transport code that evolves the relevant plasma parameters. In this paper, applications of this model to the prediction of the sawtooth period and amplitude in projected ITER discharges are discussed. It is found that sawteeth can be stabilized transiently by the fusion alpha particles in ITER for periods that are long on the energy confinement timescale (τ E ≈ 5 s). The sawtooth period depends on the amount of reconnected flux at the preceding sawtooth crash. When Kadomtsev's full reconnection model is used, the period can exceed 100 s. The sawtooth mixing radius following long duration sawtooth ramps can easily exceed half the plasma minor radius, raising questions about the desirability of transient sawtooth suppression.

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The onset of electromagnetic oscillations that are observed in magnetically confined plasmas where beams of fast neutrals are injected is associated with the excitation of a mode with poloidal wave number m° ** 1 and phase velocity equal to the core-ion diamagnetic velocity. The resonant interaction of the mode with the beam ions is viewed as a form of dissipation that allows the release of the mode excitation energy, related to the gradient of the plasma pressure.PACS numbers: 52.35.-g, 52.55.-s A new type of instability has been observed in magnetically confined toroidal plasmas where beams of fast neutrals are injected nearly perpendicular to the equilibrium magnetic field. The poloidal magnetic field fluctuations produced by this instability have a characteristic signature and are called "fishbone oscillations." 1,2 Particle bursts corresponding to loss of energetic beam particles are correlated with fishbone events, reducing the beam heating efficiency and thus limiting the maximum achievable ft [ = (kinetic pressure)/(magnetic pressure)] by this technique.We present the results of an analysis that supports one of the interpretations 3 advanced when these experimental observations were first reported. This consisted of proposing the following: (a) The excited mode, whose spatial structure is dominated by the component with poloidal wave number m 0ass l, has a frequency related to the ion diamagnetic frequency and is one of the two m° = l modes that are found under the conditions for ideal MHD instability, but are rendered marginally stable by finite ion Larmor radius effects 4 ; (b) the mode "excergy" (excitation energy) is related to the plasma pressure gradient; and (c) the presence of a "viscous" dissipative process (e.g., produced by a mode-particle resonance that scatters the beam ions) is required for the instability to develop.We refer, for simplicity, to a large-aspect-ratio axisymmetric toroidal confinement configuration with circular magnetic surfaces, and consider perturbations of the equilibrium field that are dominated by the ra 0as=: l, n 0sss \ poloidal and toroidal components. The relevant model dispersion relation is 4when we omit mode-particle resonances and other dissipative processes. Here, tOdi" -(c/eBrn)dp i± /dr is the ion diamagnetic frequency evaluated at the surface r -TQ where the pitch angle of the unperturbed equilibrium magnetic field equals that of the perturbation, and p ix is the transverse ion pressure. The ideal MHD growth rate 7MHD is given by 4 YMHD^COAXH,where co A = v A9 s/r 0 with v A e ,BS B e I(4Km i ni) U2 , s^dlnq/dlnr, q^rB^/RBe, R is the major radius of the torus, X//-Xo(r 0 //?) 2 (/3p -~/?p,crit), ^o is a finite numerical factor, p p = -(R/ ro) 2 f°drr 2 (dp/dr), and, for a parabolic q profile, 5 Pp.crit 1 ** ^13/12-The ideal stability parameter XH is the negative of the (normalized) minimum value of the perturbed potential energy 4 8W m \ n and the dispersion relation (1) is valid for X H > §.In the realistic limit where 7MHD <^d H the dispersion relation (1)...