In this chapter, we review the progress in MHD stability, disruptions and control in magnetic fusion research that has occurred over the past (more than) one and a half decades since the publication by Hender et al in 2007 on the same topic as part of the update of ITER Physics Basis. During this period, remarkable progress has been achieved in the understanding of the basic physics and overall control of MHD instabilities through a wide spectrum of dedicated experiments, theory and modeling. The sawtooth activities are probably today one of the best understood of MHD events and very robust control schemes have been developed for reliable operation of tokamaks through core heating. Similarly, significant improvements have been achieved in understanding and control of neoclassical tearing modes, resistive wall modes or locked modes and their control through ECCD or error field control. The field of disruption prediction through application of artificial intelligence, machine learning or deep learning methods, which had already started at the time of the 2007 review, has progressed significantly due to general progress in these fields and application of newer, more sophisticated algorithms. However, although remarkable progress has been achieved in the field of Disruptions, their understanding, prediction, possible avoidance and mitigation still remain probably the most active fields of R&D globally in this field. This is especially because reactor grade machines like ITER and DEMO will be much less tolerant in respect of disruptions and runaway currents, and their occurrences must be either avoided altogether or minimized to an acceptable value without causing any significant hindrance to robust machine operations. This review is intended to present a broad spectrum of the R&D that has occurred in this field in support of ITER, which will also be of immense significance for all future machines, especially reactors like DEMO.

An approach for calculating the force on the vessel wall during plasma disruptions in tokamaks is proposed. It is mainly based on the Maxwell equations and, therefore, is general. Another essential element is the integral force balance on the plasma that strongly constrains the possible solutions. The derived expressions are valid at any disruption scenario and finally give the net forces in terms of the magnetic perturbations behind the wall. The result can be used with magnetic measurements alone. It shows that the geometrical inhomogeneity of the wall and its resistivity are the key factors determining the direction and amplitude of the force.

Plasma stabilization due to a nearby conducting wall can provide access to better performance in some scenarios in tokamaks. This was proved by experiments with an essential gain in ${\it\beta}$ and demonstrated as a long-lasting effect at sufficiently fast plasma rotation in the DIII-D tokamak (see, for example, Straitet al.,Nucl. Fusion, vol. 43, 2003, pp. 430–440). The rotational stabilization is the central topic of this review, though eventually the mode rotation gains significance. The analysis is based on the first-principle equations describing the energy balance with dissipation in the resistive wall. The method emphasizes derivation of the dispersion relations for the modes which are faster than the conventional resistive wall modes, but slower than the ideal magnetohydrodynamics modes. Both the standard thin wall and ideal-wall approximations are not valid in this range. Here, these are replaced by an approach incorporating the skin effect in the wall. This new element in the stability theory makes the energy sink a nonlinear function of the complex growth rate. An important consequence is that a mode rotating above a critical level can provide a damping effect sufficient for instability suppression. Estimates are given and applications are discussed.

The study is devoted to theoretical analysis of some models for calculating the disruption forces in tokamaks and scalings for these forces which can be proposed for ITER. It is motivated by the necessity of reliable predictions for ITER. The task includes the evaluation of the existing models, resolution of the conflicts between them, elimination of contradictions by proper improvements, elaboration of recommendations for dedicated studies. Better qualities of the modelling and higher accuracy are the ultimate theoretical goals. In recent years, there was a steady progress in developing a physics basis for calculating the forces, which gave rise to new trends and ideas. It was discovered, in particular, that the wall resistivity, penetration of the magnetic perturbation through the wall, the poloidal current induced in the wall, the kink-mode coupling, plasma position in the vacuum vessel must be the elements essentially affecting the disruption forces. These and related predictions along with earlier less sophisticated concepts and results are analysed here.

Electromagnetic forces generated during hard-to-predict transient events, represent a serious constraint for the operation and design of tokamaks. A sudden loss of plasma stability, triggering plasma thermal and current quenches, leads to the induction of eddy currents in the conducting structures surrounding the plasma column. Interaction of these currents with the magnetic field is responsible for a j × B local force that might compromise the integrity of the device. Here we evaluate the effect of poloidal currents induced in the wall on the local and global forces. To test the earlier analytical predictions (Pustovitov and Kiramov 2018 Plasma Phys. Controlled Fusion 60 , 045011), we consider a circular tokamak by the numerical tool CarMa0NL (Villone et al 2013 Plasma Phys. Controlled Fusion 55 , 095008). The results confirm the necessity of incorporating the poloidal currents into the task, as these strongly affect the local stress distribution and the global radial force. The overall agreement between analytical and numerical computation is an additional evidence that CarMa0NL is a sound tool for the prediction of disruption forces in tokamaks. At the same time, the simulation conditions in which the agreement is less satisfactory allow to identify which are the most restrictive assumptions of the analytical model, pointing out the way for future theoretical work.

The possibility of generation of the rotating sideways force on the wall by the kink modes is analytically investigated. The approach is basically the same as that developed earlier in (Mironov and Pustovitov 2017 Phys. Plasmas 24 092508) for the locked modes, but now their rotation is allowed. Its main elements are ∂b/∂t ≠ 0 (described by the growth rate γ and angular rotation frequency ω of the magnetic perturbation b), resistive dissipation in the wall, and the requirement of zero sideways force on the plasma. These make the approach greatly different from those resulting in the so-called Noll’s formula. The result is also different; it predicts a force an order of magnitude smaller. Nevertheless, such a force can be dangerous at the resonance frequency of the vacuum vessel. The derived relations show that the rotating force must be maximal at ωτ _w = O(1), where τ _w is the resistive wall time. For the faster modes it decreases roughly as ∼1/ω.