Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 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 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.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S03/pdf

Chapter 3: MHD stability, operational limits and disruptions

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

The 'Progress in the ITER Physics Basis' (PIPB) document is an update of the 'ITER Physics Basis' (IPB), which was published in 1999 [1]. The IPB provided methodologies for projecting the performance of burning plasmas, developed largely through coordinated experimental, modelling and theoretical activities carried out on today's large tokamaks (ITER Physics R&D). In the IPB, projections for ITER (1998 Design) were also presented. The IPB also pointed out some outstanding issues. These issues have been addressed by the Participant Teams of ITER (the European Union, Japan, Russia and the USA), for which International Tokamak Physics Activities (ITPA) provided a forum of scientists, focusing on open issues pointed out in the IPB. The new methodologies of projection and control are applied to ITER, which was redesigned under revised technical objectives. These analyses suggest that the achievement of Q > 10 in the inductive operation is feasible. Further, improved confinement and beta observed with low shear (= high βp = 'hybrid') operation scenarios, if achieved in ITER, could provide attractive scenarios with high Q (> 10), long pulse (>1000 s) operation with beta <no-wall limit and benign ELMs.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S01/pdf

Chapter 1: Overview and summary

A nonlinear gyrokinetic formalism for low‐frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong‐turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magnetic field geometries. The specific case of axisymmetric tokamaks is then considered and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfven wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear‐Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency.

Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria

The China Fusion Engineering Test Reactor (CFETR) is the next device in the roadmap for the realization of fusion energy in China, which aims to bridge the gaps between the fusion experimental reactor ITER and the demonstration reactor (DEMO). CFETR will be operated in two phases. Steady-state operation and self-sufficiency will be the two key issues for Phase I with a modest fusion power of up to 200 MW. Phase II aims for DEMO validation with a fusion power over 1 GW. Advanced H-mode physics, high magnetic fields up to 7 T, high frequency electron cyclotron resonance heating and lower hybrid current drive together with off-axis negative-ion neutral beam injection will be developed for achieving steady-state advanced operation. The recent detailed design, research and development (R&D) activities including integrated modeling of operation scenarios, high field magnet, material, tritium plant, remote handling and future plans are introduced in this paper.

https://iopscience.iop.org/article/10.1088/1741-4326/aa686a/pdf

Overview of the present progress and activities on the CFETR

The effect is considered of the amplification of an external resonant error field near the stability boundary of the so-called resistive wall modes observed in the DIII-D tokamak. The analysis is performed in a standard cylindrical approximation. The model is based on Maxwell’s equations and Ohm’s law; therefore, the results of the analysis are valid for any large-scale modes interacting with a conducting wall. In contrast to earlier approaches, the model considers the resonant field amplification as a dynamic effect. It is shown that, when the effect is the strongest, the stationary solutions proposed earlier are inapplicable. The problem of plasma response to a probing pulse of the resonant field of a given amplitude and duration is analyzed. The relationships obtained explain the basic features of the observed phenomena in the DIII-D tokamak and allow direct experimental verification.

Error field amplification near the stability boundary of the modes interacting with a conducting wall

A theoretical framework to describe the magnetic coupling of the toroidal plasma with the resistive wall and other sources of the field asymmetry is formulated. This is done for general toroidal geometry without restrictions on the plasma, while the wall is considered as a thin shell. Mathematically, the approach here exploits the Chance concept [M. S. Chance, Phys. Plasmas 4, 2161 (1997)], but with an essential difference: each source of the magnetic perturbation b (plasma, wall, external currents) is treated separately with account of their differences in space and nature. This allows much simpler formulation of the problem than was known before. The final equation couples the normal component of ∂b∕∂t at the wall to the perturbation at the plasma surface. Step by step reduction of this first-principle equation is performed with demonstration of its main features, starting from the known problem of singularities. This also includes the reduction to axially symmetric geometry, large-aspect-ratio, and the...

General formulation of the resistive wall mode coupling equations

Equilibrium and Stability of Plasmas in Stellarators

The role of polarization current in the problem of rotating magnetic islands in the absence of drift effects is discussed for the case of nonregularized and regularized velocity profiles governed by the perpendicular viscosity. The polarization current is calculated taking into account the finite ion Larmor radius effects. It is shown that, in correspondence with the general rule by Waelbroeck and Fitzpatrick [Phys. Rev. Lett. 78, 1703 (1997)], this current is destabilizing. The destabilizing contribution of the polarization current into the generalized Rutherford equation for the magnetic island width does not depend on whether the profile function is regularized or not. It is shown that the Larmor corrections to the current consist of the sum of two oppositely directed currents and do not contribute into the generalized Rutherford equation.

Regularized magnetic islands. II. The role of polarization current

A study is made of the problem of active stabilization of the resistive wall modes in a tokamak with two conducting walls between the plasma column and the stabilizing system. The problem is analyzed for a steady-state configuration (without rotation) in the standard cylindrical approximation under the assumption that the stabilizing system responds instantaneously to a magnetic field perturbation by generating an in-phase signal with the required amplitude.

V. D. Pustovitov

Papers

Error field amplification near the stability boundary of the modes interacting with a conducting wall

General formulation of the resistive wall mode coupling equations

Equilibrium and Stability of Plasmas in Stellarators

Regularized magnetic islands. II. The role of polarization current

Feedback stabilization of resistive wall modes in a tokamak with a double resistive wall