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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.

Transient magneto-hydrodynamic (MHD) events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here in a concise way to provide a complete overview, while we refer to the original publications for details. Experimental validation for unmitigated vertical displacement events progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection was simulated in JET, KSTAR, ASDEX Upgrade (AUG) and ITER. Benign runaway electron beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f particle in cell models for ion temperature gradient and trapped electron modes were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle interactions with MHD were studied. Flux pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in l = 2 stellarators, while verification for advanced stellarators progresses.

Transient phenomena and their control are of high relevance in magnetic confinement fusion plasmas to guarantee a stable and safe plasma operation. Interpretative simulations can maximize the insights gained from experiments on present machines and predictive simulations can help in the preparation of design, mitigation techniques and operational scenarios for future devices. In this article, we provide an overview of recent advances and novel scientific results obtained with the 3D non-linear hybrid fluid-kinetic code JOREK, covering physics of plasma transients from the core to the scrape-off layer (SOL) both for tokamak and stellarator devices. Substantial progress was made in the physics understanding, model validations with experiments and experiment interpretation, thus, giving confidence for predictions to DTT, ITER and DEMO. The topics addressed comprise a wide range: the edge physics of new operation scenarios and ELM suppression; major disruptions with a focus on Runaway Electrons (REs) and Vertical Displacement Events (VDEs) as well as disruption mitigation by shattered pellet injection (SPI); the physics mechanisms and operational limits of the flux pumping regime for sawtooth control; MHD limits of stellarators and work towards incorporating advanced edge/SOL/exhaust dynamics; continuing improvements of the code for more efficient hybrid simulations on conventional and accelerated high performance computing architectures.

A reversed-field pinch is a toroidal device for magnetically confining plasmas, and a potential alternative to the tokamak for a future fusion reactor. Observations of the evolution of a reversed-field-pinch plasma towards a self-organized single-helicity state suggest that instability problems, which have previously hindered the development of these devices, could now be overcome. In the quest for new energy sources, the research on controlled thermonuclear fusion 1 has been boosted by the start of the construction phase of the International Thermonuclear Experimental Reactor 2 (ITER). ITER is based on the tokamak magnetic configuration 3 , which is the best performing one in terms of energy confinement. Alternative concepts are however actively researched, which in the long term could be considered for a second generation of reactors. Here, we show results concerning one of these configurations, the reversed-field pinch 4 , 5 (RFP). By increasing the plasma current, a spontaneous transition to a helical equilibrium occurs, with a change of magnetic topology. Partially conserved magnetic flux surfaces emerge within residual magnetic chaos, resulting in the onset of a transport barrier. This is a structural change and sheds new light on the potential of the RFP as the basis for a low-magnetic-field ohmic fusion reactor.

Mechanisms of plasmoid drift following massive material injection are studied via 3D non-linear MHD modelling with the JOREK code, using a transient neutral source deposited at the low field side midplane of a JET H-mode plasma to clarify basic processes and compare with existing theories. The simulations confirm the important role of the propagation of shear Alfvén wave (SAW) packets from both ends of the plasmoid (‘SAW braking’) and the development of external resistive currents along magnetic field lines (‘Pégourié braking’) in limiting charge separation and thus the E×B plasmoid drift, where E and B are the electric and magnetic fields, respectively. The drift velocity is found to be limited by the SAW braking on the few microseconds timescale for cases with relatively small source amplitude while the Pégourié braking acting on a longer timescale is shown to set in earlier with larger toroidal extent of the source, both in good agreement with existing theories. The simulations also identify the key role of the size of the E×B flow region on plasmoid drift and show that the saturated velocity caused by dominant SAW braking agrees well with theory when considering an effective pressure within the E×B flow region. The existence of SAWs in the simulations is demonstrated and the 3D picture of plasmoid drift is discussed.

This paper is in the framework of the nondestructive evaluation of conductive materials by means of eddy current testing. In particular, we consider the imaging of surface breaking volumetric defects. In this case, it is possible to use relatively “high-frequencies” and, in the limit of skin-depth negligible with respect to the relevant geometrical sizes and negligible displacement current, the problem can be modeled as a magnetostatic one. The elliptic nature of magnetostatic allows proving a monotonicity property of the operator mapping the defects geometry into the measured quantity. This makes possible to use a recently proposed fast (noniterative) imaging algorithm.

Purpose - The paper is focused on the numerical modelling of the interaction between electromagnetic fields and metallic nanoparticle.Design methodology approach - A full-wave solution of the field problem is modelled in terms of an integral equation where the unknown is the displacement current. For treating nanoparticles having sizes smaller than the relevant wavelength, particular care is devoted to the choice of the discrete representation of the unknown in view of the condition number of the resulting linear system of equations.Findings - A critical analysis of the issues to be considered for developing a proper numerical model of the problem is presented. Specifically, it is shown that the electric field inside the nanoparticle is not purely irrotational, as usually assumed in the widespread models based on the electrostatic approximation.Originality value - The proposed formulation is applied for the first time to the problem of evaluating the interaction between electromagnetic fields and metallic nanoparticle.

Purpose - The paper aims to apply an innovative inversion method to the problem of imaging (location, direction and size) of concrete rebars by means of eddy current measurements.Design methodology approach - An accurate numerical model of the probe-rebar interaction, including eddy currents and skin effect, is considered. The inverse problem is approached with a very efficient inversion procedure previously introduced in a different context.Findings - A critical analysis of the issues to be considered for the quantitative imaging of rebars is given, and the possibility of relevant simplifications in the numerical model outlined, allowing the development of an accurate and computationally efficient method.Originality value - The proposed formulation is applied for the first time to the problem of rebars imaging. Experimental tests have been carried out to validate the numerical model and its underlying hypothesis.

A surface integral formulation is used for a broad-band characterization of wire interconnects. A suitable definition of effective impedance accounts for the penetration of currents and charges inside lossy conductors. The results are successfully compared to a volumetric integral approach.

Power transformers based on High Temperature Superconductors (HTS) technology are an appealing promise for several practical applications. The present designs still leave wide margins of possible improvement in terms of both layout optimisation and introduction of new technologies. In the framework of a technical-scientific cooperation among scientific and industrial subjects, a 10 kVA single-phase transformer was designed and manufactured, using copper for primary windings and BSCCO-2223 HTS tape for secondary windings. The layout has been optimized taking into account the particular characteristics of BSCCO tapes, in particular their AC losses, and the usual figures (stray flux, Joule and iron losses, weight and overall footprint) considered in transformers design. The prototype has then been realized and characterized, using general as well as specific tests. The performance of the device has been evaluated and compared with numerical calculation. In the paper, an overview of the device design and manufacturing will be presented, together with a critical comparison between computed and measured performance.