The sawtooth-free hybrid scenario has been achieved recently in ASDEX Upgrade (AUG) with applied non-inductive current sources and auxiliary heating [A. Burckhart et al 2023 Nucl. Fusion 63 126056]. Control experiments in AUG suggest that the self-regulating magnetic flux pumping mechanism, characterized by anomalous current redistribution, is responsible for clamping the central safety factor (q_0) close to unity, thereby preventing the sawtooth onset. This work presents a numerical and theoretical investigation of flux pumping in the AUG hybrid scenario based on the two-temperature, visco-resistive, full magnetohydrodynamic (MHD) model with the JOREK code. To quantitatively model the flux pumping, we choose realistic parameters, plasma configurations, and source terms based on AUG experiments. During the initial saturation stage of the unstable 1/1 quasi-interchange mode (on millisecond timescales), q_0 exhibits fast under-damped oscillation and reaches a value closer to unity, which is attributed to the self-regulation of core plasma and the fast dynamo effect on the order of V/m. On the longer resistive diffusion timescale of seconds, the slow negative dynamo effect on the order of mV/m induced by the 1/1 MHD instability plays an effective role in flux pumping, which provides quantitative agreement with experimental observations for the first time. The final saturated 1/1 MHD instability exhibits features of the quasi-interchange mode and tearing mode, and the associated convective plasma flow velocity is a few m/s. The toroidal negative electric field from the slow dynamo dominantly offsets the positive current drive and continuously redistributes the current density and pressure. As a result, q_0 is maintained close to unity due to the low-shear profiles of current density and pressure in the plasma core, and the system enters a sawtooth-free and quasi-stationary helical state.

Mercier's criterion is typically enforced as a hard operational limit in stellarator design. At the same time, past experimental and numerical studies have shown that this limit may often be surpassed, though the exact mechanism behind this nonlinear stability is not well understood. This work aims to contribute to our current understanding by comparing the nonlinear evolution of Mercier unstable Wendelstein stellarators with that of nonlinearly stable quasi-interchange modes in tokamaks. A high mirror, very low $\iota$ , W7-X-like configuration is first simulated. Broad flow structures are observed, which produce a similar magnetohydrodynamic (MHD) dynamo term to that in hybrid tokamak discharges, leading to flux pumping. Unlike in tokamaks, there is no net toroidal current to counterbalance this dynamo, and it is unclear if it can be sustained to obtain a similar quasistationary nonlinear state. In the simulation, partial reconnection induced by the overlap of multiple interchange instabilities leads to a core temperature crash. A second case is then considered using experimental reconstructions of intermediate $\beta$ W7-AS discharges, where saturated low-n modes were observed experimentally, with sustained MHD signatures over tens of milliseconds. It is shown that these modes do not saturate in a benign quasistationary way in current simulations even in the presence of background equilibrium $\boldsymbol{E} \times \boldsymbol{B}$ flow shear. This leads to a burst of MHD behaviour, inconsistent with the sustained MHD signatures in the experiment. Nevertheless, the (1, 2) mode is observed at the experimental Spitzer resistivity, and its induced anomalous transport can be overcome using an experimentally relevant heat source, reproducing these aspects of the dynamics. The possible reasons for the discrepancies between experiment and simulation, and the observation of partial reconnection in contrast to flux pumping are discussed, in view of reproducing and designing for operation of stellarators beyond the Mercier stability limit.

Real-time reconstruction of the magnetic equilibrium provides fundamental control of plasma shape and position in a tokamak. Details of the implementation of the equilibrium reconstruction code developed for the ASDEX Upgrade tokamak (JANET++) are summarized. Cubic Hermite splines are introduced as current density basis functions for solving the Grad-Shafranov equation. The choice of the optimal Tikhonov regularization parameter is discussed. The code is validated by comparing the results of the equilibrium reconstruction with those of further equilibrium reconstructions available on ASDEX Upgrade (CLISTE and IDE). In a high time resolution study of a discharge with edge localized modes (ELM), the poloidal asymmetry of the fits and magnetic probe measurements suggest that the real-time equilibrium reconstruction captures the essential features of the current density redistribution in an ELMing edge plasma. An efficient algorithm to locate multiple X-points and identify the active one in advanced X-divertor and snowflake divertor configurations is presented.

ASDEX Upgrade has developed multiple massive gas injection (MGI) scenarios to investigate runaway electron (RE) dynamics. During the current quench of the MGI induced disruptions, Alfvénic activity is observed in the 300–800 kHz range. With the help of a mode tracing algorithm based on Fourier spectrograms, mode behaviour was classified for 180 discharges. The modes have been identified as global Alfvén eigenmodes using linear gyrokinetic MHD simulations. Changes in the Alfvén continuum during the quench are proposed as explanation for the strong frequency sweep observed. A systematic statistical analysis shows no significant connection of the mode characteristics to the dynamics of the subsequent runaway electron beams. In our studies, the appearance and amplitude of the modes does not seem to affect the potential subsequent runaway beam. Beyond the scope of the 180 investigated dedicated RE experiments, the Alfvénic activity is also observed in natural disruptions with no RE beam forming.

Experiments on ASDEX Upgrade (AUG) in 2021 and 2022 have addressed a number of critical issues for ITER and EU DEMO. A major objective of the AUG programme is to shed light on the underlying physics of confinement, stability, and plasma exhaust in order to allow reliable extrapolation of results obtained on present day machines to these reactor-grade devices. Concerning pedestal physics, the mitigation of edge localised modes (ELMs) using resonant magnetic perturbations (RMPs) was found to be consistent with a reduction of the linear peeling-ballooning stability threshold due to the helical deformation of the plasma. Conversely, ELM suppression by RMPs is ascribed to an increased pedestal transport that keeps the plasma away from this boundary. Candidates for this increased transport are locally enhanced turbulence and a locked magnetic island in the pedestal. The enhanced D-alpha (EDA) and quasi-continuous exhaust (QCE) regimes have been established as promising ELM-free scenarios. Here, the pressure gradient at the foot of the H-mode pedestal is reduced by a quasi-coherent mode, consistent with violation of the high-n ballooning mode stability limit there. This is suggestive that the EDA and QCE regimes have a common underlying physics origin. In the area of transport physics, full radius models for both L- and H-modes have been developed. These models predict energy confinement in AUG better than the commonly used global scaling laws, representing a large step towards the goal of predictive capability. A new momentum transport analysis framework has been developed that provides access to the intrinsic torque in the plasma core. In the field of exhaust, the X-Point Radiator (XPR), a cold and dense plasma region on closed flux surfaces close to the X-point, was described by an analytical model that provides an understanding of its formation as well as its stability, i.e., the conditions under which it transitions into a deleterious MARFE with the potential to result in a disruptive termination. With the XPR close to the divertor target, a new detached divertor concept, the compact radiative divertor, was developed. Here, the exhaust power is radiated before reaching the target, allowing close proximity of the X-point to the target. No limitations by the shallow field line angle due to the large flux expansion were observed, and sufficient compression of neutral density was demonstrated. With respect to the pumping of non-recycling impurities, the divertor enrichment was found to mainly depend on the ionisation energy of the impurity under consideration. In the area of MHD physics, analysis of the hot plasma core motion in sawtooth crashes showed good agreement with nonlinear 2-fluid simulations. This indicates that the fast reconnection observed in these events is adequately described including the pressure gradient and the electron inertia in the parallel Ohm’s law. Concerning disruption physics, a shattered pellet injection system was installed in collaboration with the ITER International Organisation. Thanks to the ability to vary the shard size distribution independently of the injection velocity, as well as its impurity admixture, it was possible to tailor the current quench rate, which is an important requirement for future large devices such as ITER. Progress was also made modelling the force reduction of VDEs induced by massive gas injection on AUG. The H-mode density limit was characterised in terms of safe operational space with a newly developed active feedback control method that allowed the stability boundary to be probed several times within a single discharge without inducing a disruptive termination. Regarding integrated operation scenarios, the role of density peaking in the confinement of the ITER baseline scenario (high plasma current) was clarified. The usual energy confinement scaling ITER98( p,y ) does not capture this effect, but the more recent H20 scaling does, highlighting again the importance of developing adequate physics based models. Advanced tokamak scenarios, aiming at large non-inductive current fraction due to non-standard profiles of the safety factor in combination with high normalised plasma pressure were studied with a focus on their access conditions. A method to guide the approach of the targeted safety factor profiles was developed, and the conditions for achieving good confinement were clarified. Based on this, two types of advanced scenarios (‘hybrid’ and ‘elevated’ q -profile) were established on AUG and characterised concerning their plasma performance.

The Shattered Pellet Injector (SPI) installed at ASDEX Upgrade (AUG) is one of the most flexible SPI systems currently in operation. It was specifically designed to provide input to the ITER disruption mitigation system [1]. The AUG SPI was so far used in approx. 240 plasma discharges to explore SPI efficacy in disruption mitigation, to optimize material assimilation, reduce heat loads and radiation asymmetries, and to generate a diverse dataset for model validation. Our results indicate that rectangular shatter heads with relatively shallow mitre bends lead to more reproducible

Sawteeth oscillations are periodic relaxations of the core plasma density and temperature in tokamaks. The rise of the temperature due to external heating is terminated by the crash phase, which involves magnetic reconnection. This is the case of fast magnetic reconnection in collisionless plasmas (Lundquist number S≥108) with a strong guide field. (The toroidal magnetic field in a tokamak is a few orders larger compared to the reconnected helical field.) Experimental measurements show non-linear behavior before and during the crash phase. Simplified single-fluid models are not able to explain the reconnection dynamics during the crash, and two-fluid effects have to be considered. In this case, numerical simulations give good agreement with the observations for the crash duration. At the same time, the present simulations explain experimentally observed phenomena only partially, and several questions remain an area of active research: evolution during the crash, the onset of the fast phase, the existence of the post-cursors, the degree of stochasticity, and others. This overview paper summarizes the current understanding of the crash process, highlights remaining problems, and shows connections to magnetic reconnection research in other plasmas.

Tokamak plasmas can amplify very small resonant components of error fields (EFs) when operating close to the ideal magneto-hydrodynamic (MHD) limits. Such EFs are well diagnosed in ASDEX Upgrade tokamak (Igochine V et al 2017 Nucl. Fusion 57 116027, Maraschek M et al 40th EPS Conf. on Plasma Physics 2013 P4.127), which allows to model EF as well as the correction required for the optimal compensation. Experiments on ASDEX Upgrade show that EF correction considering the plasma effect, as it is foreseen for ITER, is necessary even in the case of small resonant EF. Such correction improves the achievable β N by 10% and makes discharges more stable with respect to ideal modes.

In high- β scenarios with on-axis co-current electron cyclotron current drive, which normally lowers q 0 below unity, the absence of sawteeth suggests the involvement of an additional current redistribution mechanism beyond neoclassical current diffusion. This is supported by imaging motional Stark effect diagnostic measurements, which indicate that q 0 remains consistently around 1. This phenomenon is observed in the presence of a 1/1 mode, indicating its potential role in the current redistribution. It is shown that the mode’s ability to modify the central current and suppress sawteeth increases with plasma pressure. These findings align with a recent theoretical model, which predicts a pressure threshold for sawtooth avoidance by a 1/1 quasi-interchange mode and where this threshold increases with the strength of inward current diffusion. Moreover, the advantages of the flux pumping scenario for future machines are highlighted.

DIII-D physics research addresses critical challenges for the operation of ITER and the next generation of fusion energy devices. This is done through a focus on innovations to provide solutions for high performance long pulse operation, coupled with fundamental plasma physics understanding and model validation, to drive scenario development by integrating high performance core and boundary plasmas. Substantial increases in off-axis current drive efficiency from an innovative top launch system for EC power, and in pressure broadening for Alfven eigenmode control from a co-/counter- I p steerable off-axis neutral beam, all improve the prospects for optimization of future long pulse/steady state high performance tokamak operation. Fundamental studies into the modes that drive the evolution of the pedestal pressure profile and electron vs ion heat flux validate predictive models of pedestal recovery after ELMs. Understanding the physics mechanisms of ELM control and density pumpout by 3D magnetic perturbation fields leads to confident predictions for ITER and future devices. Validated modeling of high- Z shattered pellet injection for disruption mitigation, runaway electron dissipation, and techniques for disruption prediction and avoidance including machine learning, give confidence in handling disruptivity for future devices. For the non-nuclear phase of ITER, two actuators are identified to lower the L–H threshold power in hydrogen plasmas. With this physics understanding and suite of capabilities, a high poloidal beta optimized-core scenario with an internal transport barrier that projects nearly to Q = 10 in ITER at ∼ 8 MA was coupled to a detached divertor, and a near super H-mode optimized-pedestal scenario with co- I p beam injection was coupled to a radiative divertor. The hybrid core scenario was achieved directly, without the need for anomalous current diffusion, using off-axis current drive actuators. Also, a controller to assess proximity to stability limits and regulate β N in the ITER baseline scenario, based on plasma response to probing 3D fields, was demonstrated. Finally, innovative tokamak operation using a negative triangularity shape showed many attractive features for future pilot plant operation.

An overview of recent results obtained at the tokamak ASDEX Upgrade (AUG) is given. A work flow for predictive profile modelling of AUG discharges was established which is able to reproduce experimental H-mode plasma profiles based on engineering parameters only. In the plasma center, theoretical predictions on plasma current redistribution by a dynamo effect were confirmed experimentally. For core transport, the stabilizing effect of fast ion distributions on turbulent transport is shown to be important to explain the core isotope effect and improves the description of hollow low-Z impurity profiles. The L–H power threshold of hydrogen plasmas is not affected by small helium admixtures and it increases continuously from the deuterium to the hydrogen level when the hydrogen concentration is raised from 0 to 100%. One focus of recent campaigns was the search for a fusion relevant integrated plasma scenario without large edge localised modes (ELMs). Results from six different ELM-free confinement regimes are compared with respect to reactor relevance: ELM suppression by magnetic perturbation coils could be attributed to toroidally asymmetric turbulent fluctuations in the vicinity of the separatrix. Stable improved confinement mode plasma phases with a detached inner divertor were obtained using a feedback control of the plasma β. The enhanced D α H-mode regime was extended to higher heating power by feedback controlled radiative cooling with argon. The quasi-coherent exhaust regime was developed into an integrated scenario at high heating power and energy confinement, with a detached divertor and without large ELMs. Small ELMs close to the separatrix lead to peeling-ballooning stability and quasi continuous power exhaust. Helium beam density fluctuation measurements confirm that transport close to the separatrix is important to achieve the different ELM-free regimes. Based on separatrix plasma parameters and interchange-drift-Alfvén turbulence, an analytic model was derived that reproduces the experimentally found important operational boundaries of the density limit and between L- and H-mode confinement. Feedback control for the X-point radiator (XPR) position was established as an important element for divertor detachment control. Stable and detached ELM-free phases with H-mode confinement quality were obtained when the XPR was moved 10 cm above the X-point. Investigations of the plasma in the future flexible snow-flake divertor of AUG by means of first SOLPS-ITER simulations with drifts activated predict beneficial detachment properties and the activation of an additional strike point by the drifts.

The radial velocity of the plasma core during the sawtooth crashes has been measured for the first time with electron cyclotron emission imaging diagnostic. The measurements have been compared with nonlinear two-fluid simulation. The comparison reveals good qualitative and quantitative agreement, which indicates that two-fluid effects (inertia and pressure gradient of electrons) are sufficient for the correct prediction of the experimental results. Contrarily, the crash time of the Kadomtsev model, which is based on a single-fluid picture of magnetic reconnection, disagrees with the experimental results.

This paper discusses the toroidal localisation of magnetic reconnection during sawtooth crashes. Numerical analysis with realistic heat diffusion coefficients shows that heat distributes itself helically along the torus faster than the temporal resolution of any existing ECE diagnostics. It makes local and global (helically axisymmetric) magnetic reconnection indistinguishable for an observer, while a local crash where the heat stays confined within a finite helical region could be distinguished. Statistical analysis of sawtooth crashes with the ECEI diagnostic is conducted in ASDEX Upgrade. The displacement of the heat within a finite helical region has not been observed. The statistical data supports global magnetic reconnection.

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

In this work, a surface current plasma model is coupled to a volume integral formulation for studying the interaction between tokamak tearing modes (TMs) and the machine metallic structures surrounding the plasma. By evaluating the passive response on a set of pickup probes, TMs’ amplitude is estimated.

Tearing modes are a major concern for large tokamak devices. Therefore their detection and characterization is of importance for timely countermeasures to avoid significant impact on the discharge or at least prevent possible machine damage. In case of phase-locked tearing modes, the poloidal variation of induced magnetic field fluctuation depends on the amplitudes of and the phase difference between the individual modes. This affects mode detection and identification when not considered appropriately. The phase between phase-locked (2, 1) and (3, 1) tearing modes in ASDEX Upgrade has been determined from local electron temperature and magnetic measurements independently. It is shown that the modes can be in phase at any poloidal position starting from the low field side plasma midplane over the plasma top to the high field side midplane. This observation invalidates the widespread assumption that phase-locked tearing modes are in phase near the low field side midplane. Dependence of the in-phase position on both, the plasma pressure and the plasma rotation velocity, is observed.

In ASDEX Upgrade hybrid discharges, it is found that an externally applied n = 1 field preferentially distorts the plasma in the core, leading to significant flow damping there and elsewhere across the plasma radius. MARS-F/Q modeling of a neoclassical toroidal viscous NTV) torque that results from an amplified internal kink-type displacement in the plasma core is qualitatively consistent with the measured internal displacements, beta dependence, and rotation damping. Sensitivity studies indicate that the internal kink response and the resulting core flow damping critically depend on the plasma equilibrium pressure, the initial flow speed, the coil phasing and the proximity of q0 to 1. No appreciable flow damping is found for a βN plasma. A relatively slower initial toroidal flow results in a stronger core flow damping, due to the enhanced NTV torque. Weaker flow damping is achieved as q0 is assumed to be farther away from 1. Finally, a systematic coil phasing scan finds the strongest (weakest) flow damping occurring at the coil phasing of approximately 20 (200) degrees, quantitatively agreeing with experiments. This study points to the important role played by the internal kink response in plasma core flow damping in high-beta hybrid scenario plasmas such as that foreseen for ITER.