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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.

In a shattered pellet injection (SPI) system the penetration and assimilation of the injected material depends on the speed and size distribution of the SPI fragments. ASDEX Upgrade (AUG) was recently equipped with a flexible SPI to study the effect of these parameters on disruption mitigation efficiency. In this paper we study the impact of different parameters on SPI assimilation with the 1.5D INDEX code. Scans of fragment sizes, speeds and different pellet compositions are carried out for single SPI into AUG H-mode plasmas. We use a semi-empirical thermal quench (TQ) onset condition to study the material assimilation trends. For mixed deuterium-neon pellets, smaller/faster fragments start to assimilate quicker. However, at the expected onset of the global reconnection event (GRE),larger/faster fragments end up assimilating more material. Variations in the injected neon content lead to a large difference in the assimilated neon for neon content below $< 10^{21}$ atoms. For larger injected neon content, a self-regulating mechanism limits the variation in the amount of assimilated neon. We use a back-averaging model to simulate the plasmoid drift during pure deuterium injections with the back-averaging parameter determined by a interpretative simulation of an experimental pure deuterium injection discharge. Again, larger and faster fragments are found to lead to higher assimilation with the material assimilation limited to the plasma edge in general, due to the plasmoid drift. The trends of assimilation for varying fragment sizes, speeds and pellet composition qualitatively agree with the previously reported experimental observations.

Plasma-terminating disruptions represent a critical outstanding issue for reactor-relevant tokamaks. ITER will use shattered pellet injection (SPI) as its disruption mitigation system to reduce heat loads, vessel forces, and to suppress the formation of runaway electrons. In this paper we demonstrate that reduced kinetic modelling of SPI is capable of capturing the major experimental trends in ASDEX Upgrade SPI experiments, such as dependence of the radiated energy fraction on neon content, or the current quench dynamics. Simulations are also consistent with the experimental observation of no runaway electron generation with neon and mixed deuterium-neon pellet composition. We also show that statistical variations in the fragmentation process only have a notable impact on disruption dynamics at intermediate neon doping, as was observed in experiments.

Shattered pellet injection (SPI) is selected for the disruption mitigation system in ITER, due to deeper penetration, expected assimilation efficiency and prompt material delivery. This article describes non-linear simulations of SPI in the ASDEX Upgrade tokamak to test the mitigation efficiency of different injection parameters for neon-doped deuterium pellets using the JOREK code. The simulations are executed as fluid simulations. Additional marker particles are used to evolve the charge state distribution of impurities based on OpenADAS atomic data, i.e., no coronal equilibrium assumption is made. Regarding the pellet composition, neon fraction scans from 0 - 10% are performed. Numerical results show that the thermal quench (TQ) occurs in two stages. In the first stage, approximately half of the thermal energy is lost abruptly, primarily through convective and conductive transport in the stochastic fields. This stage is relatively independent of the injection parameters. In the second stage, where the majority of the remaining thermal energy is lost, radiation plays a dominant role. In cases of very low neon content, this second stage may not occur at all. A larger fraction ($\sim $20%) of the total material in the pellet is assimilated in the plasma for low neon fraction pellets (0.12%) since the full thermal collapse of the plasma occurs later than in high neon fraction scenarios. Nevertheless, the total number of assimilated neon atoms increases with increasing neon fraction. The effects of fragment size and penetration speed are further studied. Slower and smaller fragments promote edge cooling and the formation of a cold front. Faster fragments result in shorter TQ duration and higher assimilation as they reach the hotter plasma regions quicker. Using synthetic diagnostics, comparisons of general trend between simulations and experiments are conducted.

A new axisymmetric equilibrium solver has been written, called FEQIS (Flexible EQuIlibrium Solver), which purpose is to be used inside integrated modeling of tokamak plasmas. The FEQIS code solves the Grad-Shafranov equation and the "circuit" equations for the external coils and passive conducting structures that are toroidally connected. The code has been specifically equipped with flexibility in choice of circuit connections, and a stripped-down numerical scheme for the solution of the Grad-Shafranov equation through a structure of multi-level simplifications which can be tested against the required accuracy.

Future large tokamaks will operate at high plasma currents and high stored plasma energies. To ensure machine protection in case of a sudden loss of plasma confinement (major disruption), a large fraction of the magnetic and thermal energy must be radiated to reduce thermal loads. The disruption mitigation system for ITER is based on massive material injection in the form of shattered pellet injection (SPI). To support ITER, a versatile SPI system was installed at the tokamak ASDEX Upgrade (AUG). The AUG SPI features three independent pellet generation cells and guide tubes, and each was equipped with different shatter heads for the 2022 experimental campaign. We dedicated over 200 plasma discharges to the study of SPI plasma termination, and in this manuscript report on the results of bolometry (total radiation) analysis. The amount of neon inside the pellets is the dominant factor determining the radiated energy fraction (frad). Large and fast fragments, produced by the $12.5^\circ$ rectangular shatter head, lead to somewhat higher values of frad compared to the $25^\circ$ circular or rectangular heads. This effect is strongest for neon content of $< 4\times10^{20}$ neon atoms injected, where a higher normal velocity component (larger fragments) seems slightly beneficial. While full-sized, 8 mm diameter, pure deuterium (D2) pellets lead to a disruption, the 4 mm or shortened 8 mm pellets of pure D2 did not lead to a disruption. The disruption threshold for pure D2 is found to be around $1\times10^{22}$ deuterium molecules inside the pellet. While the radiated energy fraction of non-disruptive SPI is below 20%, this is increased to 40% during the TQ and VDE phase of the disruptive injections. For deuterium-neon-mix pellets, frad values of $< 90$% are observed, and the curve saturates around 80% for 10% neon mixed into the 8 mm pellets ($2\times10^{21}$ neon atoms)., Comment: 15 pages, 9 figures

Fusion power plants require ELM-free, detached operation to prevent divertor damage and erosion. The separatrix operational space (SepOS) is proposed as a tool for identifying access to the type-I ELM-free quasi-continuous exhaust regime. In this work, we recast the SepOS framework using simple parameters and present dedicated ASDEX Upgrade discharges to demonstrate how to interpret its results. Analyzing an extended ASDEX Upgrade database consisting of 6688 individual measurements, we show that SepOS accurately describes how the H-mode boundary varies with plasma current and magnetic field strength. We then introduce a normalized SepOS framework and LH minimum scaling and show that normalized boundaries across multiple machines are nearly identical, suggesting that the normalized SepOS can be used to translate results between different machines. The LH minimum density predicted by SepOS is found to closely match an experimentally determined multi-machine scaling, which provides a further indirect validation of SepOS across multiple devices. Finally, we demonstrate how SepOS can be used predictively, identifying a viable QCE operational point for SPARC, at a separatrix density of 4e20/m3, a separatrix temperature of 156eV and an alpha-t of 0.7 - a value solidly within the QCE operational space on ASDEX Upgrade. This demonstrates how SepOS provides a concise, intuitive method for scoping ELM-free operation on next-step devices., Comment: Conference paper for PSI-26 (Plasma Surface Interactions)

The "density limit" is one of the fundamental bounds on tokamak operating space, and is commonly estimated via the empirical Greenwald scaling. This limit has garnered renewed interest in recent years as it has become clear that ITER and many tokamak pilot plant concepts must operate near or above the widely-used Greenwald limit to achieve their objectives. Evidence has also grown that the Greenwald scaling - in its remarkable simplicity - may not capture the full complexity of the disruptive density limit. In this study, we assemble a multi-machine database to quantify the effectiveness of the Greenwald limit as a predictor of the L-mode density limit and identify alternative stability metrics. We find that a two-parameter dimensionless boundary in the plasma edge, $\nu_{*\rm, edge}^{\rm limit} = 3.0 \beta_{T,{\rm edge}}^{-0.4}$, achieves significantly higher accuracy (true negative rate of 97.7% at a true positive rate of 95%) than the Greenwald limit (true negative rate 86.1% at a true positive rate of 95%) across a multi-machine dataset including metal- and carbon-wall tokamaks (AUG, C-Mod, DIII-D, and TCV). The collisionality boundary presented here can be applied for density limit avoidance in current devices and in ITER, where it can be measured and responded to in real time., Comment: 27 pages, 9 figures

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, Alfv\'enic 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 Alfv\'en eigenmodes using linear gyrokinetic MHD simulations. Changes in the Alfv\'en 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 Alfv\'enic activity is also observed in natural disruptions with no RE beam forming., Comment: 15 (+5 Appendix) pages, 15 (+1 Appendix) figures, submitted paper, Additional details on each classification/method openly available in my master's thesis, see http://hdl.handle.net/21.11116/0000-0008-ED5A-9

The theoretical investigation of relevant turbulent transport mechanisms in H-mode pedestals is a great scientific and numerical challenge. In this study, we address this challenge by global, nonlinear gyrokinetic simulations of a full pedestal up to the separatrix, supported by a detailed characterisation of gyrokinetic instabilities from just inside the pedestal top to pedestal centre and foot. We present ASDEX Upgrade pedestal simulations using an upgraded version of the gyrokinetic, Eulerian, delta-f code GENE (genecode.org) that enables stable global simulations at experimental plasma beta values. The turbulent transport is found to exhibit a multi-channel, multi-scale character throughout the pedestal with the dominant contribution transitioning from ion scale Trapped Electron Modes (TEMs)/Micro Tearing Modes (MTMs) at the pedestal top to electron scale Electron Temperature Gradient modes (ETG) in the steep gradient region. Consequently, the turbulent electron heat flux changes from ion to electron scales and the ion heat flux reduces to almost neoclassic values in the pedestal centre. ExB shear is found to strongly reduce heat flux levels in all channels (electron, ion, electrostatic, electromagnetic) and the interplay of magnetic shear and pressure gradient is found to locally stabilise ion scale instabilities.

Regimes of operation in tokamaks that are devoid of large ELMs have to be better understood to extrapolate their applicability to reactor-relevant devices. This paper describes non-linear extended MHD simulations that use an experimental equilibrium from an EDA H-mode in ASDEX Upgrade. Linear ideal MHD analysis indicates that the operational point lies slightly inside of the stable region. The non-linear simulations with the visco-resistive extended MHD code, JOREK, sustain non-axisymmetric perturbations that are linearly most unstable with toroidal mode numbers of n = \{6 \dots 9\}, but non-linearly higher and lower n become driven and the low-n become dominant. The poloidal mode velocity during the linear phase is found to correspond to the expected velocity for resistive ballooning modes. The perturbations that exist in the simulations have somewhat smaller poloidal wavenumbers (k_{\theta} \sim 0.1 to 0.5 cm^{-1} ) than the experimental expectations for the quasi-coherent mode in EDA, and cause non-negligible transport in both the heat and particle channels. In the transition from linear to non-linear phase, the mode frequency chirps down from approximately 35 kHz to 13 kHz, which corresponds approximately to the lower end of frequencies that are typically observed in EDA H-modes in ASDEX Upgrade.

The High Field High Density Region (HFSFD) has been experimentally observed in both divertor and limiter tokamak devices. In order to numerically reproduced the HFSHD region in the limiter tokamak device J-TEXT, we first performed SOLPS-ITER simulations on the J-TEXT limiter tokamak with the activation of drifts, which is associated with the HFSHD region. The validated physical models, which is from ASDEX Upgrade (AUG) divertor modelling including full drifts and currents, were applied. Through a gas puffing rate scan, both attached and detached regimes were numerically obtained in the AUG divertor and J-TEXT limiter. The key plasma parameters in the J-TEXT limiter are evaluated with and without drifts that have a qualitative performance like AUG except the roll-overment of the total ion flux at the targets. The drift effects on the target profiles are investigated in which the maximum electron temperature at the outer targets is 15eV and 5eV respectively. When the outer targets are attached in the J-TEXT limiter and AUG divertor, the drifts result in the partial detachment of the inner targets. In the detached regimes, the drifts decrease the electron temperature on AUG divertor targets. However, for the J-TEXT limiter, the electron temperature only decreases at the far SOL region. The effect of drifts on the neutral density is also presented.

An accurate description of turbulence up to the transport time scale is essential for predicting core plasma profiles and enabling reliable calculations for designing advanced scenarios and future devices. Here, we exploit the gap separation between turbulence and transport time scales and couple the global gyrokinetic code GENE to the transport-solver Tango, including kinetic electrons, collisions, realistic geometries, toroidal rotation and electromagnetic effects for the first time. This approach overcomes gyrokinetic codes' limitations and enables high-fidelity profile calculations in experimentally relevant plasma conditions, significantly reducing the computational cost. We present numerical results of GENE-Tango for two ASDEX Upgrade discharges, one of which exhibits a pronounced peaking of the ion temperature profile not reproduced by TGLF-ASTRA. We show that GENE-Tango can correctly capture the ion temperature peaking observed in the experiment. By retaining different physical effects in the GENE simulations, e.g., collisions, toroidal rotation and electromagnetic effects, we demonstrate that the ion temperature profile's peaking is due to electromagnetic effects of submarginal MHD instability. Based on these results, the expected GENE-Tango speedup for the ITER standard scenario is larger than two orders of magnitude compared to a single gyrokinetic simulation up to the transport time scale, possibly making first-principles ITER simulations feasible on current computing resources.

An Imaging Neutral Particle Analyser (INPA) diagnostic has been designed for the ASDEX Upgrade (AUG) tokamak. The AUG INPA diagnostic will measure fast neutrals escaping the plasma after CX reactions. The neutrals will be ionised by a 20 nm carbon foil and deflected towards a scintillator by the local magnetic field. The use of a neutral beam injector (NBI) as active source of neutrals will provide radially resolved measurements while the use of a scintillator as active component will allow us to cover the whole plasma along the NBI line with unprecedented phase-space resolution ($ < $ 12 keV and 8 cm) and fast temporal response (up to 1 kHz with the high resolution acquisition system and above 100 kHz with the low resolution one); making it suitable to study localised fast-ions redistributions in phase-space.

A synthetic Fast-Ion Loss Detector (FILD) and an imaging Heavy Ion Beam Probe (i-HIBP) have been implemented in the 3D hybrid kinetic-magnetohydrodynamic code MEGA. First synthetic measurements from these two diagnostics have been obtained for neutral beam injection (NBI) driven Alfv\'en Eigenmode (AE) simulated with MEGA. The synthetic fast-ion losses show a strong correlation with the AE amplitude. This correlation is observed in the phase-space, represented in coordinates toroidal canonical momentum and energy. Fast-ion losses and the energy exchange diagrams of the confined population are connected with lines of constant E' , a linear combination of E and P{\phi} . First i-HIBP synthetic signals also have been computed for the simulated AE, showing displacements in the strikeline of the order of around 1 mm, above the expected resolution in the i-HIBP scintillator of approximately 100 {\mu}m.

Tokamak operational regimes with small edge localized modes (ELMs) could be a solution to the problem of large transient heat loads in future fusion reactors because they provide quasi-continuous exhaust while keeping a good plasma confinement. A ballooning mode mechanism near the last closed flux surface (LCFS) governed by an interplay of the pressure gradient and the magnetic shear there has been proposed for small ELMs in high density ASDEX Upgrade and TCV discharges. In this manuscript we explore different factors relevant for plasma edge stability in a wide range of edge safety factors by changing the connection length between the good and the bad curvature side. Simultaneously this influences the stabilizing effect of the local magnetic shear close to the LCFS as well as the $E \times B$ flow shear. Ideal ballooning stability calculations with the HELENA code reveal that small ELM plasmas are indeed unstable against ballooning modes very close to the LCFS but can exhibit second ballooning stability in the steep gradient region which correlates with enhanced confinement. We also present first non-linear simulations of small ELM regimes with the JOREK code including the $E \times B$ shear which indeed develop ballooning like fluctuations in the high triangularity limit. In the region where the small ELMs originate the dimensionless parameters are very similar in our investigated discharges and in a reactor, making this regime the ideal exhaust scenario for a future reactor.

The development of small- and no-ELM regimes for ITER is a high priority topic due to the risks associated to type-I ELMs. By considering non-linear extended MHD simulations of the ASDEX Upgrade tokamak with the JOREK code, we probe a regime that avoids type-I ELMs completely provided that the separatrix density is high enough. The dynamics of the pedestal in this regime are observed to be qualitatively similar to the so-called quasi-continuous exhaust (QCE) regime in several ways. Repetitive type-I ELMs are substituted by roughly constant levels of outwards transport caused by peeling-ballooning modes (with dominant ballooning characteristics) which are localised in the last 5\% of the confined region (in normalised poloidal flux). The simulated low triangularity plasma transitions to a type-I ELMy H-mode if the separatrix density is sufficiently reduced or if the input heating power is sufficiently increased. The stabilising factors that play a role in the suppression of the small ELMs are also investigated by analysing the simulations, and the importance of including diamagnetic effects in the simulations is highlighted. By considering a scan in the pedestal resistivity and by measuring the poloidal velocity of the modes (and comparing to theoretical estimates for ideal and resistive modes), we identify the underlying instabilities as resistive peeling-ballooning modes. Decreasing the resistivity below experimentally-relevant conditions (i.e., going towards ideal MHD), the peeling-ballooning modes that constrain the pedestal below the type-I ELM stability boundary display sharply decreasing growth rates.

In some conditions, I-mode plasmas can feature pedestal relaxation events (PREs) that transiently enhance the energy reaching the divertor target plates. To shed light into their appearance, characteristics and energy reaching the divertor targets, a comparative study between two tokamaks $-$ Alcator C-Mod and ASDEX Upgrade $-$ is carried out. It is found that PREs appear only in a subset of I-mode discharges, mainly when the plasma is close to the H-mode transition. Also, the nature of the triggering instability is discussed by comparing measurements close to the separatrix in both devices. The PRE relative energy loss from the confined region increases with decreasing pedestal top collisionality $\nu_{\mathrm{ped}}^*$. In addition, the relative electron temperature drop at the pedestal top, which is related to the conductive energy loss, rises with decreasing $\nu_{\mathrm{ped}}^*$. Finally, the peak parallel energy fluence due to the PRE measured on the divertor in both devices is compared to the model introduced in [1] for type-I ELMs. The model is shown to provide an upper boundary for PRE energy fluence data, while a lower boundary is found by dividing the model by three. These two boundaries are used to make projections to future devices such as DEMO and ARC.

This paper presents a study of the interaction between Alfv\'en modes and zonal structures, considering a realistic ASDEX Upgrade equilibrium. The results of gyrokinetic simulations with the global, electromagnetic, particle-in-cell code ORB5 are presented, where the modes are driven unstable by energetic particles with a bump-on-tail equilibrium distribution function, with radial density gradient. Two regimes have been observed: at low energetic particles concentration, the Alfv\'en mode saturates at much higher level in presence of zonal structures; on the other hand at high energetic particles concentration the difference is less pronounced. The former regime is characterized by the zonal structure (identified as an energetic particle driven geodesic acoustic mode), being more unstable than the Alfv\'en mode. In the latter regime the Alfv\'en mode is more unstable than the zonal structure. The theoretical explanation is given in terms of a 3-wave coupling of the energetic particle driven geodesic acoustic mode and Alfv\'en mode, mediated by the curvature-pressure coupling term of the energetic particles.

Injecting frozen deuterium pellets into an ELMy H-mode plasma is a well established scheme for triggering edge localized modes (ELMs) before they naturally occur. Based on an ASDEX Upgrade H-mode plasma, this article presents a comparison of extended MHD simulations of spontaneous type-I ELMs and pellet-triggered ELMs allowing to study their non-linear dynamics in detail. In particular, pellet-triggered ELMs are simulated by injecting deuterium pellets into different time points during the pedestal build-up described in [A. Cathey et al. Nuclear Fusion 60, 124007 (2020)]. Realistic ExB and diamagnetic background plasma flows as well as the time dependent bootstrap current evolution are included during the build-up to capture the balance between stabilising and destabilising terms for the edge instabilities accurately. Dependencies on the pellet size and injection times are studied. The spatio-temporal structures of the modes and the resulting divertor heat fluxes are compared in detail between spontaneous and triggered ELMs. We observe that the premature excitation of ELMs by means of pellet injection is caused by a helical perturbation described by a toroidal mode number of n = 1. In accordance with experimental observations, the pellet-triggered ELMs show reduced thermal energy losses and narrower divertor wetted area with respect to spontaneous ELMs. The peak divertor energy fluency is seen to decrease when ELMs are triggered by pellets injected earlier during the pedestal build-up.

The formation of a substantial post-disruption runaway electron current in ASDEX Upgrade material injection experiments is determined by avalanche multiplication of a small seed population of runaway electrons. For the investigation of these scenarios, the runaway electron description of the coupled 1.5D transport solvers ASTRA-STRAHL is amended by a fluid-model describing electron runaway caused by the hot-tail mechanism. Applied in simulations of combined background plasma evolution, material injection, and runaway electron generation in ASDEX Upgrade discharge #33108, both the Dreicer and hot-tail mechanism for electron runaway produce only $\sim$ 3$~$kA of runaway current. In colder plasmas with core electron temperatures $T_\mathrm{e,c}$ below 9$~$keV, the post-disruption runaway current is predicted to be insensitive to the initial temperature, in agreement with experimental observations. Yet in hotter plasmas with $T_\mathrm{e,c} > 10~\mathrm{keV}$, hot-tail runaway can be increased by up to an order of magnitude, contributing considerably to the total post-disruption runaway current. In ASDEX Upgrade high temperature runaway experiments, however, no runaway current is observed at the end of the disruption, despite favourable conditions for both primary and secondary runaway., Comment: 26 pages, 11 figures; published in the Journal of Plasma Physics

Disruptions in tokamak plasmas may lead to the generation of runaway electrons that have the potential to damage plasma-facing components. Improved understanding of the runaway generation process requires interpretative modelling of experiments. In this work we simulate eight discharges in the ASDEX Upgrade and JET tokamaks, where argon gas was injected to trigger the disruption. We use a fluid modelling framework with the capability to model the generation of runaway electrons through the hot-tail, Dreicer and avalanche mechanisms, as well as runaway electron losses. Using experimentally based initial values of plasma current and electron temperature and density, we can reproduce the plasma current evolution using realistic assumptions about temperature evolution and assimilation of the injected argon in the plasma. The assumptions and results are similar for the modelled discharges in ASDEX Upgrade and JET, indicating that the implemented models are applicable to machines of varying size, which is important for the modelling of future, larger machines. For the modelled discharges in ASDEX Upgrade, where the initial temperature was comparatively high, we had to assume that a large fraction of the hot-tail runaway electrons were lost in order to reproduce the measured current evolution., Comment: 17 pages, 7 figures

The key result of the present work is the theoretical prediction and observation of the formation of a new type of transport barrier in fusion plasmas, called F-ATB (fast ion-induced anomalous transport barrier). As demonstrated through state-of-the-art global electrostatic and electromagnetic simulations, the F-ATB is characterized by a full suppression of the turbulent transport - caused by strongly sheared, axisymmetric $E \times B$ flows - and an increase of the neoclassical counterpart, albeit keeping the overall fluxes at significantly reduced levels. The trigger mechanism is shown to be a mainly electrostatic resonant interaction between supra-thermal particles, generated via ion-cyclotron-resonance heating, and plasma micro-turbulence. These findings are obtained by realistic simulations of the ASDEX Upgrade discharge $\#36637$ - properly designed to maximized the beneficial role of the wave-particle resonance interaction - which exhibits the expected properties of improved confinement produced by energetic particles., Comment: Version 2

A triggering mechanism responsible for the explosive onset of edge localised modes (ELMs) in fusion plasmas is identified by performing, for the first time, non-linear magnetohydrodynamic simulations of repetitive type-I ELMs. Briefly prior to the ELM crash, destabilising and stabilising terms are affected at different timescales by an increasingly ergodic magnetic field caused by non-linear interactions between the axisymmetric background plasma and growing non-axisymmetric perturbations. The separation of timescales prompts the explosive, i.e. faster than exponential, growth of an ELM crash which lasts ${\sim}$ 500 ${\mu}$s. The duration and size of the simulated ELM crashes compare qualitatively well with type-I ELMs in ASDEX Upgrade. As expected for type-I ELMs, a direct proportionality between the heating power in the simulations and the ELM repetition frequency is obtained. The simulations presented here are a major step forward towards predictive modelling of ELMs and of the assessment of mitigation techniques in ITER and other future tokamaks.

The I-mode confinement regime can feature small edge temperature drops that can lead to an increase in the energy deposited onto the divertor targets. In this work, we show that these events are associated with a relaxation of both electron temperature and density edge profiles, with the largest drop found at the pedestal top position. Stability analysis of edge profiles reveals that the operational points are far from the ideal peeling-ballooning boundary. Also, we show that these events appear close to the H-mode transition in the typical I-mode operational space in ASDEX Upgrade, and that no further enhancement of energy confinement is found when they occur. Moreover, scrape-off layer transport during these events is found to be very similar to type-I ELMs, with regard to timescales ($\approx$ 800 $\mu$s), filament propagation, toroidally asymmetric energy effluxes at the midplane and asymmetry between inner and outer divertor deposited energy. In particular, the latter reveals that more energy reaches the outer divertor target. Lastly, first measurements of the divertor peak energy fluence are reported, and projections to ARC - a reactor designed to operate in I-mode - are drawn.

Synchrotron radiation images from runaway electrons (REs) in an ASDEX Upgrade discharge disrupted by argon injection are analyzed using the synchrotron diagnostic tool SOFT and coupled fluid-kinetic simulations. We show that the evolution of the runaway distribution is well described by an initial hot-tail seed population, which is accelerated to energies between 25-50 MeV during the current quench, together with an avalanche runaway tail which has an exponentially decreasing energy spectrum. We find that, although the avalanche component carries the vast majority of the current, it is the high-energy seed remnant that dominates synchrotron emission. With insights from the fluid-kinetic simulations, an analytic model for the evolution of the runaway seed component is developed and used to reconstruct the radial density profile of the RE beam. The analysis shows that the observed change of the synchrotron pattern from circular to crescent shape is caused by a rapid redistribution of the radial profile of the runaway density., Comment: 25 pages, 12 figures

In this work we carry out quantitative measurements of particle and heat transport associated to SOL filaments in a tokamak, and relate density shoulder formation to the advection of energy in the far SOL. For the first time, this attempt includes direct measurements of ion and electron temperatures for background and filaments. With this aim, we combine data from a number of equivalent L-mode discharges from the ASDEX Upgrade tokamak in which different probe heads were installed on the midplane manipulator. This approach is validated by a comparison with independent diagnostics. Results indicate an increase of heat transport associated to filaments after the shoulder formation. Several centimeters into the SOL, filaments are still found to carry a substantial fraction (up to one fifth) of the power ejected at the separatrix., Comment: Published in Nucler Fusion

Massive material injection has been proposed as a way to mitigate the formation of a beam of relativistic runaway electrons that may result from a disruption in tokamak plasmas. In this paper we analyse runaway generation observed in eleven ASDEX Upgrade discharges where disruption was triggered using massive gas injection. We present numerical simulations in scenarios characteristic of on-axis plasma conditions, constrained by experimental observations, using a description of the runaway dynamics with self-consistent electric field and temperature evolution in two-dimensional momentum space and zero-dimensional real space. We describe the evolution of the electron distribution function during the disruption, and show that the runaway seed generation is dominated by hot-tail in all of the simulated discharges. We reproduce the observed dependence of the current dissipation rate on the amount of injected argon during the runaway plateau phase. Our simulations also indicate that above a threshold amount of injected argon, the current density after the current quench depends strongly on the argon densities. This trend is not observed in the experiments, which suggests that effects not captured by 0D kinetic modeling -- such as runaway seed transport -- are also important., Comment: 17 pages, 15 figures, published in Journal of Plasma Physics (Invited Contributions from the 18th European Fusion Theory Conference)

We present the first successful simulation of a induced disruption in ASDEX Upgrade from massive material injection (MMI) up to established runaway electron (RE) beam, thus covering pre-thermal quench, thermal quench and current quench (CQ) of the discharge. For future high-current fusion devices such as ITER, the successful suppression of REs through MMI is of critical importance to ensure the structural integrity of the vessel. To computationally study the interplay between MMI, background plasma response, and RE generation, a toolkit based on the 1.5D transport code coupling ASTRA-STRAHL is developed. Electron runaway is described by state-of-the-art reduced kinetic models in the presence of partially ionized impurities. Applied to argon MMI in ASDEX Upgrade discharge #33108, key plasma parameters measured experimentally, such as temporal evolution of the line averaged electron density, plasma current decay rate and post-CQ RE current, are well reproduced by the simulation presented. Impurity ions are transported into the central plasma by the combined effect of neoclassical processes and additional effects prescribed inside the $q = 2$ rational surface to explain experimental time scales. Thus, a thermal collapse is induced through strong impurity radiation, giving rise to a substantial RE population as observed experimentally., Comment: 15 pages, 11 figures; submitted to Nuclear Fusion

Neoclassical and turbulent heavy impurity transport in tokamak core plasmas are determined by main ion temperature, density and toroidal rotation profiles. Thus, in order to understand and prevent experimental behaviour of W accumulation, flux-driven integrated modelling of main ion heat and particle transport over multiple confinement times is a vital prerequisite. For the first time, the quasilinear gyrokinetic code QuaLiKiz has been applied for successful predictions of core kinetic profiles in an ASDEX Upgrade H-mode discharge in the turbulence dominated region within the integrated modelling suite JETTO. Neoclassical contributions are calculated by NCLASS; auxiliary heat and particle deposition profiles due to NBI and ECRH prescribed from previous analysis with TRANSP. Turbulent and neoclassical contributions are insufficient in explaining main ion heat and particle transport inside the $q=1$ surface, necessitating the prescription of further transport coefficients to mimic the impact of MHD activity on central transport. The ion to electron temperature ratio at the simulation boundary at $\rho_\mathrm{tor} = 0.85$ stabilizes ion scale modes while destabilizing ETG modes when significantly exceeding unity. Careful analysis of experimental measurements using Gaussian process regression techniques is carried out to explore reasonable uncertainties. In following trace W impurity transport simulations performed with additionally NEO, neoclassical transport under consideration of poloidal asymmetries alone is found to be insufficient to establish hollow central W density profiles. Reproduction of these conditions measured experimentally is found possible only when assuming the direct impact of a saturated $(m,n)=(1,1)$ MHD mode on heavy impurity transport., Comment: 26 pages, 17 figures

The linear destabilization and nonlinear saturation of energetic-particle driven Alfv\'enic instabilities in tokamaks strongly depend on the damping channels. In this work, the collisionless damping mechanisms of Alfv\'enic modes are investigated within a gyrokinetic framework, by means of global simulations with the particle-in-cell code ORB5, and compared with the eigenvalue code LIGKA and reduced models. In particular, the continuum damping and the Landau damping (of ions and electrons) are considered. The electron Landau damping is found to be dominant on the ion Landau damping for experimentally relevant cases. As an application, the linear and nonlinear dynamics of toroidicity induced Alfv\'en eigenmodes and energetic-particle driven modes in ASDEX Upgrade is investigated theoretically and compared with experimental measurements.

Geodesic acoustic modes (GAMs) are studied by means of the gyrokinetic global particle-in-cell code ORB5. Linear electromagnetic simulations in the low electron beta limit have been performed, in order to separate acoustic and Alfv\'enic time scales and obtain more accurate measurements. The dependence of the frequency and damping rate on several parameters such as the safety factor, the GAM radial wavenumber and the plasma elongation is studied. All simulations have been performed with kinetic electrons with realistic electron/ion mass ratio. Interpolating formulae for the GAM frequency and damping rate, based on the results of the gyrokinetic simulations, have been derived. Using these expressions, the influence of the temperature gradient on the damping rate is also investigated. Finally, the results are applied to the study of a real discharge of the ASDEX Upgrade tokamak.

Field-line localized ballooning modes have been observed at the edge of high confinement mode plasmas in ASDEX Upgrade with rotating 3D perturbations induced by an externally applied n = 2 error field and during a moderate level of edge localized mode-mitigation. The observed ballooning modes are localized to the field-lines which experience one of the two zero-crossings of the radial flux surface displacement during one rotation period. The localization of the ballooning modes agrees very well with the localization of the largest growth rates from infinite-n ideal ballooning stability calculations using a realistic 3D ideal magnetohydrodynamic equilibrium. This analysis predicts a lower stability with respect to the axisymmetric case. The primary mechanism for the local lower stability is the 3D distortion of the local magnetic shear., Comment: 11 pages, 5 figures, for submission to Physical Review Letter

Power exhaust is one of the major challenges for a future fusion device. Applying a non-axisymmetric external magnetic perturbation is one technique that is studied in order to mitigate or suppress large edge localized modes which accompany the high confinement regime in tokamaks. The external magnetic perturbation brakes the axisymmetry of a tokamak and leads to a 2D heat flux pattern on the divertor target. The 2D heat flux pattern at the outer divertor target is studied on ASDEX Upgrade in stationary L-Mode discharges. The amplitude of the 2D characteristic of the heat flux depends on the alignment between the field lines at the edge and the vacuum response of the applied magnetic perturbation spectrum. The 2D characteristic reduces with increasing density. The increasing divertor broadening $S$ with increasing density is proposed as the main actuator. This is supported by a generic model using field line tracing and the vacuum field approach that is in quantitative agreement with the measured heat flux. The perturbed heat flux, averaged over a full toroidal rotation of the magnetic perturbation, is identical to the non-perturbed heat flux without magnetic perturbation. The transport qualifiers, power fall-off length $\lambda_q$ and divertor broadening $S$, are the same within the uncertainty compared to the unperturbed reference. No additional cross field transport is observed., Comment: 23 pages, 28 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

In low-collisionality scenarios exhibiting mitigation of edge localized modes (ELMs), stable ideal kink modes at the edge are excited by externally applied magnetic perturbation (MP)-fields. In ASDEX Upgrade these modes can cause three-dimensional (3D) boundary displacements up to the centimeter range. These displacements have been measured using toroidally localized high resolution diagnostics and rigidly rotating n = 2 MP-fields with various applied poloidal mode spectra. These measurements are compared to non-linear 3D ideal magnetohydrodynamics (MHD) equilibria calculated by VMEC. Comprehensive comparisons have been conducted, which consider for instance plasma movements due to the position control system, attenuation due to internal conductors and changes in the edge pressure profiles. VMEC accurately reproduces the amplitude of the displacement and its dependencies on the applied poloidal mode spectra. Quantitative agreement is found around the low field side (LFS) midplane. The response at the plasma top is qualitatively compared. The measured and predicted displacements at the plasma top maximize when the applied spectra is optimized for ELM-mitigation. The predictions from the vacuum modeling generally fails to describe the displacement at the LFS midplane as well as at the plasma top. When the applied mode spectra is set to maximize the displacement, VMEC and the measurements clearly surpass the predictions from the vacuum modeling by a factor of four. Minor disagreements between VMEC and the measurements are discussed. This study underlines the importance of the stable ideal kink modes at the edge for the 3D boundary displacement in scenarios relevant for ELM-mitigation., Comment: 22 pages, 12 figure, for submission to nuclear fusion

Due to their high cross-field mobility, neutrals can contribute to momentum transport even at the low relative densities found inside the separatrix and they can generate intrinsic rotation. We use a charge-exchange dominated solution to the neutral kinetic equation, coupled to neoclassical ions, to evaluate the momentum transport due to neutrals. Numerical solutions to the drift-kinetic equation allow us to cover the full range of collisionality, including the intermediate levels typical of the tokamak edge. In the edge there are several processes likely to contribute to momentum transport in addition to neutrals. Therefore, we present here an interpretive framework that can evaluate the momentum transport through neutrals based on radial plasma profiles. We demonstrate its application by analysing the neutral angular momentum flux for an L-mode discharge in the ASDEX Upgrade tokamak. The magnitudes of the angular momentum fluxes we find here due to neutrals of up to $1{-}2\;\mathrm{N\, m}$ are comparable to the net torque on the plasma from neutral beam injection, indicating the importance of neutrals for rotation in the edge., Comment: To be submitted to Nuclear Fusion

The plasma response to Resonant Magnetic Perturbations (RMPs) in ASDEX Upgrade is modeled with the non-linear resistive MHD code JOREK, using input profiles that match those of the experiments as closely as possible. The RMP configuration for which Edge Localized Modes are best mitigated in experiments is related to the largest edge kink response observed near the X-point in modeling. On the edge resonant surfaces $q = m/n$, the coupling between the m + 2 kink component and the m resonant component is found to induce the amplification of the resonant magnetic perturbation. The ergodicity and the 3D-displacement near the X-point induced by the resonant amplification can only partly explain the density pumpout observed in experiments., Comment: Submitted to Nuclear Fusion 18 pages (19 pages with Arxiv's compilation formatting), 13 figures

A new parallel equilibrium reconstruction code for tokamak plasmas is presented. GPEC allows to compute equilibrium flux distributions sufficiently accurate to derive parameters for plasma control within 1 ms of runtime which enables real-time applications at the ASDEX Upgrade experiment (AUG) and other machines with a control cycle of at least this size. The underlying algorithms are based on the well-established offline-analysis code CLISTE, following the classical concept of iteratively solving the Grad-Shafranov equation and feeding in diagnostic signals from the experiment. The new code adopts a hybrid parallelization scheme for computing the equilibrium flux distribution and extends the fast, shared-memory-parallel Poisson solver which we have described previously by a distributed computation of the individual Poisson problems corresponding to different basis functions. The code is based entirely on open-source software components and runs on standard server hardware and software environments. The real-time capability of GPEC is demonstrated by performing an offline-computation of a sequence of 1000 flux distributions which are taken from one second of operation of a typical AUG discharge and deriving the relevant control parameters with a time resolution of a millisecond. On current server hardware the new code allows employing a grid size of 32x64 zones for the spatial discretization and up to 15 basis functions. It takes into account about 90 diagnostic signals while using up to 4 equilibrium iterations and computing more than 20 plasma-control parameters, including the computationally expensive safety-factor q on at least 4 different levels of the normalized flux., Comment: minor typos corrected and reference updated, matches published version

The complete refuelling of the plasma density loss (pump-out) caused by mitigation of Edge Localised Modes (ELMs) is demonstrated on the ASDEX Upgrade tokamak. The plasma is refuelled by injection of frozen deuterium pellets and ELMs are mitigated by external resonant magnetic perturbations (RMPs). In this experiment relevant dimensionless parameters, such as relative pellet size, relative RMP amplitude and pedestal collisionality are kept at the ITER like values. Refuelling of density pump out requires a factor of two increase of nominal fuelling rate. Energy confinement and pedestal temperatures are not restored to pre-RMP values by pellet refuelling., Comment: 10 pages, 5 figures. This is an author-created, un-copyedited version of an article submitted for publication in Nuclear Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

We present the first measurement of a local fast-ion 2D velocity distribution function $f(v_\parallel, v_\perp)$. To this end, we heated a plasma in ASDEX Upgrade by neutral beam injection and measured spectra of fast-ion D-alpha (FIDA) light from the plasma center in three views simultaneously. The measured spectra agree very well with synthetic spectra calculated from a TRANSP/NUBEAM simulation. Based on the measured FIDA spectra alone, we infer $f(v_\parallel, v_\perp)$ by tomographic inversion. Salient features of our measurement of $f(v_\parallel, v_\perp)$ agree reasonably well with the simulation: the measured as well as the simulated $f(v_\parallel, v_\perp)$ are lopsided towards negative velocities parallel to the magnetic field, and they have similar shapes. Further, the peaks in the simulation of $f(v_\parallel, v_\perp)$ at full and half injection energies of the neutral beam also appear in the measurement at similar velocity-space locations. We expect that we can measure spectra in up to seven views simultaneously in the next ASDEX Upgrade campaign which would further improve measurements of $f(v_\parallel, v_\perp)$ by tomographic inversion.

Doppler tomography is a well-known method in astrophysics to image the accretion flow, often in the shape of thin discs, in compact binary stars. As accretion discs rotate, all emitted line radiation is Doppler-shifted. In fast-ion D-alpha (FIDA) spectroscopy measurements in magnetically confined plasma, the D-alpha-photons are likewise Doppler-shifted ultimately due to gyration of the fast ions. In either case, spectra of Doppler-shifted line emission are sensitive to the velocity distribution of the emitters. Astrophysical Doppler tomography has lead to images of accretion discs of binaries revealing bright spots, spiral structures, and flow patterns. Fusion plasma Doppler tomography has lead to an image of the fast-ion velocity distribution function in the tokamak ASDEX Upgrade. This image matched numerical simulations very well. Here we discuss achievements of the Doppler tomography approach, its promise and limits, analogies and differences in astrophysical and fusion plasma Doppler tomography, and what can be learned by comparison of these applications.

Gyrokinetic validation studies are crucial in developing confidence in the model incorporated in numerical simulations and thus improving their predictive capabilities. As one step in this direction, we simulate an ASDEX Upgrade discharge with the GENE code, and analyze various fluctuating quantities and compare them to experimental measurements. The approach taken is the following. First, linear simulations are performed in order to determine the turbulence regime. Second, the heat fluxes in nonlinear simulations are matched to experimental fluxes by varying the logarithmic ion temperature gradient within the expected experimental error bars. Finally, the dependence of various quantities with respect to the ion temperature gradient is analyzed in detail. It is found that density and temperature fluctuations can vary significantly with small changes in this parameter, thus making comparisons with experiments very sensitive to uncertainties in the experimental profiles. However, cross-phases are more robust, indicating that they are better observables for comparisons between gyrokinetic simulations and experimental measurements.

A multidiagnostic approach, utilizing Langmuir probes in the midplane, X-point and divertor walls, along with Lithium beam and infrared measurements is employed to evaluate the evolution of the Scrape-off Layer (SOL) of ASDEX Upgrade across the L-mode density transition leading to the formation of a density shoulder. The flattening of the SOL density profiles is linked to a regime change of filaments, which become faster and larger, and to a similar flattening of the $q_{\parallel}$ profile. This transition is related to the beginning of outer divertor detachment and leads to the onset of a velocity shear layer in the SOL. Experimental measurements are in good agreement with several filament models which describe the process as a transition from conduction to convection-dominated SOL perpendicular transport caused by an increase of parallel collisionality. These results could be of great relevance since both ITER and DEMO will feature detached divertors and densities largely over the transition values, and might therefore exhibit convective transport levels different to those observed typically in present-day devices.

The Large Eddy Simulation (LES) approach - solving numerically the large scales of a turbulent system and accounting for the small-scale influence through a model - is applied to nonlinear gyrokinetic systems that are driven by a number of different microinstabilities. Comparisons between modeled, lower resolution, and higher resolution simulations are performed for an experimental measurable quantity, the electron density fluctuation spectrum. Moreover, the validation and applicability of LES is demonstrated through a series of diagnostics based on the free energetics of the system., Comment: 14 pages, 9 figures

In many discharges at ASDEX Upgrade fast particle losses can be observed due to Alfv\'enic gap modes, Reversed Shear Alfv\'en Eigenmodes or core-localized Beta Alfv\'en Eigenmodes. For the first time, simulations of experimental conditions in the ASDEX Upgrade fusion device are performed for different plasma equilibria (particularly for different, also non-monotonic q profiles). The numerical tool is the extended version of the HAGIS code [Pinches'98, Br\"udgam PhD Thesis, 2010], which also computes the particle motion in the vacuum region between vessel wall in addition to the internal plasma volume. For this work, a consistent fast particle distribution function was implemented to represent the strongly anisotropic fast particle population as generated by ICRH minority heating. Furthermore, HAGIS was extended to use more realistic eigenfunctions, calculated by the gyrokinetic eigenvalue solver LIGKA [Lauber'07]. The main aim of these simulations is to allow fast ion loss measurements to be interpreted with a theoretical basis. Fast particle losses are modeled and directly compared with experimental measurements [Garc\'ia-Mu\~noz'10]. The phase space distribution and the mode-correlation signature of the fast particle losses allows them to be characterized as prompt, resonant or diffusive (non-resonant). The experimental findings are reproduced numerically. It is found that a large number of diffuse losses occur in the lower energy range (at around 1/3 of the birth energy) particularly in multiple mode scenarios (with different mode frequencies), due to a phase space overlap of resonances leading to a so-called domino [Berk'95] transport process. In inverted q profile equilibria, the combination of radially extended global modes and large particle orbits leads to losses with energies down to 1/10th of the birth energy., Comment: 16 Pages, 17 Figures