Global turbulence simulations of the tokamak edge region with GRILLIX

Turbulent dynamics in the scrape-off layer (SOL) of magnetic fusion devices is intermittent with large fluctuations in density and pressure. Therefore, a model is required that allows perturbations of similar or even larger magnitude to the time-averaged background value. The fluid-turbulence code GRILLIX is extended to such a global model, which consistently accounts for large variation in plasma parameters. Derived from the drift reduced Braginskii equations, the new GRILLIX model includes electromagnetic and electron-thermal dynamics, retains global parametric dependencies and the Boussinesq approximation is not applied. The penalisation technique is combined with the flux-coordinate independent (FCI) approach [F. Hariri and M. Ottaviani, Comput.Phys.Commun. 184:2419, (2013); A. Stegmeir et al., Comput.Phys.Commun. 198:139, (2016)], which allows to study realistic diverted geometries with X-point(s) and general boundary contours. We characterise results from turbulence simulations and investigate the effect of geometry by comparing simulations in circular geometry with toroidal limiter against realistic diverted geometry at otherwise comparable parameters. Turbulence is found to be intermittent with relative fluctuation levels of up to 40% showing that a global description is indeed important. At the same time via direct comparison, we find that the Boussinesq approximation has only a small quantitative impact in a turbulent environment. In comparison to circular geometry the fluctuations are reduced in diverted geometry, which is related to a different zonal flow structure. Moreover, the fluctuation level has a more complex spatial distribution in diverted geometry. Due to local magnetic shear, which differs fundamentally in circular and diverted geometry, turbulent structures become strongly distorted in the perpendicular direction and are eventually damped away towards the X-point

Validation of edge turbulence codes against the TCV-X21 diverted L-mode reference case

Self-consistent full-size turbulent-transport simulations of the divertor and scrape-off-layer (SOL) of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted ohmic L-mode discharges on the tokamak à configuration variable (TCV) tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from five diagnostic systems from the outboard midplane (OMP) to the divertor targets - giving a total of 45 one- and two-dimensional comparison observables in two toroidal magnetic field directions. The experimental dataset is used to validate three flux-driven 3D fluid-turbulence models - GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, individually tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the OMP - both in terms of profile shape and absolute magnitude - while a comparatively poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset and validation analysis, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and SOL

Preliminary analysis of alternative divertors for DEMO

A physics and engineering analysis of alternative divertor configurations is carried out by examining benefits and problems by comparing the baseline single null solution with a Snowflake, an X- and a Super-X divertor. It is observed that alternative configurations can provide margin and resilience against large power fluctuations, but their engineering has intrinsic difficulties, especially in the balance between structural solidity and accessibility of the components and when the specific poloidal field coil positioning poses further constraints. A hybrid between the X- and Super-X divertor is proposed as a possible solution to the integration challenge

Preliminary analysis of alternative divertors for DEMO

A physics and engineering analysis of alternative divertor configurations is carried out by examining benefits and problems by comparing the baseline single null solution with a Snowflake, an X- and a Super-X divertor. It is observed that alternative configurations can provide margin and resilience against large power fluctuations, but their engineering has intrinsic difficulties, especially in the balance between structural solidity and accessibility of the components and when the specific poloidal field coil positioning poses further constraints. A hybrid between the X- and Super-X divertor is proposed as a possible solution to the integration challenge

TORBEAM 2.0, a paraxial beam tracing code for electron-cyclotron beams in fusion plasmas for extended physics applications

The paraxial WKB code TORBEAM (Poli, 2001) is widely used for the description of electron-cyclotron waves in fusion plasmas, retaining diffraction effects through the solution of a set of ordinary differential equations. With respect to its original form, the code has undergone significant transformations and extensions, in terms of both the physical model and the spectrum of applications. The code has been rewritten in Fortran 90 and transformed into a library, which can be called from within different (not necessarily Fortran-based) workflows. The models for both absorption and current drive have been extended, including e.g. fully-relativistic calculation of the absorption coefficient, momentum conservation in electron–electron collisions and the contribution of more than one harmonic to current drive. The code can be run also for reflectometry applications, with relativistic corrections for the electron mass. Formulas that provide the coupling between the reflected beam and the receiver have been developed. Accelerated versions of the code are available, with the reduced physics goal of inferring the location of maximum absorption (including or not the total driven current) for a given setting of the launcher mirrors. Optionally, plasma volumes within given flux surfaces and corresponding values of minimum and maximum magnetic field can be provided externally to speed up the calculation of full driven-current profiles. These can be employed in real-time control algorithms or for fast data analysis.</p

Progress from ASDEX Upgrade experiments in preparing the physics basis of ITER operation and DEMO scenario development

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

Overview of ASDEX upgrade results in view of ITER and DEMO

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