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

Reduced model for H-mode sustainment in unfavorable ∇B\mathbf{ \nabla B} drift configuration in ASDEX Upgrade

A recently developed reduced model of H-mode sustainment based on interchange-drift-Alfv\'en turbulence description in the vicinity of the separatrix matching experimental observations in ASDEX Upgrade has been extended to experiments with the unfavorable $\nabla B$ drift. The combination with the theory of the magnetic-shear-induced Reynolds stress offers a possibility to quantitatively explain the phenomena. The extension of the Reynolds stress estimate in the reduced model via the magnetic shear contribution is able to reproduce the strong asymmetry in the access conditions depending on the ion $\nabla B$ drift orientation in agreement with experimental observations. The Reynolds stress profile asymmetry predicted by the magnetic shear model is further extended by comparison with GRILLIX and GENE-X simulations matched with comparable experiments in realistic X-point geometry. The predictions of the radial electric field well depth and its difference between the favorable and unfavorable configurations at the same heating power from the extended model also show consistency with experimental measurements.Comment: Submitted to Nuclear Fusio

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

Treatment of advanced divertor configurations in the flux‐coordinate independent turbulence code GRILLIX

Advanced divertor configurations modify the magnetic geometry of the diverter to achieve a combination of strong magnetic flux expansion, increased connection length and higher divertor volume - to improve detachment stability, neutral/impurity confinement and heat-channel broadening. In this paper, we discuss the modification of the Flux-Coordinate Independent (FCI) turbulence code GRILLIX to treat generalised magnetic geometry, to allow for the investigation of the effect of magnetic geometry on turbulent structures in the edge and SOL. The development of grids and parallel operators from numerically-defined magnetic equilibria is discussed, as is the application of boundary conditions via penalisation, with the finite-width method generalised to treat complex non-conformal boundaries. Initial testing of hyperbolic (advection) and parabolic (diffusion) test cases is presented for the Snowflake scenario.Comment: Submitted for 17th International Workshop on Plasma Edge Theory in Fusion Device