Plasma turbulence is a fundamental process and a key transport mechanism in magnetic confinement fusion (MCF). Due to its complex, non-linear dynamics, turbulence is typically studied through numerical simulations. While turbulence in the confined core plasma has been extensively researched for decades, recent focus has shifted toward the plasma edge and scrape-off layer (SOL). This region, although more challenging to study, is critically important as it sets the boundary conditions for the core plasma and governs physical fluxes to plasma-facing components. This holds true for both major MCF concepts: tokamaks and stellarators. In this work, we introduce a first-of-its-kind tool capable of investigating non-local gyrokinetic turbulence in the edge and SOL of both tokamaks and stellarators. The gyrokinetic turbulence code GENE-X, initially developed for tokamak simulations, has been extended to accommodate stellarator geometries. Here, we detail the modifications made to the code, describe the verification of its new capabilities, and present its first application: the study of turbulence in a stellarator configuration featuring a non-segmented island divertor. This constitutes the world’s first simulation of Eulerian gyrokinetic turbulence in the edge and SOL of stellarators.

Accurate modeling of turbulent transport in magnetic confinement fusion devices requires extending first-principles gyrokinetic simulations from the core to the edge and scrape-off layer (SOL), where additional physics-particularly plasma-neutrals interactions-must be included. Neutrals in these regions reshape radial profiles, influencing gradient-driven instabilities, and modifying transport across the separatrix and in the SOL. We present a tightly coupled scheme between a continuum gyrokinetic plasma model and a simplified fluid model for neutrals. Specifically, we extend the full-, electromagnetic, collisional code GENE-X with a neutrals density evolution equation, where charge exchange is treated as a diffusive process. This hybrid approach represents a first step toward a consistent fluid treatment of neutrals within gyrokinetic plasma simulations. We focus here on the derivation and implementation of Krook-type source terms for ionization, recombination, and associated radiative losses. These operators are constructed to ensure strict conservation of mass, total momentum, and total energy, including kinetic, binding, and radiative components. The coupling is verified in terms of its numerical convergence and in three-species relaxation tests (with electrons, deuterium ions, and neutral deuterium), with a particular focus on its impact on plasma moments, as well as, the distribution functions. Results indicate that even with a simplified neutrals model, the coupling introduces kinetic modifications to the plasma, whose influence on macroscopic quantities will need to be assessed in forthcoming turbulence simulations.

Abstract This work presents a stepwise validation of the evolution of the radial electric field E r and transport during the pre L–H transition phase in the ASDEX Upgrade (AUG) tokamak using edge and scrape-off layer full- f gyrokinetic simulations including X-point geometry. Several L-mode time slices up to the L–H transition from a dedicated hydrogen discharge, featuring stepwise increases in electron cyclotron resonance heating input power, are selected (Bonanomi et al 2024 Phys. Plasmas 31 072302) and simulated with the GENE-X code. As the edge boundary conditions are progressively increased between the time slices, particle and heat fluxes rise, and the radial electric field E r well deepens. A detailed validation of the E r profiles and of the E r well depth shows excellent agreement with experimental measurements at the successive time slices approaching the L–H transition. A force balance decomposition identifies turbulence-driven poloidal flows as the dominant contribution within the E r well. Edge turbulence is governed by a competition between electron drift waves and trapped-electron modes. The introduction of an edge density source, modeling neutral gas ionization, is shown to be essential to reproduce experimentally relevant density profiles, E r , and edge ion heat fluxes, which are dominated by both turbulent and diamagnetic contributions. This stepwise validation constitutes an important milestone toward predictive, first-principles gyrokinetic simulations of the L–H transition power threshold.

A power ramp from L- to H-mode-like conditions is carried out in a 50 ms long global full-f turbulence simulation of ASDEX Upgrade with the grillix code. After 32 ms of slow profile evolution, a sudden change in transport triggers a pedestal buildup within ∼100  μs. This transition results from an abrupt shift from drift-wave (DW) to kinetic-ballooning-mode (KBM) turbulence. The self-consistently evolved E×B flow shear first increases slowly and then sharply. Geodesic acoustic mode and Alfvénic flow oscillations intensify prior to the transition and subsequently die out. This is followed by slow oscillations of the transport and profiles, reminiscent of a dithering I-phase or edge-localized-mode (ELM) cycles observed experimentally. This study paves the way for a better understanding of confinement regime transitions.

Pedestal relaxation events (PREs) appear in I-mode discharges close to the I-H transition. Although they show certain similarities with edge localized modes (ELMs), i.e., periodic energy ejections, the underlying mechanism seems to be very different from the mechanism responsible for ELMs. In this manuscript, we present global trans-collisional fluid simulations of an I-mode discharge in ASDEX Upgrade using GRILLIX. We observe multiple PREs during the simulation, which reproduce a range of experimentally observed PRE characteristics. Furthermore, a detailed analysis of various mode properties in our simulation allows us to pinpoint the underlying mechanism responsible for triggering PREs to micro-tearing modes (MTMs). The system is analyzed dynamically by evaluating density and electron temperature gradient lengths at the OMP position, where the MTM is located and grows over time. The path taken by the system in gradient length space is compared to a growth-rate estimate calculated by linear theory in simplified slab geometry, providing excellent agreement. Building on these insights, we sketch a qualitative picture of a full PRE cycle. Finally, we discuss the influence of the recently implemented Landau-fluid closure and the challenges of simulating low collisionality regimes with trans-collisional fluid models, like the one employed by GRILLIX.

ABSTRACT Turbulence in the edge and scrape‐off layer regions plays a critical role for the performance of future magnetic confinement fusion power plants. Gyrokinetic simulations allow studying this regime with high fidelity. A key aspect in these regions is the high concentration of impurities, which can radiate energy, leading to significant losses. Due to large mass and high charge state, impurities are highly collisional, making them difficult to model accurately. This work presents discretization and algorithmic improvements for Lenard‐Bernstein collisions in gyrokinetic simulations based on previous conservative finite‐volume scheme. The new discretization improves numerical consistency by eliminating conservation errors, which were previously circumvented through the use of free parameters. While small boundary corrections remain necessary, we show that numerical conservation can be improved through careful stencil design, reducing reliance on free parameters. Its implementation is verified through conservation and relaxation tests. The algorithmic improvements focus on computational performance, achieving compute and communication performance gains in a scaled‐down TCV‐X21 benchmark. It also scales as with the number of species , significantly improving upon the previous naive implementation.

This paper presents the first gyrokinetic (GK) simulations of edge and scrape-off layer (SOL) turbulence accelerated by a velocity-space spectral approach in the full-f GK code GENE-X. Building upon the original grid velocity-space discretization, we derive and implement a new spectral formulation and verify the numerical implementation using the method of manufactured solution. We conduct a series of spectral turbulence simulations focusing on the TCV-X21 reference case [Oliveira D. S. et al., Nucl. Fusion 62, 096001 (2022)] and compare these results with previously validated grid simulations [Ulbl P. et al., Phys. Plasmas 30, 107986 (2023)]. The spectral approach reproduces the outboard midplane (OMP) profiles (density, temperature, and radial electric field), dominated by trapped electron mode (TEM) turbulence, with excellent agreement and significantly lower velocity-space resolution. Thus, the spectral approach reduces the computational cost by at least an order of magnitude, achieving a speed-up of approximately 50 for the TCV-X21 case. This enables high-fidelity GK simulations to be performed within a few days on modern CPU-based supercomputers for medium-sized devices and establishes GENE-X as a powerful tool for studying edge and SOL turbulence, moving towards reactor-relevant devices like ITER.

Achieving net-positive fusion energy and its commercialization requires not only engineering marvels but also state-of-the-art, massively parallel codes that can handle reactor-scale simulations. The GENE-X code is a global continuum gyrokinetic turbulence code designed to predict energy confinement and heat exhaust for future fusion reactors. GENE-X is capable of simulating plasma turbulence from the core region to the wall of a magnetic confinement fusion (MCF) device. Originally written in Fortran 2008, GENE-X leverages MPI+OpenMP for parallel computing. In this paper, we augment the Fortran-based compute operators in GENE-X to a C++-17 layer exposing them to a wide array of C++-compatible tools. Here we focus on offloading the augmented operators to GPUs via directive-based programming models such as OpenACC and OpenMP offload. The performance of GENE-X is comprehensively characterized, e.g., by roofline analysis on a single GPU and scaling analysis on multi-GPUs. The major compute operators achieve significant performance improvements, shifting the bottleneck to inter-GPU communications. We discuss additional opportunities to further enhance the performance, such as reducing memory traffic and improving memory utilization efficiency.

The computational power of High-Performance Computing (HPC) systems increases continuously and rapidly. Data-intensive applications are designed to leverage the high computational capacity of HPC resources and typically generate a large amount of data for traditional post-processing data analytics. However, the HPC systems' in-/output (IO) subsystem develops relatively slowly, and the storage capacity is limited. This could lead to limited actual performance and scientific discovery. In-situ techniques are a partial remedy to these problems by reducing or avoiding the data flow through the IO subsystem to/from the storage. However, in current practice, asynchronous in-situ techniques with static resource management often allocate separate computing resources for executing in-situ task(s), which remain idle if no in-situ work is at hand. In the present work, we target improving the efficiency of computing resource usage by launching and releasing necessary additional computing resources for in-situ task(s). Our approach is based on extensions for MPI Sessions that enable the required dynamic resource management. In this paper, we propose a basic and an advanced in-situ techniques with dynamic resource management enabled by MPI Sessions, their implementations on two real-world use cases, and a critical analysis of the experimental results.

A recently developed reduced model of H-mode sustainment based on interchange-drift-Alfvén turbulence description in the vicinity of the separatrix matching experimental observations in ASDEX Upgrade has been extended to experiments with the unfavorable ∇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 ∇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.

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 design of commercially feasible magnetic confinement fusion reactors strongly relies on the reduced turbulent transport in the plasma edge during operation in the high confinement mode (H-mode). We present first global turbulence simulations of the ASDEX Upgrade tokamak edge and scrape-off layer (SOL) in ITER baseline H-mode conditions. Reasonable agreement with the experiment is obtained for outboard mid-plane measurements of plasma density, electron and ion temperature, as well as the radial electric field. The radial heat transport is underpredicted by roughly 1/3. These results were obtained with the GRILLIX code implementing a transcollisional, electromagnetic, global drift-fluid plasma model, coupled to diffusive neutrals. The transcollisional extensions include neoclassical corrections for the ion viscosity, as well as either a Landau-fluid or free-streaming limited model for the parallel heat conduction. Electromagnetic fluctuations are found to play a critical role in H-mode conditions. We investigate the structure of the significant E × B flow shear, finding both neoclassical components as well as zonal flows. But unlike in L-mode, geodesic acoustic modes are not observed. The turbulence mode structure is mostly that of drift-Alfvén waves. However, in the upper part of the pedestal, it is very weak and overshadowed by neoclassical transport. At the pedestal foot, on the other hand, we find instead the (electromagnetic) kinetic ballooning mode (KBM), most clearly just inside the separatrix. Our results pave the way towards predictive simulations of fusion reactors.

Understanding and predicting turbulent transport in the edge and scrape-off-layer (SOL) of magnetic confinement fusion devices is crucial for developing feasible fusion power plants. In this work, we present the latest improvements to the gyrokinetic turbulence code GENE-X and validate the extended model against experimental results in the TCV tokamak (“TCV-X21”). GENE-X features a full-f electromagnetic gyrokinetic model and is specifically targeted for edge and SOL simulations in diverted geometries. GENE-X can model the effect of collisions using either a basic Bhatnagar–Gross–Krook (BGK) or more sophisticated Lenard–Bernstein/Dougherty (LBD) collision operator. We present the results of a series of GENE-X simulations using the BGK or LBD collision models, contrasting them to collisionless simulations. We validate the resulting plasma profiles, power balance, and SOL heat flux against experimental measurements. The match to the experiment significantly improves with the fidelity of the collision model chosen. We analyze the characteristics of the turbulence and find that in almost all cases in the confined region the turbulence is driven by trapped electron modes (TEM). Both the simulations without collisions and those with the BGK collision operator do not accurately describe turbulence driven by TEMs. The more sophisticated LBD collision operator presents a minimum requirement for accurate gyrokinetic edge turbulence simulations.

The correlation between the bifurcation of resonant magnetic perturbations (RMPs) to the unshielded state and edge localized mode (ELM) suppression in ASDEX Upgrade is studied using a kinetic plasma response model numerically and analytically. For the numerical studies, the linear kinetic Maxwell solver KiLCA for cylindrical geometry and the quasilinear transport code QL-Balance are used in combination with the ideal MHD solver GPEC to account for realistic tokamak geometry. Based on this modelling, a numerical local bifurcation criterion is introduced which estimates the effect of RMP-induced temperature plateau formation in the resonant layer. Its analytical form is derived in constant-psi approximation. The kinetic model reproduces the known gyrocenter resonance, Er=0 , and the electron fluid resonance. In contrast to MHD theory, the latter is located at the zero of the perpendicular electron fluid velocity computed only with half of the electron temperature gradient. The application of the criterion to experimental data shows a correlation between bifurcation and the ELM suppression phase. Moreover, an electron density limit is found resembling the one observed in experiments.

The understanding and the predictive capability for turbulence in the plasma edge and scrape-off layer (SOL) are crucial for the development of magnetic confinement fusion reactors. To this end, we characterise turbulent transport across the edge and SOL of the diverted ASDEX Upgrade tokamak in attached L-mode conditions by means of validated, global simulations. The collisionality is controlled by the divertor neutrals density, as their ionisation increases the plasma density and decreases the temperature. The radial E×B particle and heat transport, quantified by effective diffusivities, rises strongly with collisionality. The modest increase in fluctuation amplitudes is not a sufficient explanation. The reason is shown to be the destabilisation of resistive drift-ballooning modes, resulting in larger phase shifts between the pressure and electrostatic potential. The transport varies both radially and poloidally. Due to its ballooning nature, radial transport is close to zero on the inboard mid-plane. On the outboard mid-plane, significant transport is driven in the SOL by large filaments (blobs) with amplitudes of up to 250% of the mean, propagating ballistically from the separatrix to the wall. This non-local transport leads to large radial variations of diffusivities, as they do not necessarily correlate with the local gradient. Ion temperature fluctuations in the plasma edge are shown to be involved in blob seeding at the separatrix, and are the largest in the SOL. Radial diffusivities peak at the top and bottom of the device, since gradients are flatter there due to the flux expansion while the cross-field flow is sustained by streamers—a feature which should be considered in mean-field transport modelling. The increase of SOL E×B transport with collisionality is likely fostered by the simultaneously decreasing radial electric field, resulting from a flattened electron temperature profile. Large amplitude blobs are a hazard for plasma facing components of fusion reactors, but they could be restrained by control of SOL collisionality.

Gyrokinetic simulations are among the main tools to predict turbulent transport in the core of fusion devices. Unlike the core, the plasma edge and scrape-off layer are characterized by lower temperature and higher collisionality. To allow for realistic gyrokinetic modelling of edge and scrape-off layer turbulence, it is crucial to include collisional effects into the simulations. In this work, we present a full-f, gyro-averaged, multi-species, Lenard-Bernstein/Dougherty (LBD) collision operator, for the use in the gyrokinetic turbulence code GENE-X. The operator accounts for exact particle density, momentum, and energy conservation, with collision frequencies chosen such that the momentum or temperature relaxation rates of the Boltzmann collision operator are recovered. We provide a conservative second-order finite-volume implementation of the operator and present a thorough verification. Due to the excellent conservation properties of the finite-volume implementation, it is possible to use a coarser velocity space grid, save computational resources and, as a consequence, perform simulations of larger fusion devices.

Understanding and predicting turbulence in the edge and scrape-off layer (SOL) is critical for the optimization of magnetic confinement fusion devices. While there has been progress along these lines, especially with the help of fluid codes, the development of full-f electromagnetic gyrokinetic codes for the edge and SOL, in general, diverted geometries, remains crucial. In this work, we present simulations of the edge and SOL of the ASDEX Upgrade tokamak with the novel grid-based gyrokinetic (continuum) code GENE-X. The presented simulations are performed at both reduced and realistic electron-to-ion mass ratios on millisecond time scales, studying profile evolution. We compare the resulting plasma profiles to experimental measurements and to previous simulations with the Braginskii fluid code GRILLIX. Furthermore, we measure and validate the SOL power falloff length λq according to the Eich fit function. Based on the results, we discuss the influence of the ion-to-electron mass ratio and collisional effects on gyrokinetic SOL turbulence.

Understanding and predicting plasma turbulence in the scrape-off layer of a magnetic confinement fusion device is a key open problem in modern plasma physics. The transitional region between the core and scrape-off layer poses a difficult problem for turbulence simulations. The poloidal magnetic field vanishes at the X-point of a fusion device, which introduces a coordinate singularity in the commonly used field-aligned coordinates. In the present work, we present a full-f gyrokinetic code based on a locally field-aligned coordinate system that is flux-coordinate independent and free of singularities. The coordinate system, as well as the equations and numerical methods are described. In addition, careful numerical and physical verifications in closed magnetic flux surfaces are included.