This paper extends a 1D dynamic physics-based model of the scrape-off layer (SOL) plasma, DIV1D, to include the core SOL and possibly a second target. The extended model is benchmarked on 1D mapped SOLPS-ITER simulations to find input settings for DIV1D that allow it to describe SOL plasmas from upstream to target-calibrating it on a scenario and device basis. The benchmark shows a quantitative match between DIV1D and 1D mapped SOLPS-ITER profiles for the heat flux, electron temperature, and electron density within roughly 50% on: (1) the Tokamak Configuration Variable (TCV) for a gas puff scan; (2) a single SOLPS-ITER simulation of the Upgraded Mega Ampere Spherical Tokamak; and (3) the Upgraded Axially Symmetric Divertor EXperiment in Garching Tokamak (AUG) for a simultaneous scan in heating power and gas puff. Once calibrated, DIV1D self-consistently describes dependencies of the SOL solution on core fluxes and external neutral gas densities for a density scan on TCV whereas a varying SOL width is used in DIV1D for AUG to match a simultaneous change in power and density. The ability to calibrate DIV1D on a scenario and device basis is enabled by accounting for cross field transport with an effective flux expansion factor and by allowing neutrals to be exchanged between SOL and adjacent domains.

A review is given on the highlights of a scatter-shot approach of developing machine-learning methods and artificial neural networks based fast predictors for the application to fusion exhaust. The aim is to enable and facilitate optimized and improved modeling allowing more flexible integration of physics models in the light of extrapolations towards future fusion devices. The project encompasses various research objectives: (a) developments of surrogate model predictors for power & particle exhaust in fusion power plants; (b) assessments of surrogate models for time-dependent phenomena in the plasma-edge; (c) feasibility studies of micro-macro model discovery for plasma-facing components surface morphology & durability; and (d) enhancements of pedestal models & databases through interpolators and generators exploiting uncertainty quantification. Presented results demonstrate useful applications for machine-learning and artificial intelligence in fusion exhaust modeling schemes, enabling an unprecedented combination of both fast and accurate simulation.

Heat loads of 10 MW m(-2) are expected for steady state operation at ITER and up to 20 MW m(-2) in slow transient situations. Plasma linear devices like Magnum-PSI can recreate situations close as those expected to be achieved at ITER divertor, providing easier access for diagnostics than in a tokamak. Numerical models are still necessary to complement experiments and to extrapolate relevant information to fusion devices, as the relevant atomic and molecular processes. SOLPS-ITER (formerly known as B2.5-Eirene) is typically employed to solve the plasma and neutral distribution in a coupled way for tokamak devices. For Magnum-PSI, B2.5 has been coupled with a different neutral module, named Eunomia, developed mostly for linear devices. Nevertheless, there is an interest in using SOLPS-ITER for simulating Magnum-PSI, as it would ease the process of relating linear device results with tokamaks. A previous work found significant differences in the implementation of relevant plasma-neutral processes in Eirene and Eunomia. A wide range of plasma scenarios are compared between B2.5-Eunomia and SOLPS-ITER. Although both codes produce results close to experimental Thomson scattering density and temperature near the target once the electric potential at the source is adjusted, these are achieved with completely different plasma and neutral distributions. Anomalous transport coefficients, which are other of the free-parameters in Magnum-PSI simulation, are set equal between the two codes. When studied in a wide range of neutral pressures, SOLPS-ITER shows a trend closer to experiments, as well as providing a converged solution at neutral pressures higher than 4 Pa for which B2.5-Eunomia was unable to provide a converged solution. Additional measurements of the neutral distribution in the target chamber as well as the electric potential at the source are required to determine which code is producing results closer to the experiment.

Self-healing liquid metal divertors (LMDs) based on the Capillary Porous Structure (CPS) concept are currently being considered among the possible solutions to the power exhaust problem in future fusion reactors. Indeed, the passive replenishment of the plasma-facing surface by capillary forces and the self-shielding of the target via vapor emission can potentially improve the divertor lifetime and its resilience to transient loads. On the other hand, the LMD target erosion can be significant due to evaporation and thermal sputtering, on top of physical sputtering, possibly leading to unacceptable core plasma dilution/power losses (for a low- Z /high- Z metal such as Li and Sn, respectively). For this reason, it is necessary to assess whether an LMD is compatible with an European DEMO (EU-DEMO) plasma scenario. This requires a self-consistent model of the impurity emission from the target, the plasma in both the scrape-off layer (SOL) and the core regions and the transport of impurities therein. In this paper, an an integrated modelling approach is proposed, which is based on SOLPS-ITER and includes its coupling with a target erosion model written in FreeFem++ and a core plasma model (ASTRA/STRAHL). An application of the coupled SOL-target model to simulate experiments performed in the Magnum-PSI linear plasma device with a CPS target filled with Li is also included to provide a first demonstration of the capabilities of the approach. Results are promising, being in good agreement (within a few degrees) with the measured target temperature distribution. In perspective, the modelling framework presented here will be applied to the EU-DEMO with an Sn divertor.

Managing divertor plasmas is crucial for operating reactor scale tokamak devices due to heat and particle flux constraints on the divertor target. Simulation is an important tool to understand and control these plasmas, however, for real-time applications or exhaustive parameter scans only simple approximations are currently fast enough. We address this lack of fast simulators using neural PDE surrogates, data-driven neural network-based surrogate models trained using solutions generated with a classical numerical method. The surrogate approximates a time-stepping operator that evolves the full spatial solution of a reference physics-based model over time. We use DIV1D, a 1D dynamic model of the divertor plasma, as reference model to generate data. DIV1D's domain covers a 1D heat flux tube from the X-point (upstream) to the target. We simulate a realistic TCV divertor plasma with dynamics induced by upstream density ramps and provide an exploratory outlook towards fast transients. State-of-the-art neural PDE surrogates are evaluated in a common framework and extended for properties of the DIV1D data. We evaluate (1) the speed-accuracy trade-off; (2) recreating non-linear behavior; (3) data efficiency; and (4) parameter inter- and extrapolation. Once trained, neural PDE surrogates can faithfully approximate DIV1D's divertor plasma dynamics at sub real-time computation speeds: In the proposed configuration, 2ms of plasma dynamics can be computed in $\approx$0.63ms of wall-clock time, several orders of magnitude faster than DIV1D.

The injection of electron cyclotron (EC) waves fulfills a number of important tasks in nuclear fusion devices for which detailed knowledge of the spatial power deposition profile is critical. This deposition profile is commonly determined using forward models such as beam or ray tracing. Recent numerical and experimental studies have shown that small-angle scattering of the EC beam as it passes through the turbulent plasma edge can cause significant broadening of the effective deposition profile, leading to considerable underestimation of the deposition width by forward methods. However, traditional inverse methods to determine the deposition profile from measurements overestimate the deposition profile width due to transport broadening. In this work, we implement three novel methods to resolve the EC power deposition profile from measurements that counteract transport broadening by simultaneously resolving transport and power deposition. We validate their assumptions and compare the results from these methods to the traditional break-in-slope method as well as to the TORAY ray-tracing code in a set of DIII-D discharges spanning five different confinement modes. We show that the four different inverse methods, novel and established, paint a consistent picture of deposition broadening. Specifically, we show that the measured power deposition profile is between 1.6 and 3.6 times wider than the TORAY profiles. Moreover, we show the considerable consequences that this level of broadening can have for ITER.

Replication package for manuscript "SOLPS-ITER simulations of a vapour box design for the linear device Magnum-PSI" submitted to PPCF.

This paper presents DIV1D, a new 1D dynamic physics-based model of the divertor plasma under development to study and control the dynamics of detached plasmas. An innovative feature of DIV1D is that it mimics cross-field transport using an effective flux expansion and includes a neutral gas background outside the divertor leg. We outline a 1D mapping procedure for static 2D SOLPS-ITER simulations of divertor plasmas in the Tokamak á Configuration Variable, which can be used to benchmark 1D codes. For DIV1D good agreement is found for the most important divertor plasma quantities along the leg (e.g., densities temperature, heat flux, and velocity) both in a qualitative and quantitative sense. In addition, the comparison with SOLPS-ITER demonstrates that DIV1D self-consistently captures the evolution of divertor plasma quantities in the main heat flux channel as a function of the upstream plasma density in a scan from 2 to 3 × 10 19 m − 3 . The agreement is ascribed to the unique account of cross-field transport in DIV1D with an effective flux expansion and the interaction with an external neutral gas background.

Replication package for manuscript: Coupled simulations with SOLPS-ITER and B2.5-Eunomia for detachment experiments in Magnum-PSI Submitted to PPCF on 2022-10-27.

The interaction between plasma, neutrals and surfaces in fusion reactors is of immense importance for heat and particle control, especially for the next generation of devices. Heat loads of 10 MW m − 2 are expected for steady state operation at ITER and up to 20 MW m − 2 in slow transient situations. To study the complex physics appearing between the plasma and the divertor material, as well as techniques for heat flux mitigation, plasma linear devices are employed. Magnum-PSI, located at DIFFER, can reproduce the heat and particle loads expected at ITER. However, due to the complexity of the plasma–wall interaction, numerical models are required to better understand the experiments and to extrapolate the results to a tokamak divertor configuration. For tokamak geometries, SOLPS-ITER (formerly known as B2.5-Eirene) is employed to solve the plasma and neutral distribution in a coupled way. However, the utilization of this code for linear devices is not straightforward. Thus, a neutral module was developed with linear devices in mind, named Eunomia. Nevertheless, there is still a relevant interest in using SOLPS-ITER with linear devices, as it allows to easily transfer knowledge about relevant atomic and molecular processes close to the surface and the effect of different mitigation techniques. This work presents a systematic comparison between the two neutral modules, Eirene and Eunomia, in stand-alone and coupled runs. Special attention is paid to the implementation of plasma-neutral interactions, in which both codes diverge significantly. The sources of particles and energy that are used by B2.5 in a coupled run are analysed. Significant differences in the implementation of electron impact ionization, molecular assisted recombination and proton–molecule elastic collisions lead to disparate sources of particles and energy and, in some cases, differences in the distribution of neutrals achieved by each code. Moreover, a double counting in proton–atom collisions was identified in Eunomia as a result of this analysis, artificially increasing the plasma-neutral sink of energy. This would lead to different plasma evolutions in coupled runs. Nevertheless, additional-free parameters in both coupled code suites leave sufficient freedom to match experimental data. Additional data would be required to further constrain these parameters and the coupled solution.

Neutral gas physics and neutral interactions with the plasma are key aspects of edge plasma and divertor physics in a fusion reactor including the detachment phenomenon often seen as key to dealing with the power exhaust challenges. A full physics description of the neutral gas dynamics requires a 6D kinetic approach, potentially time dependent, where the details of the wall geometry play a substantial role, to the extent that, e.g., the subdivertor region has to be included. The Monte Carlo (MC) approach used for about 30 years in EIRENE (Reiter et al 2005 Fusion Sci. Technol. 47 172–86), is well suited to solve these types of complex problems. Indeed, the MC approach allows simulating the 6D kinetic equation without having to store the velocity distribution on a 6D grid, at the cost of introducing statistical noise. MC also provides very good flexibility in terms of geometry and atomic and molecular (A&M) processes. However, it becomes computationally extremely demanding in high-collisional regions (HCRs) as anticipated in ITER and DEMO. Parallelization on particles helps reducing the simulation wall clock time, but to provide speed-up in situations where single trajectories potentially involve a very large number of A&M events, it is important to derive a hierarchy of models in terms of accuracy and to clearly identify for what type of physics issues they provide reliable answers. It was demonstrated that advanced fluid neutral models are very accurate in HCRs, and at least an order of magnitude faster than fully kinetic simulations. Based on these fluid models, three hybrid fluid–kinetic approaches are introduced: a spatially hybrid technique, a micro–macro hybrid method, and an asymptotic-preserving MC scheme, to combine the efficiency of a fluid model with the accuracy of a kinetic description. In addition, A&M ions involved in the edge plasma chemistry can also be treated kinetically within the MC solver, opening the way for further hybridisation by enabling kinetic impurity ion transport calculations. This paper aims to give an overview of methods mentioned and suggests the most prospective combinations to be developed.

Detachment is achieved in Magnum-PSI by increasing the neutral background pressure in the target chamber using gas puffing. The plasma is studied using the B2.5 multi fluid plasma code B2.5 coupled with Eunomia, a Monte Carlo solver for neutral species. This study focuses on the effect of increasing neutral background pressure to the plasma volumetric loss of particle, momentum and energy. The plasma particle and energy loss almost linearly scale with the increase of neutral background pressure, while the momentum loss does not scale as strongly. Plasma recombination processes include molecular activated recombination (MAR), dissociative attachment, and atomic recombination. Atomic recombination, which includes radiative and three-body recombination, is the most relevant plasma process in reducing the particle flux and, consequently, the heat flux to the target. The low temperature where atomic recombination becomes dominant is achieved by plasma cooling via elastic H+−H2 collisions. The transport of vibrationally excited H2 molecules out of the plasma serves as an additional electron cooling channel with relatively small contribution. Additionally, the transport of highly vibrational H2 has a significant impact in reducing the effective MAR and dissociative attachment collision rates and should be considered properly. The relevancy of MAR and atomic recombination occupy separate electron temperature regimes, respectively, at Te=1.5 eV and Te=0.3 eV, with dissociative attachment being relevant in the intermediary. Plasma cooling via elastic H+−H2 collisions is effective at Te≤1 eV.

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

Detachment experiments have been carried out in the linear plasma device Magnum-PSI by increasing the gas pressure near the target. In order to have a proper detailed analysis of the mechanism behind momentum and power loss in detachment, a quantitative match is pursued between B2.5-Eunomia solutions and experimental data. B2.5 is a multi fluid plasma code and Eunomia is a Monte Carlo solver for neutral particles, and they are coupled together to provide steady-state solution of the plasma and neutral distribution in space. B2.5-Eunomia input parameters are adjusted to produce a close replication of the plasma beam measured in the experiments without any gas puffing in the target chamber. Using this replication as an initial condition, the neutral pressure near the plasma beam target is exclusively increased during simulation, matching the pressures measured in the experiments. Reasonable agreement is found between the electron temperature of the simulation results with experimental measurements using laser Thomson scattering near the target. The simulations also reveal the effect of increased gas pressure on the plasma current, effectively reducing the current penetration from the plasma source. B2.5-Eunomia is capable of reproducing detachment characteristics, namely the loss of plasma pressure along the magnetic field and the reduction of particle and heat flux to the target. The simulation results for plasma and neutrals will allow future studies of the exact contribution of individual plasma-neutral collisions to momentum and energy loss in detachment in Magnum-PSI.

The Warm Plasma Dispersion Relation, for waves in the electron cyclotron resonance range of frequencies, can be cast into the form of a bi-quadratic equation for $N_\perp$, where the coefficients are a function of $N_\perp^2$ and an iterative procedure is required to obtain a solution. However, this iterative procedure is not well understood and fails to converge towards a solution at the second harmonic resonance layer. In particular at higher densities where the wave can couple to an electron Bernstein wave. This paper focuses on a solution to the poor convergence of the iterative method, enabling determination of the topology of the dispersion relation around the second harmonic using a fully relativistic code for oblique waves. A feed-forward controller is proposed with the ability to adjust the rotation of a step of $N_\perp^2$ within the complex plane, while also limiting the step-size. It is shown that implementation of the controller stabilizes unstable solutions, while improving overall robustness of the iteration. This allows the evaluation of the coupling between the fast extraordinary mode and electron Bernstein waves at the second harmonic electron cyclotron resonance layer, for non-perpendicularly propagating waves.

Electron cyclotron resonance heating (ECRH) can drive large current densities through electron cyclotron current drive (ECCD). ECCD is expected to be crucial for high-performance plasmas in future fusion reactors like ITER and DEMO, making the current drive efficiency of ECCD a critical design parameter for future reactors. In present-day devices, good agreement between measured and predicted current drive efficiency has been found. However, to ensure the reliability in future machines, a direct validation of the electron momentum distribution function is needed. As a first step towards this goal, we present in this paper oblique electron cyclotron emission (ECE) measurements of a low-density plasma in the ASDEX Upgrade tokamak. Two oblique ECE diagnostics are used to allow the simultaneous measurements of electrons streaming co- and counter-directionally with the plasma current. Predictions for the distribution function are computed with the bounce-averaged Fokker-Planck code RELAX.(9) To allow direct comparison with the measurements, synthetic radiation temperatures are computed with the code ECRad.(10) Good agreement is found if radial transport occurring predominantly at low electron energies is included. We demonstrate that oblique ECE diagnostics measure the electron distribution function directly at the ECRH deposition site in phase space. Furthermore, they are sensitive to the abundance of pitch-angle scattered electrons that reduce the ECCD efficiency. Limitations and uncertainties of the measurements and the modeling are discussed.

Magnetic flux pumping in the hybrid tokamak scenario: Nonlinear MHD simulations and ASDEX Upgrade discharges Isabel Krebs1, A. Burckhart2, S.C. Jardin3, A. Bock2, R. Fischer2, M. Hoelzl2, E. Westerhof1, S.Günter2, K. Lackner2, ASDEX Upgrade team* 1DIFFER -Dutch Institute for Fundamental Energy Research, Eindhoven, the Netherlands, 2Max Planck Institute for Plasma Physics, Garching, Germany, 3Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA, *see the author list of H. Meyer et al., Nucl. Fusion 59, 112014 (2019) e-mail: i.krebs@differ.nl

In ITER and DEMO, various control objectives related to plasma control must be simultaneously achieved by the plasma control system (PCS), in both normal operation as well as off-normal conditions. The PCS must act on off-normal events and deviations from the target scenario, since certain sequences (chains) of events can precede disruptions. It is important that these decisions are made while maintaining a coherent prioritization between the real-time control tasks to ensure high-performance operation. In this paper, a generic architecture for task-based integrated plasma control is proposed. The architecture is characterized by the separation of state estimation, event detection, decisions and task execution among different algorithms, with standardized signal interfaces. Central to the architecture are a plasma state monitor and supervisory controller. In the plasma state monitor, discrete events in the continuous-valued plasma state are modeled using finite state machines. This provides a high-level representation of the plasma state. The supervisory controller coordinates the execution of multiple plasma control tasks by assigning task priorities, based on the finite states of the plasma and the pulse schedule. These algorithms were implemented on the TCV digital control system and integrated with actuator resource management and existing state estimation algorithms and controllers. The plasma state monitor on TCV can track a multitude of plasma events, related to plasma current, rotating and locked neoclassical tearing modes, and position displacements. In TCV experiments on simultaneous control of plasma pressure, safety factor profile and NTMs using electron cyclotron heating (ECH) and current drive (ECCD), the supervisory controller assigns priorities to the relevant control tasks. The tasks are then executed by feedback controllers and actuator allocation management. This work forms a significant step forward in the ongoing integration of control capabilities in experiments on TCV, in support of tokamak reactor operation.