Ivan Kudashev

In the K-epsilon framework, a predator-prey like model determines the plasma turbulent transport. It depends on the underlying plasma turbulence via the growth rate chosen for the turbulent energy, the prey K, and its predator epsilon. Compared to our previous work [1], we propose in this paper modifications of the model to be tested in future simulations. A more appropriate expression of the growth rate is proposed by taking into account the fast dynamics of the parallel electron transport. The stabilising terms that are introduced allow for negative values of the growth rate of interchange coupled to drift wave turbulence. Changes to the K-epsilon model are made to adapt it to handle close to marginal states, then allowing one to address a Landau like bifurcation from negative growth rates, without turbulence, to positive growth rates, with turbulence. The closure using the multi-machine SOL width scaling law is revisited to allow the K-epsilon turbulent transport to depend on the growth rate. This is mandatory in the present model to yield increasing turbulent transport towards the edge and enhanced SOL transport governed by the sheath resistivity. Usual predator-prey limit cycles can be achieved whenever the growth rate of the predator is smaller than that of the prey. The growth rates are determined by a simplified 2D turbulence model taking into account magnetic field inhomogeneity and parallel losses, mostly of electrons. These are computed in Fourier space and must be adapted to plasma coarse grained simulations, in particular for edge-SOL-divertor simulations. A growth rate maximisation procedure then determines the wave vector in terms of the plasma parameters. Although the maximisation results are different for drift wave and interchange instabilities, their spectral properties are not discernable and the two instabilities are shown to be difficult to disentangle. Both facets of turbulence are therefore accounted for in the analytical expressions that are obtained for the growth rates, which are to be implemented in K-epsilon simulations of plasma-wall interaction with consistent turbulent transport.

This paper presents a joint experimental and numerical investigation into the physics of long limited plasma ramp-up in tokamaks with tungsten (W) first walls, a critical phase for ITER operation. The comparison between the average plasma quantities simulated using the SolEdge-HDG code and the measurements taken during three successive WEST discharges after boronisation shows how challenging it is to predict this phase. While simulations reproduce the general trends at the midplane, with reasonable match in density profiles, they consistently underestimate core temperatures possibly due to too large perpendicular heat conductivity. On the contrary, at the HFS limiter, simulations overestimate the measured quantities, and highlights the limitation of using Bohm boundary conditions at grazing magnetic angles. Experimental measurements reveal that the boron layer is rapidly eroded, on a timescale comparable to a single ITER discharge. The subsequent transition from a boron-coated to a tungsten wall increases recycling and significantly degrades the core plasma, reducing the electron temperature by nearly half due to W contamination, despite wall parameters remaining stable. Furthermore, comparisons with Langmuir probes, bolometry, reflectometry, and spectroscopy indicate that the experimental far Scrape-Off Layer (SOL) is significantly wider than simulated. This wide SOL implies that boron erosion extends along the entire High Field Side (HFS) limiter rather than being confined to the contact point. This work highlights some characteristics of the plasma during this phase of the discharge and emphasises the current modelling issues that need to be resolved in order to obtain reliable predictions concerning the ITER ramp-up.

Efficient and fast predictive simulations of turbulent transport in the tokamak edge plasma remain a challenge and are key for preparing the operation and heat exhaust on fusion power plants. In this contribution, we present the application of a hierarchy of models to describe turbulent transport in edge fluid codes from empirical mean-field transport modelling to first principles 3D turbulent simulations. A reduced turbulent model is also presented to improve predictability of mean-field simulations. The three approaches are applied to simulate the same L-mode attached plasma on TCV. The models are compared with each other as well as with experimental measurements.

Modélisation numérique avancée du transport dans le plasma tokamak et confrontation aux expériences: Afin de contrôler le dépôt de chaleur sur les composants face au plasma des tokamaks actuels et des réacteurs futurs, un effort majeur est consacré au développement de codes capables de modéliser le transport turbulent. La compréhension des processus physiques sous-jacents est un défi majeur pour la fusion magnétique, en particulier avec le démarrage d'ITER (International Thermonuclear Experimental Reactor). Malgré des progrès significatifs réalisés dans les simulations fluides des plasmas de fusion, plusieurs verrous limitent encore la capacité des codes comme l'hypothèse d'un équilibre magnétique fixe, des conditions aux limites simplifiées pour modéliser l'interaction plasma-paroi, un transport des neutres trop coûteux, des modèles de fermeture pour le transport perpendiculaire très rudimentaires et un couplage limité entre le cœur et le bord (Scrape-Off Layer) du plasma. Ces faiblesses dans les codes limitent l'analyse de la décharge complète à quelques captures instantanées du plasma dans son état stable, et introduisent des incertitudes importantes dans les solutions. Cette thèse s'inscrit dans un effort de développement du code SolEdge-HDG (Hybridized Discontinuous Galerkin), un solveur fluide bidimensionnel pour le calcul des équilibres plasma. Les travaux se concentrent sur l'amélioration du modèle physique dans le code ainsi que sur sa capacité à être validé expérimentalement. Un aperçu détaillé du code est présenté, avec un accent sur les modèles et hypothèses initiaux. La méthode HDG, qui permet de gérer des maillages éléments-finis d’ordre élevé non alignés sur le champ magnétique et de décrire précisément la géométrie des parois du tokamak, est détaillée. Les développements proposés incluent la création de diagnostics synthétiques de bolomètrie et caméra visible. Les comparaisons avec l'expérience ont révélé des faiblesses dans les modèles physiques initiaux, traitées au cours de cette thèse. Parmi les améliorations, on note une meilleure cohérence du modèle de fluide neutre, essentielle pour comprendre le ravitaillement du, ainsi que l'ajout de nouvelles sources de chaleur et un modèle de transport turbulent perpendiculaire auto-consistent. Le code amélioré capture avec succès les régimes plasma clés : les états limités par la gaine, à haut recyclage, et détachés. Une étude détaillée des réponses du plasma aux variations du taux d'injection de gaz a été menée, démontrant l'impact sur l’érosion du tungstène. L’intérêt de l’extension du système de bolomètrie avec les lignes de visées verticales dans WEST est également exploré, ainsi que les applications potentielles des caméras visibles. La thèse présente la première simulation complète d’une décharge WEST lors de la phase de montée en puissance avec le modèle turbulent auto-cohérent. Les résultats sont en accord qualitatif avec les données expérimentales. L’interaction entre l'évolution de l'équilibre du plasma et le modèle turbulent est discutée, ainsi que son impact sur le flux de chaleur vers le divertor. Les applications du modèle SolEdge-HDG amélioré sont également explorées pour des plasmas en régime stable avec chauffage additionnel. Une attention particulière est portée à la réponse du modèle turbulent face à divers modes de chauffage, ainsi qu’à la répartition de l'énergie entre ions et électrons. Enfin, SolEdge-HDG et ses diagnostics synthétiques sont appliqués au design de tokamaks. L’impact des réflexions sur les signaux des bolomètres est étudié, ainsi que différentes approches pour les inversions tomographiques de l’émission du plasma. Une application à la conception finale du système de bolomètres ITER est présentée. Ce travail démontre les nouvelles capacités du code SolEdge-HDG pour la conception et l’exploitation des tokamaks. L'intégration des diagnostics synthétiques permet non seulement de comparer les simulations aux expériences, mais aussi de révéler les faiblesses des modèles, apportant des solutions aux défis de conception opérationnelle

This paper deals with the distribution of sources, transport, and exhaust of particles in a tokamak. Knowledge and understanding of all the physical phenomena involved in the global particle buildup are necessary to study and predict density regimes and subsequently to develop optimized scenarios for tokamak operation in order to control heat and particle exhaust. Neutral particles and their interactions with plasma are central in this perspective. This paper discusses the impact of varying the intensity of particle fueling in 2D transport simulations of a WEST discharge. Simulations are performed with an updated version of SOLEDGE-HDG that allows a more realistic transport of neutrals using a self-consistent diffusive model based on charge exchange and ionization processes. New code capabilities allow the entire WEST poloidal cross section to be simulated in a realistic configuration for both geometry and the range of control parameters. A gas puff scan illustrates the main features of the sheath-limited, high-recycling, and detached regimes, such as the buildup of the temperature gradient and the pressure drop in the scrape-off layer (SOL), the target temperature falling to 1 eV, and the ionization source moving away from the targets, as well as the particle flux rollover. A crude estimate of wall erosion is also provided, showing the respective role of each plasma wall component in each of these regimes.

Plasma–wall interaction is one of the key research topics on the way to controlled fusion. To study the best operational designs with reduced heat and particle fluxes onto tokamak plasma facing components (PFCs) comprehensive plasma simulations are required. A recent implementation of a hybridized discontinuous Galerkin scheme into a new version of SolEdge code has the advantage of using magnetic equilibrium-free mesh. This allows us to conduct pioneering 2-D transport simulations of a full discharge in the WEST tokamak. In this work, we implemented plasma transport coefficients as functions of coordinate in the poloidal plane and neutral diffusion as a function of neutral mean free path. Moreover, the perpendicular convection flux terms were added to the code. Using the new features, a few test cases were investigated. The influence of nonconstant transport coefficients on the simulated particle and heat fluxes onto the WEST tokamak PFCs are demonstrated.

Bolometer cameras in ITER (lat.: the way) are designed as pinhole and collimator cameras, optimizing the requirements from available physical space, constraints in design options and desired line-of-sight (LOS) distribution. While for both camera types of internal reflections can be significant and lead to an increase in the effective viewing cone, collimator cameras may also suffer from crosstalk of light between channels in case internal apertures are not optimized. The concepts and simulations employed to optimize bolometer collimator cameras are presented. They are based on geometrical considerations for choosing the number and distribution of internal apertures, using the desired viewing cones as input. In the second step, ray-tracing simulations based on the Raysect packages are applied to assess internal reflections as a function of wavelength in the range IR to X-rays for the chosen geometry as well as to assess the impact of choices for material and material finishings (e.g., roughness). Examples presented focus on port-mounted bolometer cameras. The results allow us to improve the geometrical description of bolometer cameras in the ITER database of synthetic diagnostics and thus support performance assessments and studies in the preparation of tomographic reconstructions of plasma radiation. For example, the calculated measurements for LOS assuming standard radiation distributions for ITER are presented.

Significant scientific effort has been focused on optimizing the scenarios and plasma parameters for tokamak operations. The lack of comprehensive understanding of underlying physical processes leads to simplifications used both in plasma simulation codes and for diagnostics, which is also complicated by the harsh plasma environment. One of the main tools to couple, check and verify these assumptions are the synthetic diagnostics. In this work we demonstrate current results of the development of the set of synthetic diagnostics for the WEST tokamak to couple experimental data with the SolEdge3X-HDG 2D transport code.

Transport codes are frequently used for describing fusion plasmas with the aim to prepare tokamak operations. Considering novel codes, such as SolEdge3X-HDG, synthetic diagnostics are a common technique used to validate new models and confront them with experimental data. The purpose of this study is to develop a set of synthetic diagnostics, starting from bolometer and visible cameras for the WEST tokamak, in order to compare the code results with the experimental data. This research is done in the framework of Raysect and Cherab Python libraries. This allows us to process various synthetic diagnostics in the same fashion in terms of 3D ray tracing with volume emitters developed specifically for fusion plasmas. We were able to implement the WEST tokamak model and the design of bolometer and visible cameras. Synthetic signals, based on full-discharge WEST plasma simulation, were used for to compare the SolEdge3X-HDG output plasma with experimental data. The study also considers the optical properties of the plasma-facing components (PFCs) and their influence on the performance of diagnostics. The paper shows a unified approach to synthetic diagnostic design, which will be further extended to cover the remaining diagnostics on the WEST tokamak.