The present project is put into the context of the international projects ITER and DEMO aiming at managing nuclear fusion to produce energy. In tokamaks (nuclear fusion reactors), a hot plasma composed of deuterium and tritium nuclei is magnetically confined to achieve fusion. The heating of the plasma is mainly obtained by the injection of high-energy deuterium neutral beams, coming from the neutralization of high-intensity D- negative-ion beams. D- negative-ions are produced in a low-pressure plasma source and subsequently extracted and accelerated. The standard and most efficient solution to produce high negative-ion current uses cesium (Cs) injection and deposition inside the source to enhance negative-ion surface-production mechanisms. However, ITER and DEMO requirements in terms of extracted current push this technology to its limits. The already identified drawbacks of cesium injection are becoming real technological and scientific bottlenecks, and alternative solutions to produce negative-ions would be highly valuable. The first objective of the present project is to find an alternative solution to produce high yields of H-/D- negative-ions on surfaces in Cs-free H2/D2 plasmas. The proposed study is based on a physical effect discovered at PIIM in collaboration with LSPM, namely the enhancement of negative-ion yield on boron-doped-diamond at high temperature. The yield increase observed places diamond material as the most up to date relevant alternative solution for the generation of negative-ions in Cs-free plasmas. The project aims at fully characterizing and evaluating the relevance and the capabilities of diamond films (intrinsic and doped polycrystalline, single crystal as well as nanodiamond films…) as negative-ion enhancers in a negative-ion source. The second objective is to investigate diamond erosion under hydrogen (deuterium) plasma irradiation, with two main motivations. First, material erosion could be a limitation of the use of diamond as a negative-ion enhancer in a negative-ion source and must be evaluated. Second, the inner-parts of the tokamaks receiving the highest flux of particles and power are supposed to be made of tungsten, but its self-sputtering and its melting under high thermal loads are still major issues limiting its use. It has been shown in the past by one of the partners that diamond is a serious candidate as an efficient alternative-material for fusion reactors. Therefore, diamond erosion in hydrogen plasmas will also be investigated from this perspective. At the moment when all the efforts are put on tungsten, maintaining a scientific watch on backup solutions for tokamak materials is crucial. The project associates partners with complementary expertise in the field of plasma-surface interactions on the one hand, and diamond deposition and characterization on the other hand. Furthermore, in order to span the gap between fundamental science and real-life applications, negative-ion surface-production and diamond erosion will be studied in laboratory plasmas (PIIM in collaboration with LSPM ) as well as in real devices (Cybele negative-ion source at IRFM and Magnum-PSI experiment at DIFFER ). PIIM: Physique des Interactions Ioniques et Moléculaires, Université Aix-Marseille, CNRS LSPM: Laboratoire des Sciences des Procédés et des Matériaux, CNRS, Université de Paris 13 IRFM: Institut de Recherche sur la Fusion Magnétique, Commissariat à l’Energie Atomique, Cadarache DIFFER: Dutch Institute For Fundamental Energy Research, The Netherlands

The International Tokamak Experimental Reactor (ITER) currently underconstruction in South France has been designed as the key step between today's fusion research machines and tomorrow's fusion power plants. Regarding the expected thermonuclear plasma performance, ITER will require an unprecedented effort on the way to controlling plasmas heat and particle fluxes. This will call for the design of optimized plasma scenarios during ITER operation to control the heat flow from the thermonuclear source to the wall. The difficulty to get global experimental measurements in a nuclear environment in ITER, will require complementary numerical simulations based on fluid models to fine tune the magnetic configuration and adjust accordingly the edge plasma conditions. However, the capability of current solvers to perform such simulations, both for magnetic equilibrium and turbulence transport accounting for plasma-wall interactions, is still acknowledged by the international community as being largely insufficient. The SISTEM project aims to successfully achieve the strong scaling-up of plasma simulations in view of the fusion operation in a tokamak of unprecedented size, and with stringent plasma conditions. The effort will be twofold : - enhance numerical performance and capability of solvers resolving fluid models of high-fidelity (3D), in order to tackle a much larger range of spatio-temporal scales than in current machines, and so, the inherent increase in the number of degrees of freedom. - enhance the reliability of low-fidelity models (2D ensemble averaged equations) that will remain the only ones able to perform routine simulations prior to experiment, allowing us to vary engineering plasma parameters (power, pumping, …) as well as geometries of the magnetic equilibrium. On one side, the enhance accuracy and geometrical flexibility of the Hybrid Discontinuous Galerkin (HDG) method has the potential to satisfy a certain number of numerical issues, so as to progress towards predictive ITER simulations. New techniques will be developed to handle the strongly anisotropic equations describing a rapid compressible dynamics in the parallel direction to the magnetic field, and a slower incompressible-turbulence-like dynamics in the transverse direction. Specific nonlinear boundary conditions at the wall for the plasma and the magnetic equilibrium will be also addressed. An original implicit-explicit time-discretization scheme will also be developed in order to exploit HDG capabilities while satisfying HPC requirements for parallelization and memory management to tackle ITER size problems. On the other side, we will explore the development of various data assimilation techniques to improve the reliability of the turbulence modelling, which remain a major challenge nowadays for low-fidelity models. We will use experimental and numerical data from tokamak measurements and high-fidelity simulations, respectively, to reduce uncertainties on the free parameters inherently occurring in the models. The techniques will concern an automative feed-back loop model to a variational approach based on the minimization of a cost function by direct calculations of the derivatives, the number of free parameter being reduced. This way has never been explored in the fusion community. Finally, using the same grids and jointly developed numerical schemes for low and high fidelity models are important assets of the project to prepare future work, either via code-coupling or code-merging. All these challenging issues will be addressed by 3 teams from Ecole Centrale Marseille, CEA Cadarache and University of Nice, which share a multidisciplinary expertise around the same numerical tools. The combined development and use of a chain of codes based on low and high-fidelity models together with the operation of WEST in Cadarache puts our teams in a quasi-unique position in the fusion community and is one of the major assets of the project.

Energetic particles are ubiquitous in magnetically confined fusion plasmas. They contain a significant fraction of the plasma energy and are thus vital for the performance of fusion devices such as ITER. However, the presence of energetic particles and the fact that fusion plasmas are complex systems heated up to hundred million degrees result in instabilities that reduce the confinement of energetic particles. Understanding, predicting and controlling their transport and losses is of prime importance and constitutes our main goal. This is a high-dimensional multi-scale nonlinear problem, for which a complete description is so far unaffordable. Therefore, we propose a novel and inter-disciplinary approach to develop numerical tools based on Artificial Intelligence techniques applied to two lines of research: (1) derive data-driven reduced models for transport of energetic particles and (2) optimize the information extracted from HPC gyro-kinetic simulations and from experiments.

The Moonrise project aims at exploring modeling, mathematical and numerical issues originating from the presence of high oscillations in nonlinear PDEs mainly from the physics of nanotechnologies and from the physics of plasmas. Simulating numerically a fast-oscillating phenomenon usually imposes severe step-size restrictions in order to correctly capture the stiff dynamics. In many occurences of high oscillation, ad-hoc numerical methods have been developed – with partial success – which aim at capturing the long-time dynamics of the solutions in contrast with standard techniques which are enslaved to follow oscillations at a formidable computational cost. At the other end of the spectrum, several mathematical techniques aim at describing the solutions in their asymptotic limit, i.e. when a small parameter (which could be the inverse of a frequency or a normalized Planck’s constant) tends to zero. Instead of having sophisticated tools of analysis on the one hand, and heuristic numerical methods on the other hand, this project aspires to accommodate the two and to provide not only fruitful high-order asymptotic models for the purpose of mathematical analysis but also efficient numerical methods derived from them. Our target models are the following ones: - Highly oscillatory regimes in nanoscale physics, including nonlinear Schrödinger equations for confined quantum systems (electrons in nanostructures, Bose-Einstein condensates, transport in graphene), multiscale physics with semiclassical or nonrelativistic scalings. - Charged particles in strong magnetic fields, with models for strongly magnetized plasmas in Tokamaks devices or for space plasmas (the earth’s magnetopause). Here, the models are the Euler or Vlasov equations coupled to Maxwell's equations or, more simply, the Poisson equation. - Quasi-neutral regimes for kinetic, fluid or diffusive models. These models are of great interest for the modeling of tokamaks and space plasmas or corrosion of iron-based alloys in nuclear waste repositories. Our objective is to design reduced models and suitable efficient numerical schemes, for which the time steps will not be constrained by fast oscillations. In particular, we will develop strategies to construct uniformly accurate numerical schemes with respect to the highest frequencies of the phenomenon. These schemes will be assessed on configurations of increasing complexity: nanoscale devices in two or three dimensions and plasma devices up to Tokamak configurations. We will combine tools from asymptotic analysis, geometric numerical integration, high order averaging techniques and asymptotic-preserving numerical methods.

The HEBUTERNE project is linked to the development of nuclear fusion for energy production. In tokamaks, the walls of the plasma chamber will be subjected to extreme operating conditions. In particular, the tungsten chosen to cover a critical component of the machine will be exposed to a high flux of helium which may degrade its structure. This project aims at understanding of the He-W interaction by studying the formation and growth of helium bubbles in tungsten, an open question that needs to be solved in order to improve the codes that allow the prediction of the behavior of components in tokamaks. For this purpose, we propose to use state-of-the-art techniques developed in nanoscience, an innovative approach in the field of nuclear fusion. We will first characterize experimentally the dynamics of He-W interactions under model conditions, and then to approach the conditions expected in tokamaks. Six partners with complementary expertise are joining forces to carry out this project, which is divided into several tasks involving experimentation and modeling based on the results obtained: - WP1: Dynamics of the He-W interaction and in situ characterization. The objective is to describe the fundamental processes from the very beginning of the He bubble formation via the study of W single crystals of different crystallographic orientations submitted to an exposure of monokinetic He ions and characterized in operando by central X-ray scattering at grazing incidence (GISAXS) and X-ray diffraction thanks to synchrotron radiation (collaboration in progress with the BM32 line at ESRF). The energy of He implantation will be varied in order to evaluate the impact of the creation of defects during He implantation (i.e. below and above the minimum energy of displacement of the W by He). A particular focus will also be put on the impact of temperature during He implantation and post-implantation (annealing). -WP2: Towards real Plasma Facing materials interactions: larger range of He exposure and impact of grain boundaries. The study of polycrystalline samples is planned in order to evaluate the impact of grain boundaries on bubble formation and mobility. Exposures to various He plasmas will be carried out on the PHISIS and PIMAT facilities, in order to estimate the impact of the type of irradiation (higher flux and fluence) on the evolution of the morphology of the bubbles. Some exposures will use 3He for irradiation to allow the detection of small quantities accessible via nuclear reaction analysis (NRA). An important focus will be kept on a parametric study for the impact of temperature on the various mechanisms observed, once again during He implantation and after annealing. A methodology similar to the WP1 one will be adopted: characterization of the bubbles formed by microscopy (size, shape, distribution), estimation of the He inventory, impact of temperature parameters during or after implantation. - WP3: Integration of the experimental results into a multi-scale model, from the atomic level to the continuous medium, a crucial step towards the extrapolation of the mechanisms at the origin of the expected evolutions in lTER. A thermomechanical finite element model, based on Abaqus software, will be used to predict the He bubble pressure at rupture depending on temperature, depth and bubble size. The results will be used to propose a bursting model including all these dependencies. To better understand the role of dislocations, atomistic simulations will allow an accurate description of the interatomic binding energy landscape using the TAMMBER code. These new data will then be included in a cluster dynamic code. Last but not least, the evolution of the bubble shape will be modeled, based on experimental observations, by integrating the effect of plasticity on the appearance of facets.