Numerical modelling of the transport in the edge plasma of a stellarator by a high order discontinuous Galerkin method

The stellarator configuration has been chosen by the Renaissance Fusion start-up for the development of a prototype Fusion reactor. This non-axisymmetric configuration cannot currently be modelled with the SOLEDGE3X edge plasma code developed at IRFM, which is based on a finite volume algorithm with a mesh aligned on axisymmetric flux surfaces (well-suited for the tokamak configuration). In recent years, a collaboration between the IRFM and the M2P2 laboratory (Marseille) has led to the development of an finite element version of SOLEDGE using a high-order Hybrid Discontinuous Galerkin (HDG) method on a mesh not aligned with the magnetic field. By relaxing the constraint on mesh alignment with the magnetic field, this more flexible HDG version can theoretically simulate the stellarator configuration. However, current applications have focused mainly on the tokamak configuration for WEST and ITER (2D-axisymmetric modelling). An extension to a promising non-axisymmetric 3D configuration to simulate the ripple in WEST (error field linked to the finite number of coils) has demonstrated the code's ability to simulate this type of complex magnetic configuration. The aim of this thesis is to improve this finite-element version of SOLEDGE and apply it for the first time to a stellarator configuration. In particular, the high anisotropy of the heat transport requires developing innovative effective numerical methods that the student will have to investigate.

Human motion generation and dataset creation using AI techniques for human action recognition in an industrial context

In the context of industry 4.0, the analysis, recognition and prediction of human actions is becoming more important for decision-making and fluid and intuitive human-machine interaction. However, human action recognition requires large datasets to train deep learning architectures. The aim of the thesis is to generate, for industrial use cases, large motion datasets thanks to digital human animation, starting with a reduced number of motion capture samples from mixed reality simulations. These datasets will be used to train action recognition architectures, for industrial applications on human-machine interaction, assembly worksheets generation, and ergonomics evaluation.

Generation and control of virtual manikins using learning methods for the simulation of industrial processes using virtual reality

The thesis is focused on the simulation of virtual manikins in an industrial context using virtual reality. The virtual operator is meant to realize different tasks (manipulate, screw…) in virtual environments with different levels of constraints. The movements of the operator must be as faithful as possible from reality, in terms of posture, efforts and interactions with the environment.
Considering the sophistication of the gestures to reproduce and the number of parameters to define manually, it becomes too complex to use classical control methods. In the literature, studies using imitation learning methods show promising results. These methods however have important drawbacks, such as the use of big samples databases and important training times.
The aim of the thesis is to bring substantial modifications to existing methods and to propose a new one, that can learn and coordinate, using a database of moderate size, movements and interactions of a virtual manikin necessary to the realization of tasks in an industrial context. Great attention will be given to the efforts generated to produce the movements and their adequation with physics realism. The new method will be applied to industrial use cases and simulations using virtual reality.

Edge plasma turbulence study in compact fusion power plants at high magnetic field

Heat fluxes in magnetic fusion devices pose a significant challenge for plasma-facing components. The power from the plasma is concentrated on a small surface area of the vessel wall, potentially reaching fluxes of 100 MW/m² in ITER, which exceeds current engineering heat handling capabilities. Mitigating these heat fluxes involves transferring power to non-confined particles such as photons or neutral atoms before reaching the materials. This is achieved by utilizing plasma-neutral interactions and seeding radiative impurities in the plasma edge, increasing the surface area for heat deposition and reducing heat flux per unit area. Numerical simulations play a crucial role in studying these dissipative regimes, though current models often use simplified descriptions of plasma transport. The proposed PhD project aims to analyze the scaling law for the heat flux channel width using high-fidelity 3D turbulence simulations with the SOLEDGE3X code. The project involves two main tasks: scanning key plasma parameters to understand the dependencies of the heat flux channel width and developing a linear version of SOLEDGE3X to explore instabilities driving turbulent transport. This research is essential for designing high-field compact magnetic fusion devices and addressing the uncertainties in current scaling laws.

Compact source of electrons-positrons/muons-antimuons pairs

### Context
The context of this PhD thesis deals with laser plasma electron accelerators (LPA), which can be obtained by focusing a high-power laser into a gas medium. At focus, the laser field is so intense that it quasi-instantly ionizes matter into an undersense plasma, in which it can propagate. During laser propagation, the ponderomotive laser pressure expels plasma electrons from its path, forming a cavity void of electrons in its wake. This cavity, called ‘bubble’, can sustain accelerating fields (100GV/m) that are roughly three orders of magnitude larger than what can be provided by Radiofrequency cavities, which equip the current generation of conventional accelerators. These accelerating structures can trap some plasma electrons and accelerate them at relativistic energies (few GeVs) over distances of a few centimeters. This offers the prospect of producing much more compact and affordable accelerators, with the following goals: (i) democratizing their usage for existing applications currently reserved to only a few installations in the world (ii) enabling new applications in strategic sectors (fundamental research, industry, medicine, defense).

Among the applications for which a strong international competition exist we remark:

> The usage of these accelerators to provide the first high-energy (100 MeV) electron radiotherapy machine for medical treatmes

> The usage of these accelerators as a building block of a future large scale TeV electron/positron collider for high-energy physics

> The usage of these accelerators to develop a compact and mobile relativistic muon source to perform active muon tomography. Such a tool would be a major asset for industrial applications (e.g., safety diagnostic of nuclear reactors), and for defense applications (non-proliferation). It is worth to mention that in these two sectors the american agency DARPA has already funded an ambitious program ( Muons for Science and Security, MuS2) in 2022, with the aim of providing a first conceptual report of a relativistic moun source based on a plasma accelerator (cf. https://www.darpa.mil/news-events/2022-07-22).

### Challenges:

In order to enable the aforementioned applications, strong limitations of current laser-plasma accelerators need to be addressed. An important limitation is the low amount of charge at high-energies (100 MeV – few GeV) provided by these accelerators. The main reason behind the low accelerated charge is the fact that present-day injection techniques are based on the injection of electrons from the gas, whose density is very low. In order to address this limitation, we have recently proposed a new injection concept based on a remarkable physical system called “plasma-mirror”. This concept relies on the use of a hybrid solid-gas target. When impinging on such a target, the high-power laser fully ionizes the solid and the gas. The solid part is so dense that it can reflect the incident laser, forming a so-called ‘plasma mirror’. In the gas part, the laser propagates and drives a LPA. Upon reflection on the plasma mirror, ultra-dense electron bunches can be highly-precisely injected into the bubble of the LPA formed by the reflected laser field. As the solid offers orders of magnitude more charge than the gas medium and as charge is injected from a highly-localized region from the plasma (plane), it has the potential to level up the injected charge in LPAs while keeping a high electron beam quality.

The PHI group is an international leader in the study and control of these systems. In collaboration with LOA, by using a 100TW-class laser, we have demonstrated that this new concept allows for a significant increase of the accelerated charge while preserving the quality of the beam.

### Goals

The first objective of this PhD thesis will be to develop a multi-GeV laser-plasma accelerator based on a plasma-mirror injection on Petawatt-class laser installations like the APOLLON laser facility. With a Petawatt-class laser this accelerator should produce electrons beams at 4 GeV with a total charge of hundreds of pC and a few % energy spread. Such a beam quality would represent a substantial progress in the domain.

The second objective will be to send this electron beam into a high-Z converter in order to generate muons/anti-muons pairs. Our estimations show that we could obtain roughly 10^4 relativistic muons per shot, which would allow for the radiography of a high-Z material in a few minutes.

This PhD subject foresees:
> Theoretical/numerical modeling activities based on our exascale code WarpX (to model the laser-plasma accelerator) and on the Geant4 code (for the modeling of the high-Z converter).

> Experimental activities (high-intensity laser-plasma interaction, detection of relativistic muons)

The project involves several partner laboratories:

> The Laboratoire d’Optique Appliquée for the laser-plasma acceleration activities (A. Leblanc)

> The Lawrence Berkeley National Lab for code development activities (WarpX, J.L Vay)

> The CEA-IRFU for the detection part (micromegas technology, O. Limousin)

For the experimental part, we will use several laser facilities:

> The UHI100 laser installation for the setup and testing of the laser-plasma accelerator at reduced power

> The APOLLON installation for the setup and testing of the plasma accelerator with a PW-class laser. A first experience implementing the concept of a plasma-mirror injector at the PW-level is scheduled for May 2024 in the framework of a collaboration between CEA and LOA. Following this experiment, we will perform a second experiment (2025-2026) to generate muons on APOLLON or other laser facilities in Europe (e.g., the ELI installations).

Development of x-ray phase contrast and dark field imaging numerical model

Since 2013, CEA List (Université Paris Saclay) has been developing phase contrast X-ray imaging methods, in particular using multi-lateral shearing interferometry. In addition to absorption information, the phase shift of X-rays provides additional contrast and sensitivity on the image, particularly for materials with low atomic numbers or low density.
Various techniques have been developed to generate a phase contrast, based in particular on the addition of a random or regular intensity modulator (sandpaper or grid). In addition, dark field imaging has emerged as a valuable complementary signal to phase contrast imaging. The dark field signal comes from the small-angle scattering of fine structures in the sample. In particular, the dark field signal has proven it sensibility to reveal features of the sample that remain invisible by conventional means. It can, for example, reveal the microstructural properties of the lung in cases of chronic obstructive pulmonary diseases.
The continuation of these developments requires the implementation of a numerical model producing sufficiently accurate images that are representative of an experimental system.
The aim of the thesis is to develop a numerical model that takes into account the phenomena of phase contrast and scattering, in particularby refraining from a classic modelling hypothesis, which is the consideration of an thin object (projected thickness hypotheseis). Failure to take this assumption into account will have to be dealt with in order to move towards phase imaging on a thick object (e.g. a thorax).
As a general rule, phase contrast is represented using models based on wave propagation. In contrast, scattering phenomena are usually simulated using a particle-based approach, often using Monte Carlo techniques. In this study, a combined approach will be developed with experimental validation.
The thesis will be carried out in CEA List with people who have solid numerical and experimental skills.

Modeling catalyst layer degradation in fuel cells

The lifetime of fuel cells is one of the limiting factors in their large-scale deployment. A good understanding of the mechanisms involved in material degradation is a prerequisite for the development of these solutions, particularly catalyst degradation.
We propose to develop a comprehensive model coupling all the phenomena required to simulate catalyst degradation during cycling at potentials representative of cell use. Studies on the effect of cycling frequency and amplitude will enable us to define a validation experiment.
A first existing degradation model will be validated, then coupled to an oxidation model. We will also study the relevance/necessity of taking other reaction paths into account. The complete model will be implemented in a 2D model capable of simulating cells representative of an operational fuel cell.
The subject is therefore mainly numerical simulation with an experimental component. The thesis will be supervised and accompanied by three experts respectively in electrochemistry, numerical simulation and experiment on fuel cells.

High performance strategies for processing big data produced by numerical simulations

Numerical twin for the Flame Spray Pyrolysis process

Our ability to manufacture metal oxide nanoparticles (NPs) with well-defined composition, morphology and properties is a key to accessing new materials that can have a revolutionary technological impact, for example for photocatalysis or storage of energy. Among the different nanopowders production technologies, Flame Spray Pyrolysis (FSP) constitutes a promising option for the industrial synthesis of NPs. This synthesis route is based on the rapid evaporation of a solution - solvent plus precursors - atomized in the form of droplets in a pilot flame to obtain nanoparticles. Unfortunately, mastery of the FSP process is currently limited due to too much variability in operating conditions to explore for the multitude of target nanoparticles. In this context, the objective of this thesis is to develop the experimental and numerical framework required by the future deployment of artificial intelligence for the control of FSP systems. To do this, the different phenomena taking place in the synthesis flames during the formation of the nanoparticles will be simulated, in particular by means of fluid dynamics calculations. Ultimately, the creation of a digital twin of the process is expected, which will provide a predictive approach for the choice of the synthesis parameters to be used to arrive at the desired material. This will drastically reduce the number of experiments to be carried out and in consequence the time to develop new grades of materials

Numerical simulation of turbulence models on distorted meshes

Turbulence plays an important role in many industrial applications (flow, heat transfer, chemical reactions). Since Direct Simulation (DNS) is often an excessive cost in computing time, Reynolds Models (RANS) are then used in CFD (computational fluid dynamics) codes. The best known, which was published in the 70s, is the k - epsilon model.
It results in two additional non-linear equations coupled to the Navier-Stokes equations, describing the transport, for one, of turbulent kinetic energy (k) and, for the other, of its dissipation rate (epsilon). ). A very important property to check is the positivity of the parameters k and epsilon which is necessary for the system of equations modeling the turbulence to remain stable. It is therefore crucial that the discretization of these models preserves the monotony. The equations being of convection-diffusion type, it is well known that with classical linear schemes (finite elements, finite volumes, etc ...), the numerical solutions are likely to oscillate on distorted meshes. The negative values of the parameters k and epsilon are then at the origin of the stop of the simulation.
We are interested in nonlinear methods allowing to obtain compact stencils. For diffusion operators, they rely on nonlinear combinations of fluxes on either side of each edge. These approaches have proved their efficiency, especially for the suppression of oscillations on very distorted meshes. We can also take the ideas proposed in the literature where it is for example described nonlinear corrections applying on classical linear schemes. The idea would be to apply this type of method on the diffusive operators appearing in the k-epsilon models. In this context it will also be interesting to transform classical schemes of literature approaching gradients into nonlinear two-point fluxes. Fundamental questions need to be considered in the case of general meshes about the consistency and coercivity of the schemes studied.
During this thesis, we will take the time to solve the basic problems of these methods (first and second year), both on the theoretical aspects and on the computer implementation. This can be done in Castem, TrioCFD or Trust development environments. We will then focus on regular analytical solutions and application cases representative of the community.

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