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).

Line edge roughness extraction with a sub-nanometer resolution

Within the European Chips Act, CEA-Leti is strongly committed to support the reduction of component dimensions to reach the future technological nodes (below 10 nm). To detect and account the line edge roughness becomes critical for such small dimensions since ‘the few Angstrom error’ becomes critical (several % of error) for sub-10nm devices.
This PhD work will focus mainly on the use of CD-SAXS to define the sensibility of the technique. To do so, we propose to follow two main complementary directions: first to perform simulations with tools under developments to identify the exact impact of roughness on a CD-SAXS pattern; and secondly to lead the experimental measurements on samples specifically designed at the CEA-LETI with controlled roughness. . CD-SAXS measurements will be done both on the laboratory equipment at the CEA as well as at synchrotrons (ESRF, NSLS-II). These results will be compared with results obtained from CEA-LETI cleanroom metrology equipment, such as AFM-3D and CD-SEM.
This PhD will take place between the Nanocharacterization platform of the CEA–LETI witch offer world-class analytical techniques and state-of-the-art instruments and the cleanroom metrology team from the CEA-LETI.

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.

Reducing the impact of uncertainties in the optimization of low-carbon energy system at district level

Energy system optimization models (ESOM) are powerful tools for improving decision making in the transition towards carbon-free energy systems.

The results provided by ESOMs are greatly influenced by data uncertainty since they are considered on a future time horizon. For instance, the possible evolution of energy prices, energy production and demand or the efficiency of technologies must be taken into account. Although many works have started in recent years to study the impact of these uncertainties on the solutions, it has been pointed out that modeling simplifications may induce significant bias in the obtained results.

The work proposed in this new PhD topic aims at studying the response of ESOM along energy system design and transformation steps, and reducing or assessing the impact of uncertainties as early as possible in the process. It will especially aims at limiting the bias related to model simplification, by systematically propagating relevant information from more detailed models towards simplified models used for sensitivity analysis and optimization under uncertainty. To this aim, the currently envisioned path is to leverage techniques such as machine learning, and in particular the constraint learning approach, to extract relevant information from simulation and inject back into the simplified optimization models.

As a result, the work is expected to improved the methods currently in use for designing and improving energy systems at local level, in order to favor energy savings, and limit CO2 emissions as well as other environmental impacts.

Modeling and Optimization of 2D Material-Based Field-Effect Transistors: From Multi-Physics Simulations to Atomic-Scale Insights

Field-effect transistors employing 2D materials are emerging as promising candidates due to their superior mobility and atomic thinness. Nonetheless, this technology faces multiple challenges, including minimizing contact resistances, controlling variability, and optimizing short-channel transistors (< 10 nm). At CEA-Leti, a concerted experimental and computational effort is underway to address these issues and propel the development of 2D material-based technologies.

This doctoral research project is situated within this context, aiming to harness multi-physics simulations to evaluate and enhance the performance of 2D material-based FETs by exploring the interplay between technological parameters and device performance. The flexibility in choosing materials and geometric configurations opens the door to pioneering research directions. A pivotal aspect of this work will involve coupling Technology Computer-Aided Design (TCAD) simulations with ab initio methods to achieve a comprehensive understanding of the devices' structural and electronic behaviors at the atomic level.

The project benefits from access to state-of-the-art computational resources and software (Sentaurus, VASP, GPAW, etc.), supported by CEA-Leti's expertise in simulation methodologies and close collaboration with experimental teams. This doctoral endeavor offers a unique opportunity to develop a wide-ranging skill set in electronic device simulation, contributing to the scientific community through presentations at leading international conferences and publications in esteemed journals.

Molecular dynamics simulation of phase change in Ge-rich GeSbTe materials

The goal of this thesis is to study the phase change of Ge-rich GST with molecular dynamics (MD) simulations using equivariant graph neural networks interatomic potentials (GNN-IP). The candidate will train a GNN-IP model on ab initio reference calculations of Ge-rich GST in order to describe amorphous and crystalline phases. The GNN-IP will be used to compute thermodynamic and kinetic properties of the phase transitions. In a second step, further developments including the effect of impurities and the impact of an electrical field on the phase change will be addressed. Finally, physical parameters computed from MD simulations will be employed to improve our in-house mesoscopic model based on the phase-field method.

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

Development of a fully passive plenoptic thermal imaging system

Low-resolution plenoptics is becoming widespread in visible imagers for applications such as autofocus, image post-processing and sometimes depth estimation. Its principle is based on the association of three main constitutive elements, a pixels-sized microlens array, a focal plane array of detectors and reconstruction algorithms.
Through this thesis, we would like to evaluate the possibility of achieving such a plenoptic function in the infrared range for uncooled detector technologies (micro-bolometer)

Within the Optics and PhoTonics Department (DOPT), the Thermal and THz Imaging Laboratory (LI2T) designs, develops, produces and characterizes thermal infrared imager technologies, which are then transferred to an industrial partner. As a doctoral student, your role will consist of:
- Establish preliminary specifications for micro lenses adapted with our detectors and with the application of autofocusing.
- Design and simulate the behavior of this micro-optics and propose original designs in refractive solution or in meta-surface
- Manufacture these micro-optics after evaluating the feasibility of these designs in partnership with the people in charge of manufacturing
- Implement an existing reconstruction algorithm that will be identified in the literature
- Characterize the micro-optics on a dedicated bench
To carry out these missions, you will be integrated into the LI2T laboratory where you will be able to interact with different people in order to familiarize yourself with micro bolometer technologies and where you will have access to the calculation resources of CEA Leti.

Staggered schemes for the Navier-Stokes equations with general meshes

The simulation of the Navier-Stokes equations requires accurate and robust numerical methods that
take into account diffusion operators, gradient and convection terms. Operational approaches have
shown their effectiveness on simplexes. However, in some models or codes
(TrioCF, Flica5), it may be useful to improve the accuracy of solutions locally using an
error estimator or to take into account general meshes. We are here interested in staggered schemes.
This means that the pressure is calculated at the centre of the mesh and the velocities on the edges
(or faces) of the mesh. This results in methods that are naturally accurate at low Mach numbers .
New schemes have recently been presented in this context and have shown their
robustness and accuracy. However, these discretisations can be very costly in terms of memory and
computation time compared with MAC schemes on regular meshes
We are interested in the "gradient" type methods. Some of them are based on a
variational formulation with pressure unknowns at the mesh centres and velocity vector unknowns on
the edges (or faces) of the cells. This approach has been shown to be effective, particularly in terms of
robustness. It should also be noted that an algorithm with the same degrees of freedom as the
MAC methods has been proposed and gives promising results.
The idea would therefore be to combine these two approaches, namely the "gradient" method with the same degrees of freedom as MAC methods. Initially, the focus will be on recovering MAC schemes on regular meshes. Fundamental
questions need to be examined in the case of general meshes: stability, consistency, conditioning of
the system to be inverted, numerical locking. An attempt may also be made to recover the gains in
accuracy using the methods presented in for discretising pressure gradients.
During the course of the thesis, time will be taken to settle the basic problems of this method (first and
second years), both on the theoretical aspects and on the computer implementation. It may be carried
out in the Castem, TrioCFD, Trust or POLYMAC development environments. The focus will be on
application cases that are representative of the community.

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