### 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).