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We determine conditions allowing to simplify the description of the impact of a short and arbitrarily intense laser pulse onto a cold plasma at rest. If both the initial plasma density and pulse profile have plane simmetry, then suitable matched upper bounds on the maximum and the relative variations of the initial density, as well as the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid (without wave-breaking or vacuum-heating) during its whole interaction with the pulse, while ions can be regarded as immobile. We use a recently developed fully relativistic plane model whereby the system of the (Lorentz-Maxwell and continuity) PDEs is reduced into a family of highly nonlinear but decoupled systems of non-autonomous Hamilton equations with one degree of freedom, with the light-like coordinate $\xi=ct\!-\!z$ instead of time $t$ as an independent variable, and new apriori estimates (eased by use of a Liapunov function) of the solutions in terms of the input data (initial density and pulse profile). If the laser spot radius $R$ is finite but not too small the same conclusions hold for the part of the plasma close to the axis $\vec{z}$ of cylindrical symmetry. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons., Comment: 29 pages, 8 figures. To appear in the Journal "Mathematics"

In order to ensure total safety during maintenance operations within nuclear power plants, it is mandatory to preserve the optimal quality of the internal weld beads. To this end, we use Computational Magnetohydrodynamics to simulate adjacent phenomena within the plasma and the weld pool in order to improve the knowledge of welding operating process. One of the difficulties is to take into account the effects induced by the thermal gradient and the variations of surfactant element concentrations on the weld pool surface known as the Marangoni effect. In order to take into account all the physical phenomena at the plasma/weld pool interface, we use an interface tracking method (Arbitrary Lagrangian-Eulerian) to improve 3D finite volume simulation of weld pool with free surface deformation. Subsequently, it enables to capture more precisely the interfacial forces such as the Marangoni effect, the arc pressure and the gravity, and improve vertical/cornice welding simulation. Thus, this work is part of the development of a tridimensional un- steady two-way coupling in order to overcome the Gaussian boundary condition used to model the heat transfer from plasma torch towards the work piece surface. Ultimately, we could obtain a unified model for an optimal welding process simulation.; In order to ensure total safety during maintenance operations within nuclear power plants, it is mandatory to preserve the optimal quality of the internal weld beads. To this end, we use Computational Magnetohydrodynamics to simulate adjacent phenomena within the plasma and the weld pool in order to improve the knowledge of welding operating process. One of the difficulties is to take into account the effects induced by the thermal gradient and the variations of surfactant element concentrations on the weld pool surface known as the Marangoni effect. In order to take into account all the physical phenomena at the plasma/weld pool interface, we use an interface tracking method (Arbitrary Lagrangian-Eulerian) to improve 3D finite volume simulation of weld pool with free surface deformation. Subsequently, it enables to capture more precisely the interfacial forces such as the Marangoni effect, the arc pressure and the gravity, and improve vertical/cornice welding simulation. Thus, this work is part of the development of a tridimensional un- steady two-way coupling in order to overcome the Gaussian boundary condition used to model the heat transfer from plasma torch towards the work piece surface. Ultimately, we could obtain a unified model for an optimal welding process simulation.

Active plasma lenses are promising technologies for the focusing of high brightness electron beams due to their radially symmetric focusing and their high field gradients (up to several kT/m). However, in a number of experimental situations, the transverse non-uniformity of the current density flowing in the lens causes beam emittance growth and increases the minimum achievable spot size. To study the physics of the capillary discharge processes employed as active plasma lenses, we developed a 2-D hydrodynamic computational model. Here, we present preliminary simulation results and we compare the computed magnetic field profile with one from literature, which has been experimentally inferred. The result of the comparison is discussed.

We present a series of experimental results, and their interpretation, connected to various aspects of the hydrodynamics of laser produced plasmas. Experiments were performed using the Prague PALS iodine laser working at 0.44 μm wavelength and irradiances up to a few 1014W/cm2. By adopting large focal spots and smoothed laser beams, the lateral energy transport and lateral expansion have been avoided. Therefore we could reach a quasi one-dimensional regime for which experimental results can be more easily and properly compared to available analytical models.

International audience; Plasma-based seeded soft x-ray lasers (PBSXRL) have the potential to generate high-energy, fully coherent, short pulse beam. Nowadays, PBSXRL have demonstrated experimentally 1 mu J, 1 ps (1 MW) fully coherent, aberration-free pulses. Nevertheless, most exciting applications (as single-shot coherent imaging) require pulses shorter than 200 fs and energy ranging from 10 mu J to several miliJoules. In this chapter we will review the theoretical modeling tools and the results obtained related to this source.

Seeding experiments achieved with gas amplifiers demonstrated high quality X ray beams. Since amplifiers based on solid targets are denser than those generated from gas, higher energy and shorter pulse durations were expected. However, experiments demonstrated lower energy around 90 nJ and slightly shorter pulse duration down to 1 ps. We concentrated this thesis on the understanding of the mismatch between expected and measured energies for solid targets with the goal to find a way for producing seeded plasma-based soft x-ray laser emitting tens of microjoules per pulse as required by many applications. This work has been done with the code ARWEN. This code had already been used in this field but it has been improved in the frame of this thesis, adding new computational capabilities. The work presented in this thesis is: - Theoretical study of coherent X-ray sources, emphasizing the plasma-based sources. The state of the art and the physics of these amplifiers are described more thoroughly. - Description of the ARWEN code, the fundamental tool of this work, and the improvements introduced in it (ray tracing, parallelization of thermal conduction subroutines, standard HDF output, etc...). In addition to this, the codes used for prostprocessing the data are also described. - Optimization of plasma amplifiers by means of numerical models. These studies start from previous works, continuing the work and explaining the effects that lead to the differences between the predicted energy and the energy experimentally observed. Some ways to avoid these effects are proposed. An study of the amplification of the injected seed in these plasmas is also presented, concluding that pre-amplifier stages are essential. Thus, nowadays a code with new simulation capabilities (ARWEN)is available and it can be applied to several fields (not only plasma-based soft X-ray lasers). It has been used to study plasma-based amplifiers, gaining an insight into the physics of these systems, explaining the differences between experimental results and theoretical predictions. In addition to this, it has been proposed a new scheme to optimize these amplifiers., L'injection d'harmoniques dans des amplificateurs gazeux génère des faisceaux de rayonnement X de grand qualité. Puisque les amplificateurs basés sur cible solide sont plus denses que ceux générés sur cible gazeuse, des impulsions d'énergie supérieure et plus courtes sont attendue. Cependant, les expériences réalisées n'ont pas présenté d'énergies supérieures à 90 nJ et des durées inférieures à 1 ps. Dans cette thèse nous nous sommes concentrés sur le problème de la différence entre l'énergie extraite et celle prédite, avec pour objectif d'obtenir des faisceaux de quelques dizaines de microjoules par impulsion. Nous avons employé le code ARWEN, déjà utilisé dans ce domaine, et l'avons amélioré dans le cadre de cette thèse. Les travaux réalisés sont donc : - L'étude théorique des sources de rayonnement X cohérent, en insistant sur les sources basées sur plasmas. L'état de l'art et la physique de ces amplificateurs sont décrits en profondeur. - La description du code ARWEN et des améliorations introduites dans le cadre de cette thèse. Ainsi que les programmes utilisés pour le postprocess des donnés. - L'optimisation des amplificateurs au moyen de simulations numériques. Ces simulations continuent les travaux précédentes et expliquent les effets donnant lieu aux différences entre l'énergie obtenue expérimentalement et celle prédite théoriquement. En prenant en compte ces effets, nous proposons un amplificateur optimisé. Nous avons aussi étudié l'amplification du faisceau harmonique en concluant au besoin d'un pré-amplificateur. En résumé, nous avons amélioré le code ARWEN en ajoutant de nouvelles capacités de simulation et l'avons utilisé pour étudier la physique des amplificateurs de rayonnement X cohérent basés sur plasmas. L'évolution de ces plasmas a été comprise et nous a permis d'expliquer les différences entre les expériences et la théorie et proposer un moyen de réduire les pertes d'énergie.