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International audience; Ultra-intense X-ray sources have opened new avenues by creating new states of matter or probing and imaging living or inert matter. Free-electron lasers have a strong leadership by delivering pulses combining femtosecond duration and 10s of microJoules to milliJoule energy. However, these sources remain highly expensive limiting their number to a few worldwide. In parallel, laser-pumped soft X-ray lasers hold outstanding promises having demonstrated the most energetic monochromatic soft x-ray pulse and being intrinsically fully synchronized with any secondary source of the pump laser. Since the first successful demonstration of amplification of a high harmonic pulse in a plasma from gas in 2003 and from solid in 2008, we have developed an extensive numerical study. 2D hydrodynamic simulations showed that optimized Transient Collisional Excitation plasma amplifiers, may store up to 0.4 mJ in the population inversion. If carefully seeded, pulses of 80 fs and 20 mu J might be generated with table-top lasers (10J). As the energy extracted is far from the milliJoule requirements of most exciting applications, we studied the seminal experiment of Ditmire et al who seeded a plasma emitting milliJoules in the form of Amplified Spontaneous Emission (ASE).We retrieved and explained for the first time the experimental result (ASE 1,000 times stronger than amplified seed). We thus proposed and fully modeled the transposition of the so-called Chirped Pulse Amplification (CPA) in the soft X-ray range, showing that 6 mJ, 200 fs, fully coherent soft X-ray pulse is accessible with compact pump lasers.

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.