Time-dependent Bloch-Maxwell modelling of 1 mJ, 200 fs seeded soft x-ray laser

Complete text of publication follows. Seeding of high harmonic generation in a soft x-ray plasma amplifier has been first proposed and tested by T. Ditmire and collaborators. The experiment demonstrated low amplification (*2), with a very strong background coming from the soft x-ray laser ASE. Later seeding experiments reached very high amplification factors (up to 600) in both gas (Ph. Zeitoun et al.) and solid amplifiers (Wang et at.). Surprisingly, solid amplifiers extracted less energy (90 nJ) than gas amplifier (∼ 1 μJ) with equivalent pump energy. We recently demonstrated that 50-100 μJ is achievable with adequate plasma tailoring. However, this energy is still low as compared to the 10 mJ per pulse demonstrated on the ASE soft x-ray laser running at PALS facility (Czech Republic). In order to model the seeding process of PALS soft x-ray laser, we developed a time-dependent Bloch-Maxwell model that solves coherently the pumping, amplification and saturation processes. We demonstrated that direct seeding, with femtosecond pulse, a soft x-ray plasma amplifier having gain duration of several 100s of picosecond cannot extract the stored energy keeping the output beam energy in the 100 μJ range. We proposed and fully modelled a new seeding scheme that allows to achieve 10 mJ, 200 fs soft x-ray laser.