Bloch-Maxwell treatment of amplification of high harmonic seed in soft x-ray laser amplifiers in both direct and chirped amplifications

Seeding plasma-based soft x-ray laser (SXRL) demonstrated diffraction-limited, fully coherent in space and in time beam but with energy not exceeding 1 μJ per pulse. Quasi-steady-state (QSS) plasmas demonstrated to be able to store high amount of energy and then amplify incoherent SXRL up to several mJ. Using 1D time-dependant Bloch-Maxwell model including amplification of noise, we demonstrated that femtosecond HHG cannot be efficiently amplified in QSS plasmas. However, using Chirped Pulse Amplification concept on HHG seed allows to extract most of the stored energy, reaching up to 5. mJ in fully coherent pulses that can be compressed down to 130. fs.