Gain dynamics in a soft-X-ray laser amplifier perturbed by a strong injected X-ray field

Seeding soft-X-ray plasma amplifiers with high harmonics has been demonstrated to generate high-brightness soft-X-ray laser pulses with full spatial and temporal coherence1–3. The interaction between the injected coherent field and the swept-gain medium has been modelled4,5. However, no experiment has been conducted to probe the gain dynamics when perturbed by a strong external seed field. Here, we report the first X-ray pump–X-ray probe measurement of the nonlinear response of a plasma amplifier perturbed by a strong softX-ray ultra-short pulse. We injected a sequence of two timedelayed high-harmonic pulses (l5 18.9 nm) into a collisionally excited nickel-like molybdenum plasma to measure with femtosecond resolution the gain depletion induced by the saturated amplification of the high-harmonic pump and its subsequent recovery. The measured fast gain recovery in 1.5–1.75 ps confirms the possibility to generate ultra-intense, fully phasecoherent soft-X-ray lasers by chirped pulse amplification in plasma amplifiers6. Interest in the use of intense coherent soft-X-ray pulses in numerous fields has motivated the commissioning of X-ray free-electron lasers7,8 and has renewed the ongoing efforts in the development of compact plasma-based soft-X-ray lasers9–16 and high-harmonic (HH) sources17–19. Soft-X-ray lasers based on the amplification of spontaneous emission (ASE) in a plasma column are capable of producing pulses with energies exceeding several millijoules20, values that match those typically produced by the most energetic X-ray free-electron lasers. However, due to the stochastic nature of self-emission, the output of plasma-based soft-X-ray amplifiers has limited spatial coherence. Furthermore, for soft-X-ray lasers emitting millijoules of energy, the pulse duration is typically several hundred times the Fourier-limited duration. By seeding the amplifier with HH pulses, it has been demonstrated that spatial coherence can be dramatically enhanced1–3, while the pulse duration approaches the Fourier limit. A most promising solution to increasing the power of injection-seeded, plasma-based soft-X-ray lasers consists in transposing chirped pulse amplification (CPA)21 to the X-ray regime6. The seeding technique promises to increase the power of these lasers from the current megawatt level to hundreds of megawatts for optimized direct injection22 and up to 20 GW for X-ray CPA6. However, the route from current seeding experiments emitting (at most) 1 mJ, 1 ps pulses23 to the predicted 5 mJ, 200 fs pulses relies on the understanding of complex physical processes. Although the population inversion dynamics of plasma-based soft-X-ray lasers running in ASE mode is controlled by plasma thermodynamic and hydrodynamic mechanisms, which have been extensively studied, seeding these amplifiers with a high-intensity soft-X-ray beam has uncovered new processes. The nonlinear interaction of the strong seed field with the lasing ions modifies its population inversion dynamics, leading, for example, to the creation and amplification of a picosecond wake field4,23. Maxwell–Bloch equations are suited to coherently modelling the interaction of the