Amplification of a high-order harmonic pulse in an active medium of a plasma-based x-ray laser

We investigate theoretically amplification of a high-order harmonic pulse in an active medium of x-ray laser. Using a model based on Maxwell-Bloch equations, which are modified to incorporate time-dependent gain and statistical character of spontaneous emission, the time-dependent nature of the interaction including coherent process is studied. The temporal shape of the output pulse is found to consist of three components: amplified spontaneous emission, coherent transient phase, and coherent decay. Based on this analysis, energy extraction and duration of the output pulse are discussed. The expectation regarding the properties such as radiation polarization, coherence, and divergence is also considered.