Radiation-transfer modelling of double-pass saturated ASE systems

We numerically model radiation transfer in saturated ASE systems working in a double-pass regime. The goal is to obtain intensity and temporal characteristics of the output radiation emitted by a deeply saturated X-ray laser using a half-cavity. The model treats time-dependent, bi-directional amplification of axial emission in a refraction-free active medium, and accounts in full for radiation transfer of the spectral line profile. The atomic kinetics is modelled using a simplified three-level system with rates relevant to neon-like zinc, which is used as a testbed. The counter-propagating emissions produce axially dependent depletion of the population inversion, generating cross-talk between the intensity in one direction and the emissivity in the opposite direction. As a consequence, the output signal exhibits a presence of strongly damped oscillations, the amplitude of which depends on a number of parameters.