Saturated collisionally-pumped X-ray lasers. Modeling and comparison to experiment

Large amplification at 25.5 nm in neon-like iron has been demonstrated in experiments where prepulses are used. We show that the interaction between the X-ray laser beam and the amplifying medium must be taken into account in a reliable modeling of the saturation regime. Two approaches for intensity calculations are presented in this contribution. The first one combines the radiative transfer equation and the population rate equations. This approach is fully consistent, in the sense that beam amplification and population kinetics are treated simultaneously. A formalism based on a paraxial Maxwell-Bloch approach is presented. The Maxwell-Bloch calculations give the variation with length of intensity, local gain... Moreover, in the small-signal regime, it is possible to define an effective gain which is comparable to the measured gain. The second approach is based on a raytrace calculation where the saturation effect has been introduced empirically. The two codes need the electron density and the electron and ion temperatures as inputs. These quantities are given by the hydrocode EHYBRID. The two approaches give similar results.