Group speed effects in saturated soft X-ray lasers in transient collisional excitation regime driven with travelling wave pumping

Abstract
A monodimensional uni-directional Amplified Spontaneous Emission (ASE) model for application to the description of travelling wave pumped soft X-ray lasers in the Transient Collisional Excitation (TCE) scheme is presented. The model includes explicitly the influence of the local gain on the group velocity of the X-ray pulses propagating in the active medium and the saturation of the amplified X-ray signal. Complete analytical solutions of the model in a number of physical interesting cases are derived. The important parameters governing the behaviour of this ASE mirrorless lasers are identified and their influence on the output is investigated for conditions typical of soft X-ray lasers in the TCE regime.