Analytical modeling of group-velocity effects in saturated soft-x-ray lasers pumped with a picosecond traveling-wave excitation

A monodimensional amplified spontaneous emission model of traveling-wave pumped soft-x-ray lasers in transient collisional excitation (TCE) is presented. The model explicitly includes 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 physically interesting cases are derived. The important parameters governing the behavior of these lasers are identified, their influence on the output is investigated, and the optimum configuration required in experiments for efficient traveling-wave pumping is discussed for conditions typical of soft-x-ray lasers in the TCE regime.