Generalized linford formula and its application to traveling wave excitation

The Linford formula for the intensity output from a medium undergoing Ampli fied Spontaneous Emission (ASE) is generalized to the case when the gain co efficient is position dependent. The most evident application of this theor y relates to the frequently encountered situation that the pump intensity a nd therefore the gain coefficient vary along the line-focus. A second appli cation arises in Traveling Wave Excitation (TWE) ASE lasers if the excitati on velocity and the group velocity of the amplified pulse are not the same. Using the new formula an explanation of the early roll-off in the emitted intensity of Transient Collisional Excitation (TCE) x-ray lasers is given a nd the design of a more effective TWE set-up is put forward.