FIG. 3.

Pulse attenuation/amplification as a function of propagation length according to Eqs. (9) and (10). In order to clearly see the effect of the resonant scattering processes, the off-resonant absorption is subtracted from the results of the simulations (see text). Transmission and Raman amplification are shown for several incoming pump energies (see plot legends). The incoming dump pulse contains $N_d(0)={10}^6$ photons. The pulse duration is 100 fs. All calculations are averaged over 128 SASE shots.