Slowdown and compression of a strong X-ray free-electron pulse propagating through the Mg vapors

Here we study the propagation of a strong X-ray free-electron pulse through the resonant medium of atomic Mg accompanied by the self-seeded stimulated resonant X-ray Raman scattering. The X-ray pulse is decelerated by two orders of magnitude because of nonlinear interaction and experiences a 6-fold compression. The simulations are based on a strict numerical solution of the coupled Bloch and Maxwell equations for a 50 fs pulse tuned in the $2p_{3/2}$-$4s$ resonance (54.8 eV). The extensive ringing tail produced during propagation widens the power spectrum. This seed field triggers the Stokes channel $3s$-$2p_{3/2}$ (49.4 eV) of stimulated resonant X-ray Raman scattering and the weaker Stokes and anti-Stokes fields caused by four-wave mixing. The beating between the Stokes and pump fields quenches the population inversion at longer propagation distances where lasing without inversion enhances the Stokes component