Generation and propagation of attosecond x-ray pulses in gaseous media

Using a self-consistent model that solves both the three-dimensional Schr\"odinger equation and the wave equation ab initio, we study the propagation of subfemtosecond pulses produced by high harmonic generation in a gas. The presence of a plasma shortens the coherence length for the harmonics. However, for the case of very short pump pulses, ionization is suppressed, and the coherence length can approach that of a neutral gas. Thus, the combination of enhanced single-atom harmonic generation for short pulses and improved phase matching allows for efficient amplification of attosecond x-ray pulses, resulting in 100 times higher output intensity for 5 fs compared to 10-fs pump pulses.