Phase-matched high-order harmonic generation in an ionized medium using a buffer gas of exploding atomic clusters

Calculations are presented of the time-dependent dispersion of a cluster medium interacting with an intense, femtosecond laser, where the clusters are ``exploding'' on the time scale of the laser pulse. It is shown that the dispersion of the clusters can transiently compensate (or buffer) the dispersion of free electrons to dramatically improve the phase matching of water-window high-order harmonic generation in the presence of strong ionization. A practical implementation of this phase-matching scheme is described.