This is a copy of the author 's final draft version of an article published in the journal Ultrafast phenomena XIX: proceedings of the 19th international conference, Okinawa Convention Center, Okinawa, Japan, July 7-11, 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-13242-6_24

We show that scattering of ultrashort XUV pulses from strong-field driven electron wave packets is enhanced as compared with normal weak scattering from bound or free electrons. We predict large XUV amplification in high-order harmonic generation. Recent measurements have corroborated the main effect that we report. Parametric amplification of attosecond pulse trains at 11 nm has been observed to occur only if the seed pulse-train is perfectly synchronized to the driving laser pulse in the amplifier as predicted here theoretically: J. Seres et al. Scientific Reports 4:4254 (2014).