  Laser-driven high-order harmonic generation (HHG) provides tabletop sources
of broadband extreme-ultraviolet (XUV) light with excellent spatial and
temporal coherence. These sources are typically operated at low repetition
rates, $f_{rep}\lesssim$100 kHz, where phase-matched frequency conversion into
the XUV is readily achieved. However, there are many applications that demand
the improved counting statistics or frequency-comb precision afforded by
operation at high repetition rates, $f_{rep}$ > 10 MHz. Unfortunately, at such
high $f_{rep}$, phase matching is prevented by the accumulated steady-state
plasma in the generation volume, setting stringent limitations on the XUV
average power. Here, we use gas mixtures at high temperatures as the generation
medium to increase the translational velocity of the gas, thereby reducing the
steady-state plasma in the laser focus. This allows phase-matched XUV emission
inside a femtosecond enhancement cavity at a repetition rate of 77 MHz,
enabling a record generated power of $\sim$2 mW in a single harmonic order.
This power scaling opens up many demanding applications, including XUV
frequency-comb spectroscopy of few-electron atoms and ions for precision tests
of fundamental physical laws and constants.
