  High-harmonic generation (HHG) normally requires a careful adjustment of the
driving laser intensity (typically $10^{14} - 10^{15}$ W/cm$^2$) and gas medium
parameters to enable good phase matching conditions. In contrast with
conventional wisdom, we present experimental results indicating phase-matched
HHG in all rare gases, using a high-density medium and a driver laser intensity
of around $10^{16}$ W/cm$^2$. The experimental results are corroborated by
theoretical simulations, which indicate that ionization-induced self-phase
modulation and plasma defocusing self-regulate the driver laser intensity to a
level that is appropriate for good phase matching. A ten-fold broadening of the
NIR spectrum is observed, which results in the generation of continuous spectra
from $18-140$ eV in spite of using 50-fs-long driving pulses. The presented
scheme represents a simple and versatile concept for the generation of XUV and
soft X-ray continua, which are ideally suited for transient absorption and
reflection spectroscopy.
