Phase-matched harmonic conversion of visible laser light into soft x-r
ays was demonstrated, The recently developed technique of guided-wave
frequency conversion was used to upshift light from 800 nanometers to
the range from 17 to 32 nanometers. This process increased the coheren
t x-ray output by factors of 10(2) to 10(3) compared to the non-phase-
matched case. This source uses a small-scale (sub-millijoule) high rep
etition-rate laser and will enable a wide variety of new experimental
investigations in linear and nonlinear x-ray science.