  We have developed an extreme ultraviolet (XUV) frequency comb for performing
ultra-high precision spectroscopy on the many XUV transitions found in highly
charged ions (HCI). Femtosecond pulses from a 100 MHz phase-stabilized
near-infrared frequency comb are amplified and then fed into a femtosecond
enhancement cavity (fsEC) inside an ultra-high vacuum chamber. The
low-dispersion fsEC coherently superposes several hundred incident pulses and,
with a single cylindrical optical element, fully compensates astigmatism at the
$w_0=15\mu$m waist cavity focus. With a gas jet installed there, intensities
reaching $\sim10^{14}$ W/cm$^2$ generate coherent high harmonics with a comb
spectrum at 100 MHz rate. We couple out of the fsEC harmonics from the 7th up
to the 35th (42 eV; 30 nm) to be used in upcoming experiments on HCI frequency
metrology.
