Interrogating the temporal coherence of EUV frequency combs with highly charged ions

A scheme to infer the temporal coherence of EUV frequency combs generated from intra-cavity high-order harmonic generation is put forward. The excitation dynamics of highly charged Mg-like ions, interacting with EUV pulse trains featuring different carrier-envelope-phase fluctuations, are simulated. While demonstrating the microscopic origin of the macroscopic equivalence between excitations induced by pulse trains and continuous-wave lasers, we show that the coherence time of the pulse train can be determined from the spectrum of the excitations. The scheme will provide a verification of the comb temporal coherence at time scales several orders of magnitude longer than current state of the art, and at the same time will enable high-precision spectroscopy of EUV transitions with a relative accuracy up to $\delta\omega/\omega\sim10^{-17}$.