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

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