Determination of Diffractive Parton Densities at the LHeC and the FCC-eh

The Large Hadron-electron Collider (LHeC) is a proposed upgrade of the LHC at CERN. An ERL will provide electrons to collide with the HL-LHC, HE-LHC and the FCC-hh proton and ion beams to achieve per nucleon centre-of-mass energies 1.3-3.5 (0.8-2.2) TeV and luminosities $10^34(33) cm^{-2}s^{-1}$. These three configurations will enlarge the kinematic plane by more than one order of magnitude towards smaller $x$ and larger $Q^2$ than HERA, which translates into a range of available momentum fraction of the diffractive exchange with respect to the hadron down to $10^{-5}$ for a wide range of the momentum fraction of the parton with respect to the diffractive exchange. In this presentation we show the large possibilities that they offer for the measurement of the diffractive structure functions and subsequent determination of diffractive parton densities DPDFs in proton. For $eA$, we find that an extraction of the currently unmeasured nuclear DPDFs is possible with similar accuracy to that in $ep$.