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The quantum regime of the free-electron laser (FEL) interaction, where the recoil associated with photon emission plays a significant role, is discussed. The role of quantum effects and their relation to electron beam coherence are considered. An outline derivation of a 1D quantum high-gain FEL model and some of its predictions for the behaviour of a quantum FEL in the linear and non-linear regimes are presented. The effect of slippage and, consequently, the quantum regime of self-amplifieddoi:10.23730/cyrsp-2018-001.467 fatcat:zi2aaqslvzfyjhg7dzzao25mny