Gamma-proton collisions allow unprecedented investigations of the low x and high $Q^{2}$ regions in quantum chromodynamics. In this paper, we investigate the luminosity for ILC$times$LHC ($sqrt{s_{ep}}=1.3$ TeV) and CLIC$times$LHC ($sqrt{s_{ep}}=1.45$ TeV) based $gamma p$ colliders. Also we determine the laser properties required for high conversion efficiency.
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