Conversion efficiency and luminosity for gamma-proton colliders based on the LHC-CLIC or LHC-ILC QCD Explorer scheme

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.