Comment on Physics considerations for laser-plasma linear colliders and on Beamstrahlung considerations in laser-plasma-accelerator-based linear colliders

C. B. Schroeder, E. Esarey, C. Benedetti, and W. P. Leemans {Phys. Rev. ST Accel. Beams 13, 101301 (2010) and 15, 051301 (2012)} have proposed a set of parameters for a TeV-scale collider based on plasma wake field accelerator principles. In particular, it is suggested that the luminosities greater than 10^34 cm-2s-1 are attainable for an electron-positron collider. In this comment we dispute this set of parameters on the basis of first principles. The interactions of accelerating beam with plasma impose fundamental limitations on beam properties and, thus, on attainable luminosity values.