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C. B. Schroeder, E. Esarey, C. Benedetti, and W. P. Leemans {Phys. Rev. STAccel. Beams 13, 101301 (2010) and 15, 051301 (2012)} have proposed a set ofparameters for a TeV-scale collider based on plasma wake field acceleratorprinciples. In particular, it is suggested that the luminosities greater than10^34 cm-2s-1 are attainable for an electron-positron collider. In this commentwe dispute this set of parameters on the basis of first principles. Theinteractions of accelerating beam with plasma impose fundamental limitations onbeam properties and, thus, on attainable luminosity values.

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