Achievable Luminosities at the THERA and LinacXLHC Based ep Colliders: 1. Round Beams

Different limitations on luminosity of linac-ring type colliders coming from beam dynamics issues are considered for the examples of the $ep$ options of the THERA and LinacXLHC proposals. It is shown that $L=1.3\times 10^{31}$ for THERA and $L=2.7\times 10^{32}$ for LinacXLHC can be achieved for round beams case. Corresponding sets of parameters are given with the explanations.