Abstract

Limitations on incoherent and beam-beam tune shift values are calculated by using gaussian beam distribution for linac-ring type $ep$ colliders. The advantage of this machine is achievement of multi TeV center of mass energies in lepton-hadron interactions at sufficiently high luminosities. Tune shift puts a limit on the number of electrons per effective area for the stability of proton beam and, therefore, gives an upper bound for the luminosity.