Electron Beam Stability Requirements for Linac-Ring Electron-Ion Colliders

In recent years, linac-ring electron-ion colliders have been proposed at a number of laboratories around the world. While the linac-ring approach overcomes the beam-beam tuneshift limitation on the electron beam, it also introduces noise into the ion beam, via the beam-beam interaction with electron bunches of slightly fluctuating intensity and transverse size. The effect of these fluctuations is studied using a linearized model of the beam-beam interaction. Upper limits for the rms jitter amplitudes of electron beam parameters for various linac-ring electron-ion colliders are presented.