An analytic approach to emittance growth from the beam-beam effect with applications to the LHeC

In colliders with asymmetric rigidity such as the proposed Large Hadron electron Collider, jitter in the weaker beam can cause emittance growth via coherent beam-beam interactions. The LHeC in this case would collide 7 TeV protons on 60 GeV electrons, which can be modeled using a weak-strong model. In this work we estimate the proton beam emittance growth by separating out the longitudinal angular kicks from an off-center bunch interaction and produce an analytic expression for the emittance growth per turn in systems like the LHeC.