Analysis of beam-beam kink instability in a linac-ring electron-ion collider

A linac-ring collision scheme was considered in recent proposals of electron-gold colliders (eRHIC) and polarized-electron light-ion colliders (EPIC). The advantages of using an energy-recovered linac for the electron beam is that it avoids the limitation of beam-beam tune shift inherent in a storage ring, pertains good beam quality and easy manipulation of polarization. However, the interaction of the ion beam in the storage ring with the electron beam from the linac acts analogously to a transverse impedance, and can induce unstable behavior of the ion beam similar to the strong head-tail instability. In this paper, this beam-beam kink instability with head-tail effect is analysed using the linearized Vlasov equation, and the threshold of transverse mode coupling instability is obtained.