Beam-beam limitation toward 10^34 cm^−2 s^−1 luminosity for Electron-Ion Collider

Achieving the design luminosity of in the Electron-Ion Collider (EIC) requires a deep understanding of beam-beam interaction limits in a weak-strong collision regime with flat hadron beams. This contribution presents recent studies of synchro-betatron resonances - particularly the coupling resonance 2𝜈_𝑥 −2𝜈_𝑦 + 𝑝𝜈_𝑧 = 0 - that can induce emittance transfer between the horizontal and vertical planes and limit luminosity performance. We identify the hourglass effect, caused by the proton bunch length being comparable to the vertical beta functions of both beams at the interaction point (IP), as the dominant source driving this resonance. We further investigate how physical noise, such as intra-beam scattering and fluctuations in the electron orbit and beam size, couples with the beam-beam interaction to amplify emittance growth and reduce luminosity. Mitigation strategies are also discussed. These studies provide important guidance for future EIC operation and inform strategies for potential upgrades.