Impact of electron beam size ripple on proton emittance growth for EIC

The Electron-Ion Collider (EIC) employs a flat hadron beam to achieve high luminosity, with the proton beam's vertical emittance being an order of magnitude smaller than its horizontal one. The smaller vertical emittance is sensitive to external noise. This study examines electron beam size ripple, a narrow-band noise centered around $60~\mathrm{Hz}$ in the US. Through beam-beam interaction, the electron size ripple contributes to vertical emittance growth. Mitigation strategies are discussed to preserve the flat beam aspect ratio.