The Electron-Ion Collider (EIC) is a cutting-edge accelerator designed to collide highly polarized electrons and ions. For enhanced luminosity, the ion beam is cooled via an electron beam sourced from an energy recovery linac (ERL). The current ERL design accommodates one RF cavity per cryomodule, presenting both beam transport and cost-related challenges. This study investigates the feasibility of reducing the cavity size to accommodate two cavities within a single cryomodule. We analyze two compact cavity design options through frequency scaling, assuming constant loaded quality factor Q and R/Q scaling proportional to the square of the frequency ratio. Our analytical and tracking Beam BreakUp (BBU) model predicts the threshold current for each option. While a smaller cavity footprint is advantageous, maintaining sufficient damping of Higher Order Modes (HOMs) is crucial. We compare the HOM damping effectiveness of the proposed compact design to the existing configuration, which achieves sufficient damping within a slightly larger footprint.

The Electron-Ion Collider (EIC) is currently under development to be built at Brookhaven National Lab and requires cooling during collisions in order to preserve the quality of the hadron beam despite degradation due to intra-beam scattering and beam-beam effect. An Energy Recovery Linac (ERL) is being designed to deliver the necessary electron beam for Coherent electron Cooling (CeC) of the hadron beam, with an electron bunch charge of 1 nC and an average current of 100 mA; two modes of operation are being developed for 150 and 55 MeV electrons, corresponding to 275 and 100 GeV protons. The injector of this Strong Hadron Cooler ERL (SHC-ERL) is shared with the Precooler ERL, which cools lower energy proton beams via bunched beam cooling, as used in the Low Energy RHIC electron Cooling (LEReC). This paper reviews the current state of the design.