To improve RHIC luminosity for heavy ion beam energies below 10 GeV/nucleon, the Low Energy RHIC electron Cooler (LEReC) is currently under commissioning at BNL. The Linac of LEReC is designed to deliver a 1.6 MeV to 2.6 MeV electron beam, with rms dp/p less than 5e-4. A 704 MHz superconducting radio frequency (SRF) booster cavity in this Linac provides up to 2.2 MeV accelerating voltage. With such a low energy and very demanding energy spread requirement, control of Higher Order Modes (HOMs) in the cavities becomes critical and needs to be carefully evaluated to ensure minimum impact on the beam. In this paper, we report the multiphysics design of the HOM damper for this cavity to meet the energy spread requirement, as well as experimental results of the cavity with and without the HOM damper.DOI: