Long Term Dynamics and Stability Studies for the High-energy Electron Cooler
The Ring Electron Cooler (REC) is being developed for the Electron-Ion Collider to provide cooling at the top proton energy of 275GeV to reduce emittance growth from intra-beam scattering (IBS) and other effects. Cooling electrons circulate in a 150 MeV storage ring equipped with strong damping wigglers. While these wigglers counteract emittance degradation driven by intra-beam scattering and proton-electron beam-beam scattering, they introduce significant nonlinear dynamics which can affect electron beam lifetime. In this paper we present the nonlinear optimization of the REC, including optimized focusing wiggler fields, chromatic correction, misalignments and orbit correction and space-charge studies. A novel sextupole-like wiggler field configuration is shown to substantially reduce chromatic aberrations compared with quadrupole-like focusing. Transverse and longitudinal dynamic apertures exceeding 5$\sigma$ are achieved in the presence of realistic alignment and BPM errors. Space-charge simulations for a Gaussian beam using the Bassetti-Erskine model show manageable tune spread and limited equilibrium emittance growth. These results demonstrate the feasibility of REC operation under the required cooling parameters.